| Title: | The Generalized DINA Model Framework |
|---|---|
| Description: | A set of psychometric tools for cognitive diagnosis modeling based on the generalized deterministic inputs, noisy and gate (G-DINA) model by de la Torre (2011) <DOI:10.1007/s11336-011-9207-7> and its extensions, including the sequential G-DINA model by Ma and de la Torre (2016) <DOI:10.1111/bmsp.12070> for polytomous responses, and the polytomous G-DINA model by Chen and de la Torre <DOI:10.1177/0146621613479818> for polytomous attributes. Joint attribute distribution can be independent, saturated, higher-order, loglinear smoothed or structured. Q-matrix validation, item and model fit statistics, model comparison at test and item level and differential item functioning can also be conducted. A graphical user interface is also provided. For tutorials, please check Ma and de la Torre (2020) <DOI:10.18637/jss.v093.i14>, Ma and de la Torre (2019) <DOI:10.1111/emip.12262>, Ma (2019) <DOI:10.1007/978-3-030-05584-4_29> and de la Torre and Akbay (2019). |
| Authors: | Wenchao Ma [aut, cre, cph], Jimmy de la Torre [aut, cph], Miguel Sorrel [ctb], Zhehan Jiang [ctb] |
| Maintainer: | Wenchao Ma <[email protected]> |
| License: | GPL-3 |
| Version: | 2.9.4 |
| Built: | 2024-11-23 06:54:11 UTC |
| Source: | CRAN |
For conducting CDM analysis within the G-DINA model framework
This package (Ma & de la Torre, 2020a) provides a framework for a series of cognitively diagnostic analyses for dichotomous and polytomous responses.
Various cognitive
diagnosis models (CDMs) can be calibrated using the GDINA
function, including the G-DINA model (de la Torre, 2011), the deterministic inputs,
noisy and gate (DINA; de la Torre, 2009; Junker & Sijtsma, 2001) model,
the deterministic inputs, noisy or gate (DINO; Templin & Henson, 2006)
model, the reduced reparametrized unified model (R-RUM; Hartz, 2002),
the additive CDM (A-CDM; de la Torre, 2011), and the linear logistic
model (LLM; Maris, 1999), the multiple-strategy DINA model (de la Torre, & Douglas, 2008) and models defined
by users under the G-DINA framework using different link functions and design
matrices (de la Torre, 2011). Note that the LLM is also called
compensatory RUM and the RRUM is equivalent to the generalized NIDA model.
For ordinal and nominal responses, the sequential G-DINA model (Ma, & de la Torre, 2016) can be fitted and most of the aforementioned CDMs can be used as the processing functions (Ma, & de la Torre, 2016) at the category level. Different CDMs can be assigned to different items within a single assessment. Item parameters are estimated using the MMLE/EM algorithm. Details about the estimation algorithm can be found in Ma and de la Torre (2020). The joint attribute distribution can be modeled using an independent model, a higher-order IRT model (de la Torre, & Douglas, 2004), a loglinear model (Xu & von Davier, 2008), a saturated model or a hierarchical structures (e.g., linear, divergent). Monotonicity constraints for item/category success probabilities can also be specified.
In addition, to handle multiple strategies, generalized multiple-strategy CDMs for dichotomous response (Ma & Guo, 2019) can be fitted using GMSCDM function and
diagnostic tree model (Ma, 2019) can also be estimated using DTM function for polytomous responses. Note that these functions are experimental, and are expected to be further extended
in the future. Other diagnostic approaches include the multiple-choice model (de la Torre, 2009) and an iterative latent class analysis (ILCA; Jiang, 2019).
Various Q-matrix validation methods (de la Torre, & Chiu, 2016; de la Torre & Ma, 2016; Ma & de la Torre, 2020b; Najera, Sorrel, & Abad, 2019; see Qval),
model-data fit statistics (Chen, de la Torre, & Zhang, 2013; Hansen, Cai, Monroe, & Li, 2016; Liu, Tian, & Xin, 2016; Ma, 2020; see modelfit and itemfit),
model comparison at test and item level (de la Torre, 2011; de la Torre, & Lee, 2013;
Ma, Iaconangelo, & de la Torre, 2016; Ma & de la Torre, 2019; Sorrel, Abad, Olea, de la Torre, & Barrada, 2017; Sorrel, de la Torre, Abad, & Olea, 2017; see modelcomp),
and differential item functioning (Hou, de la Torre, & Nandakumar, 2014; Ma, Terzi, Lee, & de la Torre, 2017;
see dif) can also be conducted.
To use the graphical user interface, check startGDINA.
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
Chen, J., & de la Torre, J. (2013). A General Cognitive Diagnosis Model for Expert-Defined Polytomous Attributes. Applied Psychological Measurement, 37, 419-437.
Chen, J., de la Torre, J., & Zhang, Z. (2013). Relative and Absolute Fit Evaluation in Cognitive Diagnosis Modeling. Journal of Educational Measurement, 50, 123-140.
de la Torre, J. (2009). DINA Model and Parameter Estimation: A Didactic. Journal of Educational and Behavioral Statistics, 34, 115-130.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.
de la Torre, J. & Chiu, C-Y. (2016). A General Method of Empirical Q-matrix Validation. Psychometrika, 81, 253-273.
de la Torre, J., & Douglas, J. A. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333-353.
de La Torre, J., & Douglas, J. A. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika, 73, 595.
de la Torre, J., & Lee, Y. S. (2013). Evaluating the wald test for item-level comparison of saturated and reduced models in cognitive diagnosis. Journal of Educational Measurement, 50, 355-373.
de la Torre, J., & Ma, W. (2016, August). Cognitive diagnosis modeling: A general framework approach and its implementation in R. A Short Course at the Fourth Conference on Statistical Methods in Psychometrics, Columbia University, New York.
Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 301-321.
Hartz, S. M. (2002). A bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality (Unpublished doctoral dissertation). University of Illinois at Urbana-Champaign.
Hou, L., de la Torre, J., & Nandakumar, R. (2014). Differential item functioning assessment in cognitive diagnostic modeling: Application of the Wald test to investigate DIF in the DINA model. Journal of Educational Measurement, 51, 98-125.
Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258-272.
Ma, W. (2019). A diagnostic tree model for polytomous responses with multiple strategies. British Journal of Mathematical and Statistical Psychology, 72, 61-82.
Ma, W. (2020). Evaluating the fit of sequential G-DINA model using limited-information measures. Applied Psychological Measurement, 44, 167-181.
Ma, W., & de la Torre, J. (2016). A sequential cognitive diagnosis model for polytomous responses. British Journal of Mathematical and Statistical Psychology. 69, 253-275.
Ma, W., & de la Torre, J. (2019). Category-Level Model Selection for the Sequential G-DINA Model. Journal of Educational and Behavioral Statistics. 44, 61-82.
Ma, W., & de la Torre, J. (2019). Digital Module 05: Diagnostic measurement-The G-DINA framework. Educational Measurement: Issues and Practice, 39, 114-115.
Ma, W., & de la Torre, J. (2020a). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Ma, W., & de la Torre, J. (2020b). An empirical Q-matrix validation method for the sequential G-DINA model. British Journal of Mathematical and Statistical Psychology, 73, 142-163.
Ma, W., & Guo, W. (2019). Cognitive diagnosis models for multiple strategies. British Journal of Mathematical and Statistical Psychology, 72, 370-392.
Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification. Applied Psychological Measurement, 40, 200-217.
Ma, W., Terzi, R., Lee, S., & de la Torre, J. (2017, April). Multiple group cognitive diagnosis models and their applications in detecting differential item functioning. Paper presented at the Annual Meeting ofthe American Educational Research Association, San Antonio, TX.
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 187-212.
Najera, P., Sorrel, M., & Abad, P. (2019). Reconsidering Cutoff Points in the General Method of Empirical Q-Matrix Validation. Educational and Psychological Measurement.
Sorrel, M. A., Abad, F. J., Olea, J., de la Torre, J., & Barrada, J. R. (2017). Inferential Item-Fit Evaluation in Cognitive Diagnosis Modeling. Applied Psychological Measurement, 41, 614-631.
Sorrel, M. A., de la Torre, J., Abad, F. J., & Olea, J. (2017). Two-Step Likelihood Ratio Test for Item-Level Model Comparison in Cognitive Diagnosis Models. Methodology, 13, 39-47. Xu, X., & von Davier, M. (2008). Fitting the structured general diagnostic model to NAEP data. ETS research report, RR-08-27.
CDM for estimating G-DINA model and a set of other CDMs; ACTCD and NPCD for nonparametric CDMs; dina for DINA model in Bayesian framework
This function can be used to generate hierarchical attributes structures, and to provide prior joint attribute distribution with hierarchical structures.
att.structure(hierarchy.list = NULL, K, Q, att.prob = "uniform")att.structure(hierarchy.list = NULL, K, Q, att.prob = "uniform")
hierarchy.list |
a list specifying the hierarchical structure between attributes. Each
element in this list specifies a DIRECT prerequisite relation between two or more attributes.
See |
K |
the number of attributes involved in the assessment |
Q |
Q-matrix |
att.prob |
How are the probabilities for latent classes simulated? It can be |
att.str reduced latent classes under the specified hierarchical structure
impossible.latentclass impossible latent classes under the specified hierarchical structure
att.prob probabilities for all latent classes; 0 for impossible latent classes
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
## Not run: ################# # # Leighton et al. (2004, p.210) # ################## # linear structure A1->A2->A3->A4->A5->A6 K <- 6 linear=list(c(1,2),c(2,3),c(3,4),c(4,5),c(5,6)) att.structure(linear,K) # convergent structure A1->A2->A3->A5->A6;A1->A2->A4->A5->A6 K <- 6 converg <- list(c(1,2),c(2,3),c(2,4), c(3,4,5), #this is how to show that either A3 or A4 is a prerequisite to A5 c(5,6)) att.structure(converg,K) # convergent structure [the difference between this one and the previous one is that # A3 and A4 are both needed in order to master A5] K <- 6 converg2 <- list(c(1,2),c(2,3),c(2,4), c(3,5), #this is how to specify that both A3 and A4 are needed for A5 c(4,5), #this is how to specify that both A3 and A4 are needed for A5 c(5,6)) att.structure(converg2,K) # divergent structure A1->A2->A3;A1->A4->A5;A1->A4->A6 diverg <- list(c(1,2), c(2,3), c(1,4), c(4,5), c(4,6)) att.structure(diverg,K) # unstructured A1->A2;A1->A3;A1->A4;A1->A5;A1->A6 unstru <- list(c(1,2),c(1,3),c(1,4),c(1,5),c(1,6)) att.structure(unstru,K) ## See Example 4 and 5 in GDINA function ## End(Not run)## Not run: ################# # # Leighton et al. (2004, p.210) # ################## # linear structure A1->A2->A3->A4->A5->A6 K <- 6 linear=list(c(1,2),c(2,3),c(3,4),c(4,5),c(5,6)) att.structure(linear,K) # convergent structure A1->A2->A3->A5->A6;A1->A2->A4->A5->A6 K <- 6 converg <- list(c(1,2),c(2,3),c(2,4), c(3,4,5), #this is how to show that either A3 or A4 is a prerequisite to A5 c(5,6)) att.structure(converg,K) # convergent structure [the difference between this one and the previous one is that # A3 and A4 are both needed in order to master A5] K <- 6 converg2 <- list(c(1,2),c(2,3),c(2,4), c(3,5), #this is how to specify that both A3 and A4 are needed for A5 c(4,5), #this is how to specify that both A3 and A4 are needed for A5 c(5,6)) att.structure(converg2,K) # divergent structure A1->A2->A3;A1->A4->A5;A1->A4->A6 diverg <- list(c(1,2), c(2,3), c(1,4), c(4,5), c(4,6)) att.structure(diverg,K) # unstructured A1->A2;A1->A3;A1->A4;A1->A5;A1->A6 unstru <- list(c(1,2),c(1,3),c(1,4),c(1,5),c(1,6)) att.structure(unstru,K) ## See Example 4 and 5 in GDINA function ## End(Not run)
This function generates all possible attribute patterns. The Q-matrix needs to be specified for polytomous attributes.
attributepattern(K, Q)attributepattern(K, Q)
K |
number of attributes |
Q |
Q-matrix; required when Q-matrix is polytomous |
A matrix consisting of attribute profiles for latent classes
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
attributepattern(3) q <- matrix(scan(text = "0 1 2 1 0 1 1 2 0"),ncol = 3) q attributepattern(Q=q) q <- matrix(scan(text = "0 1 1 1 0 1 1 1 0"),ncol = 3) q attributepattern(K=ncol(q),Q=q)attributepattern(3) q <- matrix(scan(text = "0 1 2 1 0 1 1 2 0"),ncol = 3) q attributepattern(Q=q) q <- matrix(scan(text = "0 1 1 1 0 1 1 1 0"),ncol = 3) q attributepattern(K=ncol(q),Q=q)
autoGDINA conducts a series of CDM analyses within the G-DINA framework. Particularly,
the GDINA model is fitted to the data first using the GDINA function;
then, the Q-matrix is validated using the function Qval.
Based on the suggested Q-matrix, the data is fitted by the G-DINA model again, followed
by an item level model selection via the Wald test using modelcomp. Lastly,
the selected models are calibrated based on the suggested Q-matrix using the GDINA function.
The Q-matrix validation and item-level model selection can be disabled by the users.
Possible reduced CDMs for Wald test include the DINA model, the DINO model, A-CDM, LLM and RRUM.
See Details for the rules of item-level model selection.
autoGDINA( dat, Q, modelselection = TRUE, modelselectionrule = "simpler", alpha.level = 0.05, modelselection.args = list(), Qvalid = TRUE, Qvalid.args = list(), GDINA1.args = list(), GDINA2.args = list(), CDM.args = list() ) ## S3 method for class 'autoGDINA' summary(object, ...)autoGDINA( dat, Q, modelselection = TRUE, modelselectionrule = "simpler", alpha.level = 0.05, modelselection.args = list(), Qvalid = TRUE, Qvalid.args = list(), GDINA1.args = list(), GDINA2.args = list(), CDM.args = list() ) ## S3 method for class 'autoGDINA' summary(object, ...)
dat |
A required |
Q |
A required matrix; The number of rows occupied by a single-strategy dichotomous item is 1, by a polytomous item is
the number of nonzero categories, and by a mutiple-strategy dichotomous item is the number of strategies.
The number of column is equal to the number of attributes if all items are single-strategy dichotomous items, but
the number of attributes + 2 if any items are polytomous or have multiple strategies.
For a polytomous item, the first column represents the item number and the second column indicates the nonzero category number.
For a multiple-strategy dichotomous item, the first column represents the item number and the second column indicates the strategy number.
For binary attributes, 1 denotes the attributes are measured by the items and 0 means the attributes are not
measured. For polytomous attributes, non-zero elements indicate which level
of attributes are needed (see Chen, & de la Torre, 2013). See |
modelselection |
logical; conducting model selection or not? |
modelselectionrule |
how to conducted model selection? Possible options include
|
alpha.level |
nominal level for the Wald test. The default is 0.05. |
modelselection.args |
arguments passed to |
Qvalid |
logical; validate Q-matrix or not? |
Qvalid.args |
arguments passed to |
GDINA1.args |
arguments passed to GDINA function for initial G-DINA calibration |
GDINA2.args |
arguments passed to GDINA function for the second G-DINA calibration |
CDM.args |
arguments passed to GDINA function for final calibration |
object |
GDINA object for various S3 methods |
... |
additional arguments |
After the Wald statistics for each reduced CDM were calculated for each item, the reduced models with p values less than the pre-specified alpha level were rejected. If all reduced models were rejected for an item, the G-DINA model was used as the best model; if at least one reduced model was retained, three diferent rules can be implemented for selecting the best model:
When modelselectionrule is simpler:
If (a) the DINA or DINO model was one of the retained models, then the DINA or DINO model with the larger p value was selected as the best model; but if (b) both DINA and DINO were rejected, the reduced model with the largest p value was selected as the best model for this item. Note that when the p-values of several reduced models were greater than 0.05, the DINA and DINO models were preferred over the A-CDM, LLM, and R-RUM because of their simplicity. This procedure is originally proposed by Ma, Iaconangelo, and de la Torre (2016).
When modelselectionrule is largestp:
The reduced model with the largest p-values is selected as the most appropriate model.
When modelselectionrule is DS:
The reduced model with non-significant p-values but the smallest dissimilarity index is selected as the most appropriate model. Dissimilarity index can be viewed as an effect size measure, which quatifies how dis-similar the reduced model is from the G-DINA model (See Ma, Iaconangelo, and de la Torre, 2016 for details).
a list consisting of the following elements:
initial GDINA calibration of class GDINA
second GDINA calibration of class GDINA
Q validation object of class Qval
model comparison object of class modelcomp
Final CDM calibration of class GDINA
summary(autoGDINA): print summary information
Returned GDINA1.obj, GDINA2.obj and CDM.obj are objects of class GDINA,
and all S3 methods suitable for GDINA objects can be applied. See GDINA and extract.
Similarly, returned Qval.obj and Wald.obj are objects of class Qval and modelcomp.
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification. Applied Psychological Measurement, 40, 200-217.
## Not run: # simulated responses Q <- sim10GDINA$simQ dat <- sim10GDINA$simdat #misspecified Q misQ <- Q misQ[10,] <- c(0,1,0) out1 <- autoGDINA(dat,misQ,modelselectionrule="largestp") out1 summary(out1) AIC(out1$CDM.obj) # simulated responses Q <- sim30GDINA$simQ dat <- sim30GDINA$simdat #misspecified Q misQ <- Q misQ[1,] <- c(1,1,0,1,0) auto <- autoGDINA(dat,misQ,Qvalid = TRUE, Qvalid.args = list(method = "wald"), modelselectionrule="simpler") auto summary(auto) AIC(auto$CDM.obj) #using the other selection rule out11 <- autoGDINA(dat,misQ,modelselectionrule="simpler", modelselection.args = list(models = c("DINO","DINA"))) out11 summary(out11) # disable model selection function out12 <- autoGDINA(dat,misQ,modelselection=FALSE) out12 summary(out12) # Disable Q-matrix validation out3 <- autoGDINA(dat = dat, Q = misQ, Qvalid = FALSE) out3 summary(out3) ## End(Not run)## Not run: # simulated responses Q <- sim10GDINA$simQ dat <- sim10GDINA$simdat #misspecified Q misQ <- Q misQ[10,] <- c(0,1,0) out1 <- autoGDINA(dat,misQ,modelselectionrule="largestp") out1 summary(out1) AIC(out1$CDM.obj) # simulated responses Q <- sim30GDINA$simQ dat <- sim30GDINA$simdat #misspecified Q misQ <- Q misQ[1,] <- c(1,1,0,1,0) auto <- autoGDINA(dat,misQ,Qvalid = TRUE, Qvalid.args = list(method = "wald"), modelselectionrule="simpler") auto summary(auto) AIC(auto$CDM.obj) #using the other selection rule out11 <- autoGDINA(dat,misQ,modelselectionrule="simpler", modelselection.args = list(models = c("DINO","DINA"))) out11 summary(out11) # disable model selection function out12 <- autoGDINA(dat,misQ,modelselection=FALSE) out12 summary(out12) # Disable Q-matrix validation out3 <- autoGDINA(dat = dat, Q = misQ, Qvalid = FALSE) out3 summary(out3) ## End(Not run)
Create a block diagonal matrix
bdiagMatrix(mlist, fill = 0)bdiagMatrix(mlist, fill = 0)
mlist |
a list of matrices |
fill |
value to fill the non-diagnoal elements |
a block diagonal matrix
bdiag in Matrix
m1 <- bdiagMatrix(list(matrix(1:4, 2), diag(3))) m2 <- bdiagMatrix(list(matrix(1:4, 2), diag(3)),fill = NA)m1 <- bdiagMatrix(list(matrix(1:4, 2), diag(3))) m2 <- bdiagMatrix(list(matrix(1:4, 2), diag(3)),fill = NA)
This function conducts nonparametric and parametric bootstrap to calculate standard errors of model parameters. Parametric bootstrap is only applicable to single group models.
bootSE(GDINA.obj, bootsample = 50, type = "nonparametric", randomseed = 12345)bootSE(GDINA.obj, bootsample = 50, type = "nonparametric", randomseed = 12345)
GDINA.obj |
an object of class GDINA |
bootsample |
the number of bootstrap samples |
type |
type of bootstrap method. Can be |
randomseed |
random seed for resampling |
itemparm.se standard errors for item probability of success in list format
delta.se standard errors for delta parameters in list format
lambda.se standard errors for structural parameters of joint attribute distribution
boot.est resample estimates
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
## Not run: # For illustration, only 5 resamples are run # results are definitely not reliable dat <- sim30GDINA$simdat Q <- sim30GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA",att.dist = "higher.order") boot.fit <- bootSE(fit,bootsample = 5,randomseed=123) boot.fit$delta.se boot.fit$lambda.se ## End(Not run)## Not run: # For illustration, only 5 resamples are run # results are definitely not reliable dat <- sim30GDINA$simdat Q <- sim30GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA",att.dist = "higher.order") boot.fit <- bootSE(fit,bootsample = 5,randomseed=123) boot.fit$delta.se boot.fit$lambda.se ## End(Not run)
This function calculate test-, pattern- and attribute-level classification accuracy indices based on GDINA estimates from
the GDINA function using approaches in Iaconangelo (2017) and Wang, Song, Chen, Meng, and Ding (2015).
It is only applicable for dichotomous attributes.
CA(GDINA.obj, what = "MAP")CA(GDINA.obj, what = "MAP")
GDINA.obj |
estimated GDINA object returned from |
what |
what attribute estimates are used? Default is |
a list with elements
estimated test-level classification accuracy, see Iaconangelo (2017, Eq 2.2)
estimated pattern-level classification accuracy, see Iaconangelo (2017, p. 13)
estimated attribute-level classification accuracy, see Wang, et al (2015, p. 461 Eq 6)
Conditional classification matrix, see Iaconangelo (2017, p. 13)
Wenchao Ma, The University of Alabama, [email protected]
Iaconangelo, C.(2017). Uses of Classification Error Probabilities in the Three-Step Approach to Estimating Cognitive Diagnosis Models. (Unpublished doctoral dissertation). New Brunswick, NJ: Rutgers University.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Wang, W., Song, L., Chen, P., Meng, Y., & Ding, S. (2015). Attribute-Level and Pattern-Level Classification Consistency and Accuracy Indices for Cognitive Diagnostic Assessment. Journal of Educational Measurement, 52 , 457-476.
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") fit CA(fit) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") fit CA(fit) ## End(Not run)
Combine a sequence of vector, matrix or data-frame arguments by columns. Vector is treated as a column matrix.
cjoint(..., fill = NA)cjoint(..., fill = NA)
... |
vectors or matrices |
fill |
a scalar used when these objects have different number of rows. |
a data frame
cjoint(2,c(1,2,3,4),matrix(1:6,2,3)) cjoint(v1 = 2, v2 = c(3,2), v3 = matrix(1:6,3,2), v4 = data.frame(c(3,4,5,6,7),rep("x",5)),fill = 99)cjoint(2,c(1,2,3,4),matrix(1:6,2,3)) cjoint(v1 = 2, v2 = c(3,2), v3 = matrix(1:6,3,2), v4 = data.frame(c(3,4,5,6,7),rep("x",5)),fill = 99)
This function evaluates the classification rates for two sets of attribute profiles
ClassRate(att1, att2)ClassRate(att1, att2)
att1 |
a matrix or data frame of attribute profiles |
att2 |
a matrix or data frame of attribute profiles |
a list with the following components:
the proportion of correctly classified attributes (i.e., attribute level classification rate)
a vector giving the proportions of correctly classified attribute vectors (i.e., vector level classification rate). The fist element is the proportion of at least one attribute in the vector are correctly identified; the second element is the proportion of at least two attributes in the vector are correctly identified; and so forth. The last element is the proportion of all elements in the vector are correctly identified.
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
## Not run: N <- 2000 # model does not matter if item parameter is probability of success Q <- sim30GDINA$simQ J <- nrow(Q) gs <- matrix(0.1,J,2) set.seed(12345) sim <- simGDINA(N,Q,gs.parm = gs) GDINA.est <- GDINA(sim$dat,Q) CR <- ClassRate(sim$attribute,personparm(GDINA.est)) CR ## End(Not run)## Not run: N <- 2000 # model does not matter if item parameter is probability of success Q <- sim30GDINA$simQ J <- nrow(Q) gs <- matrix(0.1,J,2) set.seed(12345) sim <- simGDINA(N,Q,gs.parm = gs) GDINA.est <- GDINA(sim$dat,Q) CR <- ClassRate(sim$attribute,personparm(GDINA.est)) CR ## End(Not run)
This function generates the design matrix for an item
designmatrix(Kj = NULL, model = "GDINA", Qj = NULL, no.bugs = 0)designmatrix(Kj = NULL, model = "GDINA", Qj = NULL, no.bugs = 0)
Kj |
Required except for the MS-DINA model; The number of attributes required for item j |
model |
the model associated with the design matrix; It can be "GDINA","DINA","DINO", "ACDM","LLM", "RRUM", "MSDINA", "BUGDINO", and "SISM". The default is "GDINA". Note that models "LLM" and "RRUM" have the same design matrix as the "ACDM". |
Qj |
the Q-matrix for item j; This is required for "MSDINA", and "SISM" models; The number of rows is equal to the number of strategies for "MSDINA", and the number of columns is equal to the number of attributes. |
no.bugs |
the number of bugs (or misconceptions). Note that bugs must be given in the last no.bugs columns. |
a design matrix (Mj). See de la Torre (2011) for details.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.
## Not run: designmatrix(Kj = 2, model = "GDINA") designmatrix(Kj = 3, model = "DINA") msQj <- matrix(c(1,0,0,1, 1,1,0,0),nrow=2,byrow=TRUE) designmatrix(model = "MSDINA",Qj = msQj) ## End(Not run)## Not run: designmatrix(Kj = 2, model = "GDINA") designmatrix(Kj = 3, model = "DINA") msQj <- matrix(c(1,0,0,1, 1,1,0,0),nrow=2,byrow=TRUE) designmatrix(model = "MSDINA",Qj = msQj) ## End(Not run)
This function is used to detect differential item functioning using the Wald test (Hou, de la Torre, & Nandakumar, 2014; Ma, Terzi, & de la Torre, 2021) and the likelihood ratio test (Ma, Terzi, & de la Torre, 2021). The forward anchor item search procedure developed in Ma, Terzi, and de la Torre (2021) was implemented. Note that it can only detect DIF for two groups currently.
dif( dat, Q, group, model = "GDINA", method = "wald", anchor.items = NULL, dif.items = "all", p.adjust.methods = "holm", approx = FALSE, SE.type = 2, FS.args = list(on = FALSE, alpha.level = 0.05, maxit = 10, verbose = FALSE), ... ) ## S3 method for class 'dif' summary(object, ...)dif( dat, Q, group, model = "GDINA", method = "wald", anchor.items = NULL, dif.items = "all", p.adjust.methods = "holm", approx = FALSE, SE.type = 2, FS.args = list(on = FALSE, alpha.level = 0.05, maxit = 10, verbose = FALSE), ... ) ## S3 method for class 'dif' summary(object, ...)
dat |
item responses from two groups; missing data need to be coded as |
Q |
Q-matrix specifying the association between items and attributes |
group |
a factor or a vector indicating the group each individual belongs to. Its length must be equal to the number of individuals. |
model |
model for each item. |
method |
DIF detection method; It can be |
anchor.items |
which items will be used as anchors? Default is |
dif.items |
which items are subject to DIF detection? Default is |
p.adjust.methods |
adjusted p-values for multiple hypothesis tests. This is conducted using |
approx |
Whether an approximated LR test is implemented? If TRUE, parameters of items except the studied one will not be re-estimated. |
SE.type |
Type of standard error estimation methods for the Wald test. |
FS.args |
arguments for the forward anchor item search procedure developed in Ma, Terzi, and de la Torre (2021). A list with the following elements:
|
... |
arguments passed to GDINA function for model calibration |
object |
dif object for S3 method |
A data frame giving the Wald statistics and associated p-values.
summary(dif): print summary information
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
Hou, L., de la Torre, J., & Nandakumar, R. (2014). Differential item functioning assessment in cognitive diagnostic modeling: Application of the Wald test to investigate DIF in the DINA model. Journal of Educational Measurement, 51, 98-125.
Ma, W., Terzi, R., & de la Torre, J. (2021). Detecting differential item functioning using multiple-group cognitive diagnosis models. Applied Psychological Measurement.
## Not run: set.seed(123456) N <- 3000 Q <- sim30GDINA$simQ gs <- matrix(.2,ncol = 2, nrow = nrow(Q)) # By default, individuals are simulated from uniform distribution # and deltas are simulated randomly sim1 <- simGDINA(N,Q,gs.parm = gs,model="DINA") sim2 <- simGDINA(N,Q,gs.parm = gs,model=c(rep("DINA",nrow(Q)-1),"DINO")) dat <- rbind(extract(sim1,"dat"),extract(sim2,"dat")) gr <- rep(c("G1","G2"),each=N) # DIF using Wald test dif.wald <- dif(dat, Q, group=gr, method = "Wald") dif.wald # DIF using LR test dif.LR <- dif(dat, Q, group=gr, method="LR") dif.LR # DIF using Wald test + forward search algorithm dif.wald.FS <- dif(dat, Q, group=gr, method = "Wald", FS.args = list(on = TRUE, verbose = TRUE)) dif.wald.FS # DIF using LR test + forward search algorithm dif.LR.FS <- dif(dat, Q, group=gr, method = "LR", FS.args = list(on = TRUE, verbose = TRUE)) dif.LR.FS ## End(Not run)## Not run: set.seed(123456) N <- 3000 Q <- sim30GDINA$simQ gs <- matrix(.2,ncol = 2, nrow = nrow(Q)) # By default, individuals are simulated from uniform distribution # and deltas are simulated randomly sim1 <- simGDINA(N,Q,gs.parm = gs,model="DINA") sim2 <- simGDINA(N,Q,gs.parm = gs,model=c(rep("DINA",nrow(Q)-1),"DINO")) dat <- rbind(extract(sim1,"dat"),extract(sim2,"dat")) gr <- rep(c("G1","G2"),each=N) # DIF using Wald test dif.wald <- dif(dat, Q, group=gr, method = "Wald") dif.wald # DIF using LR test dif.LR <- dif(dat, Q, group=gr, method="LR") dif.LR # DIF using Wald test + forward search algorithm dif.wald.FS <- dif(dat, Q, group=gr, method = "Wald", FS.args = list(on = TRUE, verbose = TRUE)) dif.wald.FS # DIF using LR test + forward search algorithm dif.LR.FS <- dif(dat, Q, group=gr, method = "LR", FS.args = list(on = TRUE, verbose = TRUE)) dif.LR.FS ## End(Not run)
This function estimates the diagnostic tree model (Ma, 2018) for polytomous responses with multiple strategies. It is an experimental function, and will be further optimized.
DTM( dat, Qc, delta = NULL, Tmatrix = NULL, conv.crit = 0.001, conv.type = "pr", maxitr = 1000 )DTM( dat, Qc, delta = NULL, Tmatrix = NULL, conv.crit = 0.001, conv.type = "pr", maxitr = 1000 )
dat |
A required |
Qc |
A required |
delta |
initial item parameters |
Tmatrix |
The mapping matrix showing the relation between the OBSERVED responses (rows) and the PSEDUO items (columns); The first column gives the observed responses. |
conv.crit |
The convergence criterion for max absolute change in item parameters. |
conv.type |
convergence criteria; Can be |
maxitr |
The maximum iterations allowed. |
Wenchao Ma, The University of Alabama, [email protected]
Ma, W. (2018). A Diagnostic Tree Model for Polytomous Responses with Multiple Strategies. British Journal of Mathematical and Statistical Psychology.
GDINA for MS-DINA model and single strategy CDMs,
and GMSCDM for generalized multiple strategies CDMs for dichotomous response data
## Not run: K=5 g=0.2 item.no <- rep(1:6,each=4) # the first node has three response categories: 0, 1 and 2 node.no <- rep(c(1,1,2,3),6) Q1 <- matrix(0,length(item.no),K) Q2 <- cbind(7:(7+K-1),rep(1,K),diag(K)) for(j in 1:length(item.no)) { Q1[j,sample(1:K,sample(3,1))] <- 1 } Qc <- rbind(cbind(item.no,node.no,Q1),Q2) Tmatrix.set <- list(cbind(c(0,1,2,3,3),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1,2,3,4),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1),c(0,1))) Tmatrix <- Tmatrix.set[c(1,1,1,1,1,1,rep(3,K))] sim <- simDTM(N=2000,Qc=Qc,gs.parm=matrix(0.2,nrow(Qc),2),Tmatrix=Tmatrix) est <- DTM(dat=sim$dat,Qc=Qc,Tmatrix = Tmatrix) ## End(Not run)## Not run: K=5 g=0.2 item.no <- rep(1:6,each=4) # the first node has three response categories: 0, 1 and 2 node.no <- rep(c(1,1,2,3),6) Q1 <- matrix(0,length(item.no),K) Q2 <- cbind(7:(7+K-1),rep(1,K),diag(K)) for(j in 1:length(item.no)) { Q1[j,sample(1:K,sample(3,1))] <- 1 } Qc <- rbind(cbind(item.no,node.no,Q1),Q2) Tmatrix.set <- list(cbind(c(0,1,2,3,3),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1,2,3,4),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1),c(0,1))) Tmatrix <- Tmatrix.set[c(1,1,1,1,1,1,rep(3,K))] sim <- simDTM(N=2000,Qc=Qc,gs.parm=matrix(0.2,nrow(Qc),2),Tmatrix=Tmatrix) est <- DTM(dat=sim$dat,Qc=Qc,Tmatrix = Tmatrix) ## End(Not run)
Examination for the Certificate of Proficiency in English (ECPE) data (the grammar section) has been used in Henson and Templin (2007), Templin and Hoffman (2013), Feng, Habing, and Huebner (2014), and Templin and Bradshaw (2014), among others.
ecpeecpe
A list of responses and Q-matrix with components:
datResponses of 2922 examinees to 28 items.
QThe Q-matrix.
The data consists of responses of 2922 examinees to 28 items involving 3 attributes. Attribute 1 is morphosyntactic rules, Attribute 2 is cohesive rules and Attribute 3 is lexical rules.
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Feng, Y., Habing, B. T., & Huebner, A. (2014). Parameter estimation of the reduced RUM using the EM algorithm. Applied Psychological Measurement, 38, 137-150.
Henson, R. A., & Templin, J. (2007, April). Large-scale language assessment using cognitive diagnosis models. Paper presented at the annual meeting of the National Council for Measurement in Education in Chicago, Illinois.
Templin, J., & Bradshaw, L. (2014). Hierarchical diagnostic classification models: A family of models for estimating and testing attribute hierarchies. Psychometrika, 79, 317-339.
Templin, J., & Hoffman, L. (2013). Obtaining diagnostic classification model estimates using Mplus. Educational Measurement: Issues and Practice, 32, 37-50.
## Not run: mod1 <- GDINA(ecpe$dat,ecpe$Q) mod1 summary(mod1) mod2 <- GDINA(ecpe$dat,ecpe$Q,model="RRUM") mod2 anova(mod1,mod2) # You may compare the following results with Feng, Habing, and Huebner (2014) coef(mod2,"rrum") # G-DINA with hierarchical structure # see Templin & Bradshaw, 2014 ast <- att.structure(list(c(3,2),c(2,1)),K=3) est.gdina2 <- GDINA(ecpe$dat,ecpe$Q,model = "GDINA", control = list(conv.crit = 1e-6), att.str = list(c(3,2),c(2,1))) # see Table 7 in Templin & Bradshaw, 2014 summary(est.gdina2) ## End(Not run)## Not run: mod1 <- GDINA(ecpe$dat,ecpe$Q) mod1 summary(mod1) mod2 <- GDINA(ecpe$dat,ecpe$Q,model="RRUM") mod2 anova(mod1,mod2) # You may compare the following results with Feng, Habing, and Huebner (2014) coef(mod2,"rrum") # G-DINA with hierarchical structure # see Templin & Bradshaw, 2014 ast <- att.structure(list(c(3,2),c(2,1)),K=3) est.gdina2 <- GDINA(ecpe$dat,ecpe$Q,model = "GDINA", control = list(conv.crit = 1e-6), att.str = list(c(3,2),c(2,1))) # see Table 7 in Templin & Bradshaw, 2014 summary(est.gdina2) ## End(Not run)
A generic function to extract elements from objects of class GDINA,
itemfit, modelcomp, Qval or simGDINA. This
page gives the elements that can be extracted from the class GDINA.
To see what can be extracted from itemfit, modelcomp, and
Qval, go to the corresponding function help page.
Objects which can be extracted from GDINA objects include:
AIC
attribute prior weights for calculating marginalized likelihood in the last EM iteration
all attribute patterns involved in the current calibration
BIC
Consistent AIC
covariance matrix of item probability parameter estimates; Need to specify SE.type
item parameter estimates
standard error of item probability parameter estimates; Need to specify SE.type
TRUE if the calibration is converged.
raw data
deleted observation number
covariance matrix of delta parameter estimates; Need to specify SE.type
delta parameter estimates
standard error of delta parameter estimates; Need to specify SE.type
A list of design matrices for each item/category
deviance, or negative two times observed marginal log likelihood
GDINA discrimination index
expected # of examinees in each latent group answering item correctly
expected # of examinees in each latent group
higher-order model specifications
success probabilities for all latent classes
observed marginal log likelihood
link functions for each item
initial item category probability parameters
number of attributes
number of categories
number of groups
number of items
number of EM iterations
number of observations, or sample size
number of latent classes
prevalence of each attribute
posterior weights for each latent class
Reduced latent group for each item
Sample size Adusted BIC
is a sequential model fitted?
extract(object, what, ...)extract(object, what, ...)
object |
objects from class |
what |
what to extract |
... |
additional arguments |
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") extract(fit,"discrim") extract(fit,"designmatrix") ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") extract(fit,"discrim") extract(fit,"designmatrix") ## End(Not run)
Fraction Subtraction data (Tatsuoka, 2002) consists of responses of 536 examinees to 20 items measuring 8 attributes.
frac20frac20
A list of responses and Q-matrix with components:
datresponses of 536 examinees to 20 items
QThe Q-matrix
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Tatsuoka, C. (2002). Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society, Series C, Applied Statistics, 51, 337-350.
## Not run: mod1 <- GDINA(frac20$dat,frac20$Q,model="DINA") mod1 summary(mod1) # Higher order model mod2 <- GDINA(frac20$dat,frac20$Q,model="DINA",att.dist="higher.order") mod2 anova(mod1,mod2) ## End(Not run)## Not run: mod1 <- GDINA(frac20$dat,frac20$Q,model="DINA") mod1 summary(mod1) # Higher order model mod2 <- GDINA(frac20$dat,frac20$Q,model="DINA",att.dist="higher.order") mod2 anova(mod1,mod2) ## End(Not run)
GDINA calibrates the generalized deterministic inputs, noisy and
gate (G-DINA; de la Torre, 2011) model for dichotomous responses, and its extension, the sequential
G-DINA model (Ma, & de la Torre, 2016a; Ma, 2017) for ordinal and nominal responses.
By setting appropriate constraints, the deterministic inputs,
noisy and gate (DINA; de la Torre, 2009; Junker & Sijtsma, 2001) model,
the deterministic inputs, noisy or gate (DINO; Templin & Henson, 2006)
model, the reduced reparametrized unified model (R-RUM; Hartz, 2002),
the additive CDM (A-CDM; de la Torre, 2011), the linear logistic
model (LLM; Maris, 1999), and the multiple-strategy DINA model (MSDINA; de la Torre & Douglas, 2008; Huo & de la Torre, 2014)
can also be calibrated. Note that the LLM is equivalent to
the C-RUM (Hartz, 2002), a special case of the GDM (von Davier, 2008), and that the R-RUM
is also known as a special case of the generalized NIDA model (de la Torre, 2011).
In addition, users are allowed to specify design matrix and link function for each item, and distinct models may be used in a single test for different items. The attributes can be either dichotomous or polytomous (Chen & de la Torre, 2013). Joint attribute distribution may be modelled using independent or saturated model, structured model, higher-order model (de la Torre & Douglas, 2004), or loglinear model (Xu & von Davier, 2008). Marginal maximum likelihood method with Expectation-Maximization (MMLE/EM) alogrithm is used for item parameter estimation.
To compare two or more GDINA objects, use method anova.
To calculate structural parameters for item and joint attribute distributions, use method coef.
To calculate lower-order incidental (person) parameters
use method personparm. To extract other components returned, use extract.
To plot item/category response function, use plot. To
check whether monotonicity is violated, use monocheck. To conduct anaysis in graphical user interface,
use startGDINA.
GDINA( dat, Q, model = "GDINA", sequential = FALSE, att.dist = "saturated", mono.constraint = FALSE, group = NULL, linkfunc = NULL, design.matrix = NULL, no.bugs = 0, att.prior = NULL, att.str = NULL, verbose = 1, higher.order = list(), loglinear = 2, catprob.parm = NULL, control = list(), item.names = NULL, solver = NULL, nloptr.args = list(), auglag.args = list(), solnp.args = list(), ... ) ## S3 method for class 'GDINA' anova(object, ...) ## S3 method for class 'GDINA' coef( object, what = c("catprob", "delta", "gs", "itemprob", "LCprob", "rrum", "lambda"), withSE = FALSE, SE.type = 2, digits = 4, ... ) ## S3 method for class 'GDINA' extract(object, what, SE.type = 2, ...) ## S3 method for class 'GDINA' personparm(object, what = c("EAP", "MAP", "MLE", "mp", "HO"), digits = 4, ...) ## S3 method for class 'GDINA' logLik(object, ...) ## S3 method for class 'GDINA' deviance(object, ...) ## S3 method for class 'GDINA' nobs(object, ...) ## S3 method for class 'GDINA' vcov(object, ...) ## S3 method for class 'GDINA' npar(object, ...) ## S3 method for class 'GDINA' indlogLik(object, ...) ## S3 method for class 'GDINA' indlogPost(object, ...) ## S3 method for class 'GDINA' summary(object, ...)GDINA( dat, Q, model = "GDINA", sequential = FALSE, att.dist = "saturated", mono.constraint = FALSE, group = NULL, linkfunc = NULL, design.matrix = NULL, no.bugs = 0, att.prior = NULL, att.str = NULL, verbose = 1, higher.order = list(), loglinear = 2, catprob.parm = NULL, control = list(), item.names = NULL, solver = NULL, nloptr.args = list(), auglag.args = list(), solnp.args = list(), ... ) ## S3 method for class 'GDINA' anova(object, ...) ## S3 method for class 'GDINA' coef( object, what = c("catprob", "delta", "gs", "itemprob", "LCprob", "rrum", "lambda"), withSE = FALSE, SE.type = 2, digits = 4, ... ) ## S3 method for class 'GDINA' extract(object, what, SE.type = 2, ...) ## S3 method for class 'GDINA' personparm(object, what = c("EAP", "MAP", "MLE", "mp", "HO"), digits = 4, ...) ## S3 method for class 'GDINA' logLik(object, ...) ## S3 method for class 'GDINA' deviance(object, ...) ## S3 method for class 'GDINA' nobs(object, ...) ## S3 method for class 'GDINA' vcov(object, ...) ## S3 method for class 'GDINA' npar(object, ...) ## S3 method for class 'GDINA' indlogLik(object, ...) ## S3 method for class 'GDINA' indlogPost(object, ...) ## S3 method for class 'GDINA' summary(object, ...)
dat |
A required |
Q |
A required matrix; The number of rows occupied by a single-strategy dichotomous item is 1, by a polytomous item is
the number of nonzero categories, and by a mutiple-strategy dichotomous item is the number of strategies.
The number of column is equal to the number of attributes if all items are single-strategy dichotomous items, but
the number of attributes + 2 if any items are polytomous or have multiple strategies.
For a polytomous item, the first column represents the item number and the second column indicates the nonzero category number.
For a multiple-strategy dichotomous item, the first column represents the item number and the second column indicates the strategy number.
For binary attributes, 1 denotes the attributes are measured by the items and 0 means the attributes are not
measured. For polytomous attributes, non-zero elements indicate which level
of attributes are needed (see Chen, & de la Torre, 2013). See |
model |
A vector for each item or nonzero category, or a scalar which will be used for all
items or nonzero categories to specify the CDMs fitted. The possible options
include |
sequential |
logical; |
att.dist |
How is the joint attribute distribution estimated? It can be (1) |
mono.constraint |
logical; |
group |
a factor or a vector indicating the group each individual belongs to. Its length must be equal to the number of individuals. |
linkfunc |
a vector of link functions for each item/category; It can be |
design.matrix |
a list of design matrices; Its length must be equal to the number of items (or nonzero categories for sequential models).
If CDM for item j is specified as "UDF" in argument |
no.bugs |
A numeric scalar (whole numbers only) indicating the number of bugs or misconceptions in the Q-matrix. The bugs must be included in the last |
att.prior |
A vector of length |
att.str |
Specify attribute structures. |
verbose |
How to print calibration information after each EM iteration? Can be 0, 1 or 2, indicating to print no information, information for current iteration, or information for all iterations. |
higher.order |
A list specifying the higher-order joint attribute distribution with the following components:
|
loglinear |
the order of loglinear smooth for attribute space. It can be either 1 or 2 indicating the loglinear model with main effect only and with main effect and first-order interaction; It can also be a matrix, representing the design matrix for the loglinear model. |
catprob.parm |
A list of initial success probability parameters for each nonzero category. |
control |
A list of control parameters with elements:
|
item.names |
A vector giving the item names. By default, items are named as "Item 1", "Item 2", etc. |
solver |
A string indicating which solver should be used in M-step. By default, the solver is automatically chosen according to the models specified. Possible options include slsqp, nloptr, solnp and auglag. |
nloptr.args |
a list of control parameters to be passed to |
auglag.args |
a list of control parameters to be passed to the alabama::auglag() function. It can contain two elements:
|
solnp.args |
a list of control parameters to be passed to |
... |
additional arguments |
object |
GDINA object for various S3 methods |
what |
argument for various S3 methods; For calculating structural parameters using
For calculating incidental parameters using
|
withSE |
argument for method |
SE.type |
type of standard errors. For now, SEs are calculated based on outper-product of gradient.
It can be |
digits |
How many decimal places in each number? The default is 4. |
GDINA returns an object of class GDINA. Methods for GDINA objects
include extract for extracting various components, coef
for extracting structural parameters, personparm
for calculating incidental (person) parameters, summary for summary information.
AIC, BIC,logLik, deviance and npar can also be used to
calculate AIC, BIC, observed log-likelihood, deviance and number of parameters.
anova(GDINA): Model comparison using likelihood ratio test
coef(GDINA): extract structural parameter estimates
extract(GDINA): extract various elements of GDINA estimates
personparm(GDINA): calculate person attribute patterns and higher-order ability
logLik(GDINA): calculate log-likelihood
deviance(GDINA): calculate deviance
nobs(GDINA): calculate number of observations
vcov(GDINA): calculate covariance-matrix for delta parameters
npar(GDINA): calculate the number of parameters
indlogLik(GDINA): extract log-likelihood for each individual
indlogPost(GDINA): extract log posterior for each individual
summary(GDINA): print summary information
The generalized DINA model (G-DINA; de la Torre, 2011) is an extension of the DINA model.
Unlike the DINA model, which collaspes all latent classes into two latent groups for
each item, if item requires
attributes, the G-DINA model collapses latent classes into
latent groups with unique success probabilities on item , where
.
Let be the reduced attribute
pattern consisting of the columns of the attributes required by item , where
. For example, if only the first and the last attributes are
required, . For notational
convenience, the first attributes can be assumed to be the required attributes
for item as in de la Torre (2011). The probability of success is denoted
by . To model this probability of success, different link functions
as in the generalized linear models are used in the G-DINA model. The item response
function of the G-DINA model using the identity link can be written as
or in matrix form,
where is the intercept for item , is the main effect
due to , is the interaction effect due to
and , is the interaction
effect due to . The log and logit links can also
be employed.
Several widely used CDMs can be obtained by setting appropriate constraints to the G-DINA model. This section introduces the parameterization of different CDMs within the G-DINA model framework very breifly. Readers interested in this please refer to de la Torre(2011) for details.
DINA modelIn DINA model, each item has two item parameters - guessing () and slip (). In traditional
parameterization of the DINA model, a latent variable for person and
item is defined as
Briefly speaking, if individual master all attributes required by item ,
; otherwise, .
Item response function of the DINA model can be written by
To obtain the DINA model from the G-DINA model,
all terms in identity link G-DINA model except and
need to be fixed to zero, that is,
In this parameterization, and .
DINO modelThe DINO model can be given by
where is an indicator variable. The DINO model is also a constrained identity
link G-DINA model. As shown by de la Torre (2011), the appropriate constraint is
for
, and .
Additive models with different link functionsThe A-CDM, LLM and R-RUM can be obtained by setting all interactions to be zero in identity, logit and log link G-DINA model, respectively. Specifically, the A-CDM can be formulated as
The item response function for LLM can be given by
and lastly, the RRUM, can be written as
It should be noted that the LLM is equivalent to the compensatory RUM, which is subsumed by the GDM, and that the RRUM is a special case of the generalized noisy inputs, deterministic “And" gate model (G-NIDA).
Simultaneously identifying skills and misconceptions (SISM)The SISM can be can be reformulated as
As a result,the success probability of students who have mastered all the measured skills and possess
none of the measured misconceptions ( in Equation 4 of Kuo, et al, 2018) is
, the success probability of students who have
mastered all the measured skills but possess some of the measured misconceptions ()
is , the success probability of students who have not mastered all the
measured skills and possess none of the measured misconceptions () is
and success probability of students who have not mastered all the
measured skills and possess at least one of the measured misconceptions() is
.
By specifying no.bugs being equal to the number of attributes, the Bug-DINO is obtained, as in
The joint attribute distribution can be modeled using various methods. This section mainly focuses on the so-called
higher-order approach, which was originally proposed by de la Torre
and Douglas (2004) for the DINA model. It has been extended in this package for all condensation rules.
Particularly, three approaches are available for the higher-order attribute structure:
intercept only approach, common slope approach and varied slope approach.
For the intercept only approach, the probability of mastering attribute for individual is defined as
For the common slope approach, the probability of mastering attribute for individual is defined as
For the varied slope approach, the probability of mastering attribute for individual is defined as
where is the ability of examinee . and are the intercept
and slope parameters for attribute , respectively.
The probability of joint attributes can be written as
.
The MMLE/EM algorithm is implemented in this package. For G-DINA, DINA and DINO models, closed-form solutions exist. See de la Torre (2009) and de la Torre (2011) for details. For ACDM, LLM and RRUM, closed-form solutions do not exist, and therefore some general optimization techniques are adopted in M-step (Ma, Iaconangelo & de la Torre, 2016). The selection of optimization techniques mainly depends on whether some specific constraints need to be added.
The sequential G-DINA model is a special case of the diagnostic tree model (DTM; Ma, 2019) and estimated using the mapping matrix accordingly (See Tutz, 1997; Ma, 2019).
For dichotomous response models:
Assume a test measures attributes and item requires attributes:
The DINA and DINO model has 2 item parameters for each item;
if item is ACDM, LLM or RRUM, it has item parameters; if it is G-DINA model, it has item parameters.
Apart from item parameters, the parameters involved in the estimation of joint attribute distribution need to be estimated as well.
When using the saturated attribute structure, there are parameters for joint attribute distribution estimation; when
using a higher-order attribute structure, there are , , and parameters for the intercept only approach, common slope approach and varied slope approach, respectively.
For polytomous response data using the sequential G-DINA model, the number of item parameters
are counted at category level.
anova function does NOT check whether models compared are nested or not.
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
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Bor-Chen Kuo, Chun-Hua Chen, Chih-Wei Yang, & Magdalena Mo Ching Mok. (2016). Cognitive diagnostic models for tests with multiple-choice and constructed-response items. Educational Psychology, 36, 1115-1133.
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de la Torre, J. (2009). DINA Model and Parameter Estimation: A Didactic. Journal of Educational and Behavioral Statistics, 34, 115-130.
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Huo, Y., & de la Torre, J. (2014). Estimating a Cognitive Diagnostic Model for Multiple Strategies via the EM Algorithm. Applied Psychological Measurement, 38, 464-485.
Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258-272.
Kuo, B.-C., Chen.-H., & de la Torre,J. (2018). A cognitive diagnosis model for identifying coexisting skills and misconceptions.Applied Psychological Measuremet, 179–191.
Ma, W., & de la Torre, J. (2016). A sequential cognitive diagnosis model for polytomous responses. British Journal of Mathematical and Statistical Psychology. 69, 253-275.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Ma, W. (2019). A diagnostic tree model for polytomous responses with multiple strategies. British Journal of Mathematical and Statistical Psychology, 72, 61-82.
Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification. Applied Psychological Measurement, 40, 200-217.
Ma, W. (2017). A Sequential Cognitive Diagnosis Model for Graded Response: Model Development, Q-Matrix Validation,and Model Comparison. Unpublished doctoral dissertation. New Brunswick, NJ: Rutgers University.
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Tatsuoka, K. K. (1983). Rule space: An approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20, 345-354.
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See autoGDINA for Q-matrix validation, item-level model comparison and model calibration
in one run; See modelfit and itemfit for model and item fit analysis, Qval for Q-matrix validation,
modelcomp for item level model comparison and simGDINA for data simulation.
GMSCDM for a series of multiple strategy CDMs for dichotomous data,
and DTM for diagnostic tree model for multiple strategies in polytomous response data
Also see gdina in CDM package for the G-DINA model estimation.
## Not run: #################################### # Example 1. # # GDINA, DINA, DINO # # ACDM, LLM and RRUM # # estimation and comparison # # # #################################### dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ #--------GDINA model --------# mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") mod1 # summary information summary(mod1) AIC(mod1) #AIC BIC(mod1) #BIC logLik(mod1) #log-likelihood value deviance(mod1) # deviance: -2 log-likelihood npar(mod1) # number of parameters head(indlogLik(mod1)) # individual log-likelihood head(indlogPost(mod1)) # individual log-posterior # structural parameters # see ?coef coef(mod1) # item probabilities of success for each latent group coef(mod1, withSE = TRUE) # item probabilities of success & standard errors coef(mod1, what = "delta") # delta parameters coef(mod1, what = "delta",withSE=TRUE) # delta parameters coef(mod1, what = "gs") # guessing and slip parameters coef(mod1, what = "gs",withSE = TRUE) # guessing and slip parameters & standard errors # person parameters # see ?personparm personparm(mod1) # EAP estimates of attribute profiles personparm(mod1, what = "MAP") # MAP estimates of attribute profiles personparm(mod1, what = "MLE") # MLE estimates of attribute profiles #plot item response functions for item 10 plot(mod1,item = 10) plot(mod1,item = 10,withSE = TRUE) # with error bars #plot mastery probability for individuals 1, 20 and 50 plot(mod1,what = "mp", person =c(1,20,50)) # Use extract function to extract more components # See ?extract # ------- DINA model --------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod2 <- GDINA(dat = dat, Q = Q, model = "DINA") mod2 coef(mod2, what = "gs") # guess and slip parameters coef(mod2, what = "gs",withSE = TRUE) # guess and slip parameters and standard errors # Model comparison at the test level via likelihood ratio test anova(mod1,mod2) # -------- DINO model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod3 <- GDINA(dat = dat, Q = Q, model = "DINO") #slip and guessing coef(mod3, what = "gs") # guess and slip parameters coef(mod3, what = "gs",withSE = TRUE) # guess and slip parameters + standard errors # Model comparison at test level via likelihood ratio test anova(mod1,mod2,mod3) # --------- ACDM model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod4 <- GDINA(dat = dat, Q = Q, model = "ACDM") mod4 # --------- LLM model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod4b <- GDINA(dat = dat, Q = Q, model = "LLM") mod4b # --------- RRUM model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod4c <- GDINA(dat = dat, Q = Q, model = "RRUM") mod4c # --- Different CDMs for different items --- # dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ models <- c(rep("GDINA",3),"LLM","DINA","DINO","ACDM","RRUM","LLM","RRUM") mod5 <- GDINA(dat = dat, Q = Q, model = models) anova(mod1,mod2,mod3,mod4,mod4b,mod4c,mod5) #################################### # Example 2. # # Model estimations # # With monotonocity constraints # #################################### dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # for item 10 only mod11 <- GDINA(dat = dat, Q = Q, model = "GDINA",mono.constraint = c(rep(FALSE,9),TRUE)) mod11 mod11a <- GDINA(dat = dat, Q = Q, model = "DINA",mono.constraint = TRUE) mod11a mod11b <- GDINA(dat = dat, Q = Q, model = "ACDM",mono.constraint = TRUE) mod11b mod11c <- GDINA(dat = dat, Q = Q, model = "LLM",mono.constraint = TRUE) mod11c mod11d <- GDINA(dat = dat, Q = Q, model = "RRUM",mono.constraint = TRUE) mod11d coef(mod11d,"delta") coef(mod11d,"rrum") #################################### # Example 3a. # # Model estimations # # With Higher-order att structure # #################################### dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # --- Higher order G-DINA model ---# mod12 <- GDINA(dat = dat, Q = Q, model = "DINA", att.dist="higher.order",higher.order=list(nquad=31,model = "2PL")) personparm(mod12,"HO") # higher-order ability # structural parameters # first column is slope and the second column is intercept coef(mod12,"lambda") # --- Higher order DINA model ---# mod22 <- GDINA(dat = dat, Q = Q, model = "DINA", att.dist="higher.order", higher.order=list(model = "2PL",Prior=TRUE)) #################################### # Example 3b. # # Model estimations # # With log-linear att structure # #################################### # --- DINA model with loglinear smoothed attribute space ---# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod23 <- GDINA(dat = dat, Q = Q, model = "DINA",att.dist="loglinear",loglinear=1) coef(mod23,"lambda") # intercept and three main effects #################################### # Example 3c. # # Model estimations # # With independent att structure # #################################### # --- GDINA model with independent attribute space ---# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod33 <- GDINA(dat = dat, Q = Q, att.dist="independent") coef(mod33,"lambda") # mastery probability for each attribute #################################### # Example 4. # # Model estimations # # With fixed att structure # #################################### # --- User-specified attribute priors ----# # prior distribution is fixed during calibration # Assume each of 000,100,010 and 001 has probability of 0.1 # and each of 110, 101,011 and 111 has probability of 0.15 # Note that the sum is equal to 1 # prior <- c(0.1,0.1,0.1,0.1,0.15,0.15,0.15,0.15) # fit GDINA model with fixed prior dist. dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ modp1 <- GDINA(dat = dat, Q = Q, att.prior = prior, att.dist = "fixed") extract(modp1, what = "att.prior") #################################### # Example 5a. # # G-DINA # # with hierarchical att structure # #################################### # --- User-specified attribute structure ----# Q <- sim30GDINA$simQ K <- ncol(Q) # divergent structure A1->A2->A3;A1->A4->A5 diverg <- list(c(1,2), c(2,3), c(1,4), c(4,5)) struc <- att.structure(diverg,K) set.seed(123) # data simulation N <- 1000 true.lc <- sample(c(1:2^K),N,replace=TRUE,prob=struc$att.prob) table(true.lc) #check the sample true.att <- attributepattern(K)[true.lc,] gs <- matrix(rep(0.1,2*nrow(Q)),ncol=2) # data simulation simD <- simGDINA(N,Q,gs.parm = gs, model = "GDINA",attribute = true.att) dat <- extract(simD,"dat") modp1 <- GDINA(dat = dat, Q = Q, att.str = diverg, att.dist = "saturated") modp1 coef(modp1,"lambda") #################################### # Example 5b. # # Reduced model (e.g.,ACDM) # # with hierarchical att structure # #################################### # --- User-specified attribute structure ----# Q <- sim30GDINA$simQ K <- ncol(Q) # linear structure A1->A2->A3->A4->A5 linear <- list(c(1,2), c(2,3), c(3,4), c(4,5)) struc <- att.structure(linear,K) set.seed(123) # data simulation N <- 1000 true.lc <- sample(c(1:2^K),N,replace=TRUE,prob=struc$att.prob) table(true.lc) #check the sample true.att <- attributepattern(K)[true.lc,] gs <- matrix(rep(0.1,2*nrow(Q)),ncol=2) # data simulation simD <- simGDINA(N,Q,gs.parm = gs, model = "ACDM",attribute = true.att) dat <- extract(simD,"dat") modp1 <- GDINA(dat = dat, Q = Q, model = "ACDM", att.str = linear, att.dist = "saturated") coef(modp1) coef(modp1,"lambda") #################################### # Example 6. # # Specify initial values for item # # parameters # #################################### # check initials to see the format for initial item parameters initials <- sim10GDINA$simItempar dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod.initial <- GDINA(dat,Q,catprob.parm = initials) # compare initial item parameters Map(rbind, initials,extract(mod.initial,"initial.catprob")) #################################### # Example 7a. # # Fix item and structure parameters# # Estimate person attribute profile# #################################### # check initials to see the format for initial item parameters initials <- sim10GDINA$simItempar prior <- c(0.1,0.1,0.1,0.1,0.15,0.15,0.15,0.15) dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod.ini <- GDINA(dat,Q,catprob.parm = initials,att.prior = prior, att.dist = "fixed",control=list(maxitr = 0)) personparm(mod.ini) # compare item parameters Map(rbind, initials,coef(mod.ini)) #################################### # Example 7b. # # Fix parameters for some items # # Estimate person attribute profile# #################################### # check initials to see the format for initial item parameters initials <- sim10GDINA$simItempar prior <- c(0.1,0.1,0.1,0.1,0.15,0.15,0.15,0.15) dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # fix parameters of the first 5 items; do not fix mixing proportion parameters mod.ini <- GDINA(dat,Q,catprob.parm = initials, att.dist = "saturated",control=list(maxitr = c(rep(0,5),rep(2000,5)))) personparm(mod.ini) # compare item parameters Map(rbind, initials,coef(mod.ini)) #################################### # Example 8. # # polytomous attribute # # model estimation # # see Chen, de la Torre 2013 # #################################### # --- polytomous attribute G-DINA model --- # dat <- sim30pGDINA$simdat Q <- sim30pGDINA$simQ #polytomous G-DINA model pout <- GDINA(dat,Q) # ----- polymous DINA model --------# pout2 <- GDINA(dat,Q,model="DINA") anova(pout,pout2) #################################### # Example 9. # # Sequential G-DINA model # # see Ma, & de la Torre 2016 # #################################### # --- polytomous attribute G-DINA model --- # dat <- sim20seqGDINA$simdat Q <- sim20seqGDINA$simQ Q # Item Cat A1 A2 A3 A4 A5 # 1 1 1 0 0 0 0 # 1 2 0 1 0 0 0 # 2 1 0 0 1 0 0 # 2 2 0 0 0 1 0 # 3 1 0 0 0 0 1 # 3 2 1 0 0 0 0 # 4 1 0 0 0 0 1 # ... #sequential G-DINA model sGDINA <- GDINA(dat,Q,sequential = TRUE) sDINA <- GDINA(dat,Q,sequential = TRUE,model = "DINA") anova(sGDINA,sDINA) coef(sDINA) # processing function coef(sDINA,"itemprob") # success probabilities for each item coef(sDINA,"LCprob") # success probabilities for each category for all latent classes #################################### # Example 10a. # # Multiple-Group G-DINA model # #################################### Q <- sim10GDINA$simQ K <- ncol(Q) # parameter simulation # Group 1 - female N1 <- 3000 gs1 <- matrix(rep(0.1,2*nrow(Q)),ncol=2) # Group 2 - male N2 <- 3000 gs2 <- matrix(rep(0.2,2*nrow(Q)),ncol=2) # data simulation for each group sim1 <- simGDINA(N1,Q,gs.parm = gs1,model = "DINA",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N1), lambda = data.frame(a=rep(1.5,K),b=seq(-1,1,length.out=K)))) sim2 <- simGDINA(N2,Q,gs.parm = gs2,model = "DINO",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N2), lambda = data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)))) # combine data - all items have the same item parameters dat <- rbind(extract(sim1,"dat"),extract(sim2,"dat")) gr <- rep(c(1,2),c(3000,3000)) # Fit G-DINA model mg.est <- GDINA(dat = dat,Q = Q,group = gr) summary(mg.est) extract(mg.est,"posterior.prob") coef(mg.est,"lambda") #################################### # Example 10b. # # Multiple-Group G-DINA model # #################################### Q <- sim30GDINA$simQ K <- ncol(Q) # parameter simulation N1 <- 3000 gs1 <- matrix(rep(0.1,2*nrow(Q)),ncol=2) N2 <- 3000 gs2 <- matrix(rep(0.2,2*nrow(Q)),ncol=2) # data simulation for each group # two groups have different theta distributions sim1 <- simGDINA(N1,Q,gs.parm = gs1,model = "DINA",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N1), lambda = data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)))) sim2 <- simGDINA(N2,Q,gs.parm = gs2,model = "DINO",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N2,1,1), lambda = data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)))) # combine data - different groups have distinct item parameters # see ?bdiagMatrix dat <- bdiagMatrix(list(extract(sim1,"dat"),extract(sim2,"dat")),fill=NA) Q <- rbind(Q,Q) gr <- rep(c(1,2),c(3000,3000)) mg.est <- GDINA(dat = dat,Q = Q,group = gr) # Fit G-DINA model mg.est <- GDINA(dat = dat,Q = Q,group = gr,att.dist="higher.order", higher.order=list(model = "Rasch")) summary(mg.est) coef(mg.est,"lambda") personparm(mg.est) personparm(mg.est,"HO") extract(mg.est,"posterior.prob") #################################### # Example 11. # # Bug DINO model # #################################### set.seed(123) Q <- sim10GDINA$simQ # 1 represents misconceptions/bugs N <- 1000 J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) sim <- simGDINA(N,Q,gs.parm = gs,model = "BUGDINO") dat <- extract(sim,"dat") est <- GDINA(dat=dat,Q=Q,model = "BUGDINO") coef(est) #################################### # Example 12. # # SISM model # #################################### # The Q-matrix used in Kuo, et al (2018) # The first four columns are for Attributes 1-4 # The last three columns are for Bugs 1-3 Q <- matrix(c(1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,0,0,0,0, 0,0,0,1,0,0,0, 0,0,0,0,1,0,0, 0,0,0,0,0,1,0, 0,0,0,0,0,0,1, 1,0,0,0,1,0,0, 0,1,0,0,1,0,0, 0,0,1,0,0,0,1, 0,0,0,1,0,1,0, 1,1,0,0,1,0,0, 1,0,1,0,0,0,1, 1,0,0,1,0,0,1, 0,1,1,0,0,0,1, 0,1,0,1,0,1,1, 0,0,1,1,0,1,1, 1,0,1,0,1,1,0, 1,1,0,1,1,1,0, 0,1,1,1,1,1,0),ncol = 7,byrow = TRUE) J <- nrow(Q) N <- 1000 gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) sim <- simGDINA(N,Q,gs.parm = gs,model = "SISM",no.bugs=3) dat <- extract(sim,"dat") est <- GDINA(dat=dat,Q=Q,model="SISM",no.bugs=3) coef(est,"delta") #################################### # Example 13a. # # user specified design matrix # # LCDM (logit G-DINA) # #################################### dat <- sim30GDINA$simdat Q <- sim30GDINA$simQ # LCDM lcdm <- GDINA(dat = dat, Q = Q, model = "logitGDINA", control=list(conv.type="neg2LL")) #Another way is to find design matrix for each item first => must be a list D <- lapply(rowSums(Q),designmatrix,model="GDINA") # for comparison, use change in -2LL as convergence criterion # LCDM lcdm2 <- GDINA(dat = dat, Q = Q, model = "UDF", design.matrix = D, linkfunc = "logit", control=list(conv.type="neg2LL"),solver="slsqp") # identity link GDINA iGDINA <- GDINA(dat = dat, Q = Q, model = "GDINA", control=list(conv.type="neg2LL"),solver="slsqp") # compare all three models => identical anova(lcdm,lcdm2,iGDINA) #################################### # Example 13b. # # user specified design matrix # # RRUM # #################################### dat <- sim30GDINA$simdat Q <- sim30GDINA$simQ # specify design matrix for each item => must be a list # D can be defined by the user D <- lapply(rowSums(Q),designmatrix,model="ACDM") # for comparison, use change in -2LL as convergence criterion # RRUM logACDM <- GDINA(dat = dat, Q = Q, model = "UDF", design.matrix = D, linkfunc = "log", control=list(conv.type="neg2LL"),solver="slsqp") # identity link GDINA RRUM <- GDINA(dat = dat, Q = Q, model = "RRUM", control=list(conv.type="neg2LL"),solver="slsqp") # compare two models => identical anova(logACDM,RRUM) #################################### # Example 14. # # Multiple-strategy DINA model # #################################### Q <- matrix(c(1,1,1,1,0, 1,2,0,1,1, 2,1,1,0,0, 3,1,0,1,0, 4,1,0,0,1, 5,1,1,0,0, 5,2,0,0,1),ncol = 5,byrow = TRUE) d <- list( item1=c(0.2,0.7), item2=c(0.1,0.6), item3=c(0.2,0.6), item4=c(0.2,0.7), item5=c(0.1,0.8)) set.seed(12345) sim <- simGDINA(N=1000,Q = Q, delta.parm = d, model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA")) # simulated data dat <- extract(sim,what = "dat") # estimation # MSDINA need to be specified for each strategy est <- GDINA(dat,Q,model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA")) coef(est,"delta") ## End(Not run)## Not run: #################################### # Example 1. # # GDINA, DINA, DINO # # ACDM, LLM and RRUM # # estimation and comparison # # # #################################### dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ #--------GDINA model --------# mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") mod1 # summary information summary(mod1) AIC(mod1) #AIC BIC(mod1) #BIC logLik(mod1) #log-likelihood value deviance(mod1) # deviance: -2 log-likelihood npar(mod1) # number of parameters head(indlogLik(mod1)) # individual log-likelihood head(indlogPost(mod1)) # individual log-posterior # structural parameters # see ?coef coef(mod1) # item probabilities of success for each latent group coef(mod1, withSE = TRUE) # item probabilities of success & standard errors coef(mod1, what = "delta") # delta parameters coef(mod1, what = "delta",withSE=TRUE) # delta parameters coef(mod1, what = "gs") # guessing and slip parameters coef(mod1, what = "gs",withSE = TRUE) # guessing and slip parameters & standard errors # person parameters # see ?personparm personparm(mod1) # EAP estimates of attribute profiles personparm(mod1, what = "MAP") # MAP estimates of attribute profiles personparm(mod1, what = "MLE") # MLE estimates of attribute profiles #plot item response functions for item 10 plot(mod1,item = 10) plot(mod1,item = 10,withSE = TRUE) # with error bars #plot mastery probability for individuals 1, 20 and 50 plot(mod1,what = "mp", person =c(1,20,50)) # Use extract function to extract more components # See ?extract # ------- DINA model --------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod2 <- GDINA(dat = dat, Q = Q, model = "DINA") mod2 coef(mod2, what = "gs") # guess and slip parameters coef(mod2, what = "gs",withSE = TRUE) # guess and slip parameters and standard errors # Model comparison at the test level via likelihood ratio test anova(mod1,mod2) # -------- DINO model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod3 <- GDINA(dat = dat, Q = Q, model = "DINO") #slip and guessing coef(mod3, what = "gs") # guess and slip parameters coef(mod3, what = "gs",withSE = TRUE) # guess and slip parameters + standard errors # Model comparison at test level via likelihood ratio test anova(mod1,mod2,mod3) # --------- ACDM model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod4 <- GDINA(dat = dat, Q = Q, model = "ACDM") mod4 # --------- LLM model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod4b <- GDINA(dat = dat, Q = Q, model = "LLM") mod4b # --------- RRUM model -------# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod4c <- GDINA(dat = dat, Q = Q, model = "RRUM") mod4c # --- Different CDMs for different items --- # dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ models <- c(rep("GDINA",3),"LLM","DINA","DINO","ACDM","RRUM","LLM","RRUM") mod5 <- GDINA(dat = dat, Q = Q, model = models) anova(mod1,mod2,mod3,mod4,mod4b,mod4c,mod5) #################################### # Example 2. # # Model estimations # # With monotonocity constraints # #################################### dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # for item 10 only mod11 <- GDINA(dat = dat, Q = Q, model = "GDINA",mono.constraint = c(rep(FALSE,9),TRUE)) mod11 mod11a <- GDINA(dat = dat, Q = Q, model = "DINA",mono.constraint = TRUE) mod11a mod11b <- GDINA(dat = dat, Q = Q, model = "ACDM",mono.constraint = TRUE) mod11b mod11c <- GDINA(dat = dat, Q = Q, model = "LLM",mono.constraint = TRUE) mod11c mod11d <- GDINA(dat = dat, Q = Q, model = "RRUM",mono.constraint = TRUE) mod11d coef(mod11d,"delta") coef(mod11d,"rrum") #################################### # Example 3a. # # Model estimations # # With Higher-order att structure # #################################### dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # --- Higher order G-DINA model ---# mod12 <- GDINA(dat = dat, Q = Q, model = "DINA", att.dist="higher.order",higher.order=list(nquad=31,model = "2PL")) personparm(mod12,"HO") # higher-order ability # structural parameters # first column is slope and the second column is intercept coef(mod12,"lambda") # --- Higher order DINA model ---# mod22 <- GDINA(dat = dat, Q = Q, model = "DINA", att.dist="higher.order", higher.order=list(model = "2PL",Prior=TRUE)) #################################### # Example 3b. # # Model estimations # # With log-linear att structure # #################################### # --- DINA model with loglinear smoothed attribute space ---# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod23 <- GDINA(dat = dat, Q = Q, model = "DINA",att.dist="loglinear",loglinear=1) coef(mod23,"lambda") # intercept and three main effects #################################### # Example 3c. # # Model estimations # # With independent att structure # #################################### # --- GDINA model with independent attribute space ---# dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod33 <- GDINA(dat = dat, Q = Q, att.dist="independent") coef(mod33,"lambda") # mastery probability for each attribute #################################### # Example 4. # # Model estimations # # With fixed att structure # #################################### # --- User-specified attribute priors ----# # prior distribution is fixed during calibration # Assume each of 000,100,010 and 001 has probability of 0.1 # and each of 110, 101,011 and 111 has probability of 0.15 # Note that the sum is equal to 1 # prior <- c(0.1,0.1,0.1,0.1,0.15,0.15,0.15,0.15) # fit GDINA model with fixed prior dist. dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ modp1 <- GDINA(dat = dat, Q = Q, att.prior = prior, att.dist = "fixed") extract(modp1, what = "att.prior") #################################### # Example 5a. # # G-DINA # # with hierarchical att structure # #################################### # --- User-specified attribute structure ----# Q <- sim30GDINA$simQ K <- ncol(Q) # divergent structure A1->A2->A3;A1->A4->A5 diverg <- list(c(1,2), c(2,3), c(1,4), c(4,5)) struc <- att.structure(diverg,K) set.seed(123) # data simulation N <- 1000 true.lc <- sample(c(1:2^K),N,replace=TRUE,prob=struc$att.prob) table(true.lc) #check the sample true.att <- attributepattern(K)[true.lc,] gs <- matrix(rep(0.1,2*nrow(Q)),ncol=2) # data simulation simD <- simGDINA(N,Q,gs.parm = gs, model = "GDINA",attribute = true.att) dat <- extract(simD,"dat") modp1 <- GDINA(dat = dat, Q = Q, att.str = diverg, att.dist = "saturated") modp1 coef(modp1,"lambda") #################################### # Example 5b. # # Reduced model (e.g.,ACDM) # # with hierarchical att structure # #################################### # --- User-specified attribute structure ----# Q <- sim30GDINA$simQ K <- ncol(Q) # linear structure A1->A2->A3->A4->A5 linear <- list(c(1,2), c(2,3), c(3,4), c(4,5)) struc <- att.structure(linear,K) set.seed(123) # data simulation N <- 1000 true.lc <- sample(c(1:2^K),N,replace=TRUE,prob=struc$att.prob) table(true.lc) #check the sample true.att <- attributepattern(K)[true.lc,] gs <- matrix(rep(0.1,2*nrow(Q)),ncol=2) # data simulation simD <- simGDINA(N,Q,gs.parm = gs, model = "ACDM",attribute = true.att) dat <- extract(simD,"dat") modp1 <- GDINA(dat = dat, Q = Q, model = "ACDM", att.str = linear, att.dist = "saturated") coef(modp1) coef(modp1,"lambda") #################################### # Example 6. # # Specify initial values for item # # parameters # #################################### # check initials to see the format for initial item parameters initials <- sim10GDINA$simItempar dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod.initial <- GDINA(dat,Q,catprob.parm = initials) # compare initial item parameters Map(rbind, initials,extract(mod.initial,"initial.catprob")) #################################### # Example 7a. # # Fix item and structure parameters# # Estimate person attribute profile# #################################### # check initials to see the format for initial item parameters initials <- sim10GDINA$simItempar prior <- c(0.1,0.1,0.1,0.1,0.15,0.15,0.15,0.15) dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod.ini <- GDINA(dat,Q,catprob.parm = initials,att.prior = prior, att.dist = "fixed",control=list(maxitr = 0)) personparm(mod.ini) # compare item parameters Map(rbind, initials,coef(mod.ini)) #################################### # Example 7b. # # Fix parameters for some items # # Estimate person attribute profile# #################################### # check initials to see the format for initial item parameters initials <- sim10GDINA$simItempar prior <- c(0.1,0.1,0.1,0.1,0.15,0.15,0.15,0.15) dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # fix parameters of the first 5 items; do not fix mixing proportion parameters mod.ini <- GDINA(dat,Q,catprob.parm = initials, att.dist = "saturated",control=list(maxitr = c(rep(0,5),rep(2000,5)))) personparm(mod.ini) # compare item parameters Map(rbind, initials,coef(mod.ini)) #################################### # Example 8. # # polytomous attribute # # model estimation # # see Chen, de la Torre 2013 # #################################### # --- polytomous attribute G-DINA model --- # dat <- sim30pGDINA$simdat Q <- sim30pGDINA$simQ #polytomous G-DINA model pout <- GDINA(dat,Q) # ----- polymous DINA model --------# pout2 <- GDINA(dat,Q,model="DINA") anova(pout,pout2) #################################### # Example 9. # # Sequential G-DINA model # # see Ma, & de la Torre 2016 # #################################### # --- polytomous attribute G-DINA model --- # dat <- sim20seqGDINA$simdat Q <- sim20seqGDINA$simQ Q # Item Cat A1 A2 A3 A4 A5 # 1 1 1 0 0 0 0 # 1 2 0 1 0 0 0 # 2 1 0 0 1 0 0 # 2 2 0 0 0 1 0 # 3 1 0 0 0 0 1 # 3 2 1 0 0 0 0 # 4 1 0 0 0 0 1 # ... #sequential G-DINA model sGDINA <- GDINA(dat,Q,sequential = TRUE) sDINA <- GDINA(dat,Q,sequential = TRUE,model = "DINA") anova(sGDINA,sDINA) coef(sDINA) # processing function coef(sDINA,"itemprob") # success probabilities for each item coef(sDINA,"LCprob") # success probabilities for each category for all latent classes #################################### # Example 10a. # # Multiple-Group G-DINA model # #################################### Q <- sim10GDINA$simQ K <- ncol(Q) # parameter simulation # Group 1 - female N1 <- 3000 gs1 <- matrix(rep(0.1,2*nrow(Q)),ncol=2) # Group 2 - male N2 <- 3000 gs2 <- matrix(rep(0.2,2*nrow(Q)),ncol=2) # data simulation for each group sim1 <- simGDINA(N1,Q,gs.parm = gs1,model = "DINA",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N1), lambda = data.frame(a=rep(1.5,K),b=seq(-1,1,length.out=K)))) sim2 <- simGDINA(N2,Q,gs.parm = gs2,model = "DINO",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N2), lambda = data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)))) # combine data - all items have the same item parameters dat <- rbind(extract(sim1,"dat"),extract(sim2,"dat")) gr <- rep(c(1,2),c(3000,3000)) # Fit G-DINA model mg.est <- GDINA(dat = dat,Q = Q,group = gr) summary(mg.est) extract(mg.est,"posterior.prob") coef(mg.est,"lambda") #################################### # Example 10b. # # Multiple-Group G-DINA model # #################################### Q <- sim30GDINA$simQ K <- ncol(Q) # parameter simulation N1 <- 3000 gs1 <- matrix(rep(0.1,2*nrow(Q)),ncol=2) N2 <- 3000 gs2 <- matrix(rep(0.2,2*nrow(Q)),ncol=2) # data simulation for each group # two groups have different theta distributions sim1 <- simGDINA(N1,Q,gs.parm = gs1,model = "DINA",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N1), lambda = data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)))) sim2 <- simGDINA(N2,Q,gs.parm = gs2,model = "DINO",att.dist = "higher.order", higher.order.parm = list(theta = rnorm(N2,1,1), lambda = data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)))) # combine data - different groups have distinct item parameters # see ?bdiagMatrix dat <- bdiagMatrix(list(extract(sim1,"dat"),extract(sim2,"dat")),fill=NA) Q <- rbind(Q,Q) gr <- rep(c(1,2),c(3000,3000)) mg.est <- GDINA(dat = dat,Q = Q,group = gr) # Fit G-DINA model mg.est <- GDINA(dat = dat,Q = Q,group = gr,att.dist="higher.order", higher.order=list(model = "Rasch")) summary(mg.est) coef(mg.est,"lambda") personparm(mg.est) personparm(mg.est,"HO") extract(mg.est,"posterior.prob") #################################### # Example 11. # # Bug DINO model # #################################### set.seed(123) Q <- sim10GDINA$simQ # 1 represents misconceptions/bugs N <- 1000 J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) sim <- simGDINA(N,Q,gs.parm = gs,model = "BUGDINO") dat <- extract(sim,"dat") est <- GDINA(dat=dat,Q=Q,model = "BUGDINO") coef(est) #################################### # Example 12. # # SISM model # #################################### # The Q-matrix used in Kuo, et al (2018) # The first four columns are for Attributes 1-4 # The last three columns are for Bugs 1-3 Q <- matrix(c(1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,0,0,0,0, 0,0,0,1,0,0,0, 0,0,0,0,1,0,0, 0,0,0,0,0,1,0, 0,0,0,0,0,0,1, 1,0,0,0,1,0,0, 0,1,0,0,1,0,0, 0,0,1,0,0,0,1, 0,0,0,1,0,1,0, 1,1,0,0,1,0,0, 1,0,1,0,0,0,1, 1,0,0,1,0,0,1, 0,1,1,0,0,0,1, 0,1,0,1,0,1,1, 0,0,1,1,0,1,1, 1,0,1,0,1,1,0, 1,1,0,1,1,1,0, 0,1,1,1,1,1,0),ncol = 7,byrow = TRUE) J <- nrow(Q) N <- 1000 gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) sim <- simGDINA(N,Q,gs.parm = gs,model = "SISM",no.bugs=3) dat <- extract(sim,"dat") est <- GDINA(dat=dat,Q=Q,model="SISM",no.bugs=3) coef(est,"delta") #################################### # Example 13a. # # user specified design matrix # # LCDM (logit G-DINA) # #################################### dat <- sim30GDINA$simdat Q <- sim30GDINA$simQ # LCDM lcdm <- GDINA(dat = dat, Q = Q, model = "logitGDINA", control=list(conv.type="neg2LL")) #Another way is to find design matrix for each item first => must be a list D <- lapply(rowSums(Q),designmatrix,model="GDINA") # for comparison, use change in -2LL as convergence criterion # LCDM lcdm2 <- GDINA(dat = dat, Q = Q, model = "UDF", design.matrix = D, linkfunc = "logit", control=list(conv.type="neg2LL"),solver="slsqp") # identity link GDINA iGDINA <- GDINA(dat = dat, Q = Q, model = "GDINA", control=list(conv.type="neg2LL"),solver="slsqp") # compare all three models => identical anova(lcdm,lcdm2,iGDINA) #################################### # Example 13b. # # user specified design matrix # # RRUM # #################################### dat <- sim30GDINA$simdat Q <- sim30GDINA$simQ # specify design matrix for each item => must be a list # D can be defined by the user D <- lapply(rowSums(Q),designmatrix,model="ACDM") # for comparison, use change in -2LL as convergence criterion # RRUM logACDM <- GDINA(dat = dat, Q = Q, model = "UDF", design.matrix = D, linkfunc = "log", control=list(conv.type="neg2LL"),solver="slsqp") # identity link GDINA RRUM <- GDINA(dat = dat, Q = Q, model = "RRUM", control=list(conv.type="neg2LL"),solver="slsqp") # compare two models => identical anova(logACDM,RRUM) #################################### # Example 14. # # Multiple-strategy DINA model # #################################### Q <- matrix(c(1,1,1,1,0, 1,2,0,1,1, 2,1,1,0,0, 3,1,0,1,0, 4,1,0,0,1, 5,1,1,0,0, 5,2,0,0,1),ncol = 5,byrow = TRUE) d <- list( item1=c(0.2,0.7), item2=c(0.1,0.6), item3=c(0.2,0.6), item4=c(0.2,0.7), item5=c(0.1,0.8)) set.seed(12345) sim <- simGDINA(N=1000,Q = Q, delta.parm = d, model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA")) # simulated data dat <- extract(sim,what = "dat") # estimation # MSDINA need to be specified for each strategy est <- GDINA(dat,Q,model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA")) coef(est,"delta") ## End(Not run)
An (experimental) function for calibrating the multiple-strategy CDMs for dichotomous response data (Ma & Guo, 2019)
GMSCDM( dat, msQ, model = "ACDM", s = 1, att.prior = NULL, delta = NULL, control = list() )GMSCDM( dat, msQ, model = "ACDM", s = 1, att.prior = NULL, delta = NULL, control = list() )
dat |
A required binary item response matrix |
msQ |
A multiple-strategy Q-matrix; the first column gives item numbers and the second column gives the strategy number. See examples. |
model |
CDM used; can be |
s |
strategy selection parameter. It is equal to 1 by default. |
att.prior |
mixing proportion parameters. |
delta |
delta parameters in list format. |
control |
a list of control arguments |
an object of class GMSCDM with the following components:
A matrix of success probabilities for each latent class on each item (IRF)
A list of delta parameters
A list of estimated attribute profiles including EAP, MLE and MAP estimates.
A list of test fit statistics including deviance, number of parameters, AIC and BIC
strategy-specific item response function
Probability of adopting each strategy on each item for each latent class
Strategy pravelence
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Ma, W., & Guo, W. (2019). Cognitive Diagnosis Models for Multiple Strategies. British Journal of Mathematical and Statistical Psychology.
GDINA for MS-DINA model and single strategy CDMs,
and DTM for diagnostic tree model for multiple strategies in polytomous response data
## Not run: ################## # # data simulation # ################## set.seed(123) msQ <- matrix( c(1,1,0,1, 1,2,1,0, 2,1,1,0, 3,1,0,1, 4,1,1,1, 5,1,1,1),6,4,byrow = T) # J x L - 00,10,01,11 LC.prob <- matrix(c( 0.2,0.7727,0.5889,0.8125, 0.1,0.9,0.1,0.9, 0.1,0.1,0.8,0.8, 0.2,0.5,0.4,0.7, 0.2,0.4,0.7,0.9),5,4,byrow=TRUE) N <- 10000 att <- sample(1:4,N,replace=TRUE) dat <- 1*(t(LC.prob[,att])>matrix(runif(N*5),N,5)) est <- GMSCDM(dat,msQ) # item response function est$IRF # strategy specific IRF est$sIRF ################################ # # Example 14 from GDINA function # ################################ Q <- matrix(c(1,1,1,1,0, 1,2,0,1,1, 2,1,1,0,0, 3,1,0,1,0, 4,1,0,0,1, 5,1,1,0,0, 5,2,0,0,1),ncol = 5,byrow = TRUE) d <- list( item1=c(0.2,0.7), item2=c(0.1,0.6), item3=c(0.2,0.6), item4=c(0.2,0.7), item5=c(0.1,0.8)) set.seed(123) sim <- simGDINA(N=1000,Q = Q, delta.parm = d, model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA")) # simulated data dat <- extract(sim,what = "dat") # estimation # MSDINA need to be specified for each strategy est <- GDINA(dat,Q,model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA"), control = list(conv.type = "neg2LL",conv.crit = .01)) # Approximate the MS-DINA model using GMS DINA model est2 <- GMSCDM(dat, Q, model = "rDINA", s = 10, control = list(conv.type = "neg2LL",conv.crit = .01)) ## End(Not run)## Not run: ################## # # data simulation # ################## set.seed(123) msQ <- matrix( c(1,1,0,1, 1,2,1,0, 2,1,1,0, 3,1,0,1, 4,1,1,1, 5,1,1,1),6,4,byrow = T) # J x L - 00,10,01,11 LC.prob <- matrix(c( 0.2,0.7727,0.5889,0.8125, 0.1,0.9,0.1,0.9, 0.1,0.1,0.8,0.8, 0.2,0.5,0.4,0.7, 0.2,0.4,0.7,0.9),5,4,byrow=TRUE) N <- 10000 att <- sample(1:4,N,replace=TRUE) dat <- 1*(t(LC.prob[,att])>matrix(runif(N*5),N,5)) est <- GMSCDM(dat,msQ) # item response function est$IRF # strategy specific IRF est$sIRF ################################ # # Example 14 from GDINA function # ################################ Q <- matrix(c(1,1,1,1,0, 1,2,0,1,1, 2,1,1,0,0, 3,1,0,1,0, 4,1,0,0,1, 5,1,1,0,0, 5,2,0,0,1),ncol = 5,byrow = TRUE) d <- list( item1=c(0.2,0.7), item2=c(0.1,0.6), item3=c(0.2,0.6), item4=c(0.2,0.7), item5=c(0.1,0.8)) set.seed(123) sim <- simGDINA(N=1000,Q = Q, delta.parm = d, model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA")) # simulated data dat <- extract(sim,what = "dat") # estimation # MSDINA need to be specified for each strategy est <- GDINA(dat,Q,model = c("MSDINA","MSDINA","DINA", "DINA","DINA","MSDINA","MSDINA"), control = list(conv.type = "neg2LL",conv.crit = .01)) # Approximate the MS-DINA model using GMS DINA model est2 <- GMSCDM(dat, Q, model = "rDINA", s = 10, control = list(conv.type = "neg2LL",conv.crit = .01)) ## End(Not run)
This function implements an iterative latent class analysis (ILCA; Jiang, 2019) approach to estimating attributes for cognitive diagnosis.
ILCA(dat, Q, seed.num = 5)ILCA(dat, Q, seed.num = 5)
dat |
A required binary item response matrix. |
Q |
A required binary item and attribute association matrix. |
seed.num |
seed number; Default = 5. |
Estimated attribute profiles.
Zhehan Jiang, The University of Alabama
Jiang, Z. (2019). Using the iterative latent-class analysis approach to improve attribute accuracy in diagnostic classification models. Behavior research methods, 1-10.
## Not run: ILCA(sim10GDINA$simdat, sim10GDINA$simQ) ## End(Not run)## Not run: ILCA(sim10GDINA$simdat, sim10GDINA$simQ) ## End(Not run)
Extract individual log-likelihood.
indlogLik(object, ...)indlogLik(object, ...)
object |
GDINA object |
... |
additional arguments |
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") iL <- indlogLik(fit) iL[1:6,] ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") iL <- indlogLik(fit) iL[1:6,] ## End(Not run)
Extract individual log posterior.
indlogPost(object, ...)indlogPost(object, ...)
object |
GDINA object |
... |
additional arguments |
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") iP <- indlogPost(fit) iP[1:6,] ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") iP <- indlogPost(fit) iP[1:6,] ## End(Not run)
Calculate item fit statistics (Chen, de la Torre, & Zhang, 2013) and draw heatmap plot for item pairs
itemfit( GDINA.obj, person.sim = "post", p.adjust.methods = "holm", cor.use = "pairwise.complete.obs", digits = 4, N.resampling = NULL, randomseed = 123456 ) ## S3 method for class 'itemfit' extract(object, what, ...) ## S3 method for class 'itemfit' summary(object, ...)itemfit( GDINA.obj, person.sim = "post", p.adjust.methods = "holm", cor.use = "pairwise.complete.obs", digits = 4, N.resampling = NULL, randomseed = 123456 ) ## S3 method for class 'itemfit' extract(object, what, ...) ## S3 method for class 'itemfit' summary(object, ...)
GDINA.obj |
An estimated model object of class |
person.sim |
Simulate expected responses from the posterior or based on EAP, MAP and MLE estimates. |
p.adjust.methods |
p-values for the proportion correct, transformed correlation, and log-odds ratio
can be adjusted for multiple comparisons at test and item level. This is conducted using |
cor.use |
how to deal with missing values when calculating correlations? This argument will be passed to |
digits |
How many decimal places in each number? The default is 4. |
N.resampling |
the sample size of resampling. By default, it is the maximum of 1e+5 and ten times of current sample size. |
randomseed |
random seed; This is used to make sure the results are replicable. The default random seed is 123456. |
object |
objects of class |
what |
argument for S3 method |
... |
additional arguments |
an object of class itemfit consisting of several elements that can be extracted using
method extract. Components that can be extracted include:
the proportion correct statistics, adjusted and unadjusted p values for each item
the transformed correlations, adjusted and unadjusted p values for each item pair
the log odds ratios, adjusted and unadjusted p values for each item pair
the maximum proportion correct, transformed correlation, and log-odds ratio for each item with associated item-level adjusted p-values
extract(itemfit): extract various elements from itemfit objects
summary(itemfit): print summary information
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
Chen, J., de la Torre, J., & Zhang, Z. (2013). Relative and Absolute Fit Evaluation in Cognitive Diagnosis Modeling. Journal of Educational Measurement, 50, 123-140.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") mod1 itmfit <- itemfit(mod1) # Print "test-level" item fit statistics # p-values are adjusted for multiple comparisons # for proportion correct, there are J comparisons # for log odds ratio and transformed correlation, # there are J*(J-1)/2 comparisons itmfit # The following gives maximum item fit statistics for # each item with item level p-value adjustment # For each item, there are J-1 comparisons for each of # log odds ratio and transformed correlation summary(itmfit) # use extract to extract various components extract(itmfit,"r") mod2 <- GDINA(dat,Q,model="DINA") itmfit2 <- itemfit(mod2) #misfit heatmap plot(itmfit2) itmfit2 ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") mod1 itmfit <- itemfit(mod1) # Print "test-level" item fit statistics # p-values are adjusted for multiple comparisons # for proportion correct, there are J comparisons # for log odds ratio and transformed correlation, # there are J*(J-1)/2 comparisons itmfit # The following gives maximum item fit statistics for # each item with item level p-value adjustment # For each item, there are J-1 comparisons for each of # log odds ratio and transformed correlation summary(itmfit) # use extract to extract various components extract(itmfit,"r") mod2 <- GDINA(dat,Q,model="DINA") itmfit2 <- itemfit(mod2) #misfit heatmap plot(itmfit2) itmfit2 ## End(Not run)
This function has been deprecated; use coef instead.
itemparm( object, what = c("catprob", "gs", "delta", "rrum", "itemprob", "LCprob"), withSE = FALSE, SE.type = 2, digits = 4, ... ) ## S3 method for class 'GDINA' itemparm( object, what = c("catprob", "gs", "delta", "rrum", "itemprob", "LCprob"), withSE = FALSE, SE.type = 2, digits = 4, ... )itemparm( object, what = c("catprob", "gs", "delta", "rrum", "itemprob", "LCprob"), withSE = FALSE, SE.type = 2, digits = 4, ... ) ## S3 method for class 'GDINA' itemparm( object, what = c("catprob", "gs", "delta", "rrum", "itemprob", "LCprob"), withSE = FALSE, SE.type = 2, digits = 4, ... )
object |
estimated GDINA object returned from |
what |
what to show. |
withSE |
show standard errors or not? |
SE.type |
Type of standard errors. |
digits |
how many decimal places for the ouput? |
... |
additional arguments |
Philipp, M., Strobl, C., de la Torre, J., & Zeileis, A.(2017). On the estimation of standard errors in cognitive diagnosis models. Journal of Educational and Behavioral Statistics, 43, 88-115.
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") # deprecated itemparm(fit) coef(fit) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") # deprecated itemparm(fit) coef(fit) ## End(Not run)
This function gives the equivalent latent classes which have the same category success probabilities for each category or item.
LC2LG(Q, sequential = FALSE, att.str = NULL)LC2LG(Q, sequential = FALSE, att.str = NULL)
Q |
A required |
sequential |
logical; whether the Q-matrix is a Qc-matrix for sequential models? |
att.str |
attribute structure. See |
An item or category by latent class matrix. In the G-DINA model,
if item j measures attributes, latent classes can
be combined into latent groups. This matrix gives
which latent group each of latent classes belongs to for each item.
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
attributepattern(3) q <- matrix(scan(text = "0 1 0 1 0 1 1 1 0"),ncol = 3) q LC2LG(Q = q)attributepattern(3) q <- matrix(scan(text = "0 1 0 1 0 1 1 1 0"),ncol = 3) q LC2LG(Q = q)
This function estimates the multiple-choice DINA model (de la Torre, 2009).
MCmodel( dat, Qc, model = "MCDINA", key = NULL, conv.crit = 0.001, maxitr = 2000, conv.type = "pr", SE = FALSE )MCmodel( dat, Qc, model = "MCDINA", key = NULL, conv.crit = 0.001, maxitr = 2000, conv.type = "pr", SE = FALSE )
dat |
A required |
Qc |
A required category and attribute association matrix. The first column gives the item number, which must be numeric (i.e., 1,2,...) and match the number of column in the data. The second column indicates the coded category of each item. The number in the second column must match with the number in the data, but if a category is not coded, it should not be included in the Q-matrix. Entry 1 indicates that the attribute is measured by the category, and 0 otherwise. Note that the MC-DINA model assumes that the category with the largest number of 1s is the key and that the coded distractors should allow to assign examinees uniquely. |
model |
|
key |
a numeric vector giving the key of each item. See |
conv.crit |
The convergence criterion for max absolute change in |
maxitr |
The maximum iterations allowed. |
conv.type |
convergence criteria; Can be |
SE |
logical; estimating standard error of item parameters? Default is |
an object of class MCmodel with the following components:
A list of success probabilities for each reduced latent class on each item (IRF)
A list of standard errors of item parameters
A list of estimated attribute profiles including EAP, MLE and MAP estimates.
A list of test fit statistics including deviance, number of parameters, AIC and BIC
expected # of individuals in each latent group choosing each option
posterior probability
Total # of iterations
Wenchao Ma, The University of Alabama, [email protected]
De La Torre, J. (2009). A cognitive diagnosis model for cognitively based multiple-choice options. Applied Psychological Measurement, 33, 163–183.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
GDINA for G-DINA model
## Not run: # check the format of the data # Entry 0 is not allowed head(sim10MCDINA$simdat) #--------------------------------- # check the format of the Q-matrix #--------------------------------- # Take item 1 as an example: # category 2 has a q-vector (1,0,0) # category 1 has a q-vector (0,1,0) # category 4 has a q-vector (1,1,0) # category 3 is not included in the Q-matrix because it is not coded # the order of the coded categories in the Q-matrix doesn't matter sim10MCDINA$simQ # Item coded cat A1 A2 A3 # 1 2 1 0 0 # 1 1 0 1 0 # 1 4 1 1 0 #... est <- MCmodel(sim10MCDINA$simdat,sim10MCDINA$simQ) est est$testfit #-------------------------------------- # Distractors involving more attributes #-------------------------------------- # some distractors may involve attributes that are not invovled by the key option # this is not allowed by the "original" MC-DINA (de la Torre, 2009) but is allowed # in the current implementation # Users need to specify the key for each item to appropriate handle such an issue # Note item 1 below: category 1 is the key (as indicated in the key argument below) # The distractor (category 4) involves an attribute not included by the key option Qc <- matrix(c(1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 1, 3, 1, 0, 0, 1, 4, 1, 0, 1, 2, 1, 1, 0, 0, 2, 3, 1, 1, 0, 2, 2, 1, 1, 1, 3, 4, 1, 1, 1, 3, 2, 1, 1, 0, 3, 3, 0, 1, 1, 4, 1, 0, 1, 1, 4, 2, 0, 0, 1, 5, 1, 1, 0, 0, 6, 3, 0, 1, 0, 7, 2, 0, 0, 1, 8, 4, 1, 0, 0, 9, 1, 0, 1, 0, 10, 4, 0, 0, 1),ncol = 5,byrow = TRUE) est2 <- MCmodel(sim10MCDINA2$simdat,Qc, key = c(1,2,4,1,1,3,2,4,1,4)) est2 est2$prob.parm est2$testfit est2$attribute ## End(Not run)## Not run: # check the format of the data # Entry 0 is not allowed head(sim10MCDINA$simdat) #--------------------------------- # check the format of the Q-matrix #--------------------------------- # Take item 1 as an example: # category 2 has a q-vector (1,0,0) # category 1 has a q-vector (0,1,0) # category 4 has a q-vector (1,1,0) # category 3 is not included in the Q-matrix because it is not coded # the order of the coded categories in the Q-matrix doesn't matter sim10MCDINA$simQ # Item coded cat A1 A2 A3 # 1 2 1 0 0 # 1 1 0 1 0 # 1 4 1 1 0 #... est <- MCmodel(sim10MCDINA$simdat,sim10MCDINA$simQ) est est$testfit #-------------------------------------- # Distractors involving more attributes #-------------------------------------- # some distractors may involve attributes that are not invovled by the key option # this is not allowed by the "original" MC-DINA (de la Torre, 2009) but is allowed # in the current implementation # Users need to specify the key for each item to appropriate handle such an issue # Note item 1 below: category 1 is the key (as indicated in the key argument below) # The distractor (category 4) involves an attribute not included by the key option Qc <- matrix(c(1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 1, 3, 1, 0, 0, 1, 4, 1, 0, 1, 2, 1, 1, 0, 0, 2, 3, 1, 1, 0, 2, 2, 1, 1, 1, 3, 4, 1, 1, 1, 3, 2, 1, 1, 0, 3, 3, 0, 1, 1, 4, 1, 0, 1, 1, 4, 2, 0, 0, 1, 5, 1, 1, 0, 0, 6, 3, 0, 1, 0, 7, 2, 0, 0, 1, 8, 4, 1, 0, 0, 9, 1, 0, 1, 0, 10, 4, 0, 0, 1),ncol = 5,byrow = TRUE) est2 <- MCmodel(sim10MCDINA2$simdat,Qc, key = c(1,2,4,1,1,3,2,4,1,4)) est2 est2$prob.parm est2$testfit est2$attribute ## End(Not run)
This function evaluates whether the saturated G-DINA model can be replaced by reduced CDMs without significant loss in model data fit for each item using the Wald test, likelihood ratio (LR) test or Lagrange multiplier (LM) test. For Wald test, see de la Torre (2011), de la Torre and Lee (2013), Ma, Iaconangelo and de la Torre (2016) and Ma & de la Torre (2018) for details. For LR test and a two-step LR approximation procedure, see Sorrel, de la Torre, Abad, and Olea (2017), Ma (2017) and Ma & de la Torre (2019). For LM test, which is only applicable for DINA, DINO and ACDM, see Sorrel, Abad, Olea, de la Torre, and Barrada (2017). This function also calculates the dissimilarity between the reduced models and the G-DINA model, which can be viewed as a measure of effect size (Ma, Iaconangelo & de la Torre, 2016).
modelcomp( GDINA.obj = NULL, method = "Wald", items = "all", p.adjust.methods = "holm", models = c("DINA", "DINO", "ACDM", "LLM", "RRUM"), decision.args = list(rule = "largestp", alpha.level = 0.05, adjusted = FALSE), DS = FALSE, Wald.args = list(SE.type = 2, varcov = NULL), LR.args = list(LR.approx = FALSE), LM.args = list(reducedMDINA = NULL, reducedMDINO = NULL, reducedMACDM = NULL, SE.type = 2) ) ## S3 method for class 'modelcomp' extract( object, what = c("stats", "pvalues", "adj.pvalues", "df", "DS", "selected.model"), digits = 4, ... ) ## S3 method for class 'modelcomp' summary(object, ...)modelcomp( GDINA.obj = NULL, method = "Wald", items = "all", p.adjust.methods = "holm", models = c("DINA", "DINO", "ACDM", "LLM", "RRUM"), decision.args = list(rule = "largestp", alpha.level = 0.05, adjusted = FALSE), DS = FALSE, Wald.args = list(SE.type = 2, varcov = NULL), LR.args = list(LR.approx = FALSE), LM.args = list(reducedMDINA = NULL, reducedMDINO = NULL, reducedMACDM = NULL, SE.type = 2) ) ## S3 method for class 'modelcomp' extract( object, what = c("stats", "pvalues", "adj.pvalues", "df", "DS", "selected.model"), digits = 4, ... ) ## S3 method for class 'modelcomp' summary(object, ...)
GDINA.obj |
An estimated model object of class |
method |
method for item level model comparison; can be |
items |
a vector of items to specify the items for model comparsion |
p.adjust.methods |
adjusted p-values for multiple hypothesis tests. This is conducted using |
models |
a vector specifying which reduced CDMs are possible reduced CDMs for each item. The default is "DINA","DINO","ACDM","LLM",and "RRUM". |
decision.args |
a list of options for determining the most appropriate models including (1) |
DS |
whether dissimilarity index should be calculated? |
Wald.args |
a list of options for Wald test including (1) |
LR.args |
a list of options for LR test including for now only |
LM.args |
a list of options for LM test including |
object |
object of class |
what |
argument for S3 method |
digits |
How many decimal places in each number? The default is 4. |
... |
additional arguments |
After the test statistics for each reduced CDM were calculated for each item, the
reduced models with p values less than the pre-specified alpha level were rejected.
If all reduced models were rejected for an item, the G-DINA model was used as the best model;
if at least one reduced model was retained, two diferent rules can be implemented for selecting
the best model specified in argument decision.args:
(1) when rule="simpler",
If (a) the DINA or DINO model was one of the retained models, then the DINA or DINO model with the larger p value was selected as the best model; but if (b) both DINA and DINO were rejected, the reduced model with the largest p value was selected as the best model for this item. Note that when the p-values of several reduced models were greater than 0.05, the DINA and DINO models were preferred over the A-CDM, LLM, and R-RUM because of their simplicity.
(2) When rule="largestp" (default),
The reduced model with the largest p-values is selected as the most appropriate model.
an object of class modelcomp. Elements that can be
extracted using extract method include
Wald or LR statistics
p-values associated with the test statistics
adjusted p-values
degrees of freedom
dissimilarity between G-DINA and other CDMs
extract(modelcomp): extract various elements from modelcomp objects
summary(modelcomp): print summary information
Wenchao Ma, The University of Alabama, [email protected]
Miguel A. Sorrel, Universidad Autonoma de Madrid
Jimmy de la Torre, The University of Hong Kong
de la Torre, J., & Lee, Y. S. (2013). Evaluating the wald test for item-level comparison of saturated and reduced models in cognitive diagnosis. Journal of Educational Measurement, 50, 355-373.
Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification. Applied Psychological Measurement, 40, 200-217.
Ma, W. (2017). A Sequential Cognitive Diagnosis Model for Graded Response: Model Development, Q-Matrix Validation,and Model Comparison. Unpublished doctoral dissertation. New Brunswick, NJ: Rutgers University.
Ma, W., & de la Torre, J. (2019). Category-Level Model Selection for the Sequential G-DINA Model. Journal of Educational and Behavioral Statistics. 44, 61-82.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Sorrel, M. A., Abad, F. J., Olea, J., de la Torre, J., & Barrada, J. R. (2017). Inferential Item-Fit Evaluation in Cognitive Diagnosis Modeling. Applied Psychological Measurement, 41, 614-631.
Sorrel, M. A., de la Torre, J., Abad, F. J., & Olea, J. (2017). Two-Step Likelihood Ratio Test for Item-Level Model Comparison in Cognitive Diagnosis Models. Methodology, 13, 39-47.
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # --- GDINA model ---# fit <- GDINA(dat = dat, Q = Q, model = "GDINA") fit ################### # # Wald test # ################### w <- modelcomp(fit) w # wald statistics extract(w,"stats") #p values extract(w,"pvalues") # selected models extract(w,"selected.model") ########################## # # LR and Two-step LR test # ########################## lr <- modelcomp(fit,method = "LR") lr TwostepLR <- modelcomp(fit,items =c(6:10),method = "LR",LR.args = list(LR.approx = TRUE)) TwostepLR ########################## # # LM test # ########################## dina <- GDINA(dat = dat, Q = Q, model = "DINA") dino <- GDINA(dat = dat, Q = Q, model = "DINO") acdm <- GDINA(dat = dat, Q = Q, model = "ACDM") lm <- modelcomp(method = "LM",LM.args=list(reducedMDINA = dina, reducedMDINO = dino, reducedMACDM = acdm)) lm ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ # --- GDINA model ---# fit <- GDINA(dat = dat, Q = Q, model = "GDINA") fit ################### # # Wald test # ################### w <- modelcomp(fit) w # wald statistics extract(w,"stats") #p values extract(w,"pvalues") # selected models extract(w,"selected.model") ########################## # # LR and Two-step LR test # ########################## lr <- modelcomp(fit,method = "LR") lr TwostepLR <- modelcomp(fit,items =c(6:10),method = "LR",LR.args = list(LR.approx = TRUE)) TwostepLR ########################## # # LM test # ########################## dina <- GDINA(dat = dat, Q = Q, model = "DINA") dino <- GDINA(dat = dat, Q = Q, model = "DINO") acdm <- GDINA(dat = dat, Q = Q, model = "ACDM") lm <- modelcomp(method = "LM",LM.args=list(reducedMDINA = dina, reducedMDINO = dino, reducedMACDM = acdm)) lm ## End(Not run)
Calculate various absolute model-data fit statistics
modelfit(GDINA.obj, CI = 0.9, ItemOnly = FALSE)modelfit(GDINA.obj, CI = 0.9, ItemOnly = FALSE)
GDINA.obj |
An estimated model object of class |
CI |
numeric value from 0 to 1 indicating the range of the confidence interval for RMSEA. Default returns the 90% interval. |
ItemOnly |
should joint attribute distribution parameters be considered? Default = FALSE. See Ma (2019). |
Various model-data fit statistics including M2 statistic for G-DINA model with dichotmous responses (Liu, Tian, & Xin, 2016; Hansen, Cai, Monroe, & Li, 2016) and for sequential G-DINA model with graded responses (Ma, 2020). It also calculates SRMSR and RMSEA2.
Wenchao Ma, The University of Alabama, [email protected]
Hansen, M., Cai, L., Monroe, S., & Li, Z. (2016). Limited-information goodness-of-fit testing of diagnostic classification item response models. British Journal of Mathematical and Statistical Psychology. 69, 225–252.
Liu, Y., Tian, W., & Xin, T. (2016). An Application of M2 Statistic to Evaluate the Fit of Cognitive Diagnostic Models. Journal of Educational and Behavioral Statistics, 41, 3-26.
Ma, W. (2020). Evaluating the fit of sequential G-DINA model using limited-information measures. Applied Psychological Measurement, 44, 167-181.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Maydeu-Olivares, A. (2013). Goodness-of-Fit Assessment of Item Response Theory Models. Measurement, 11, 71-101.
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "DINA") modelfit(mod1) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "DINA") modelfit(mod1) ## End(Not run)
If mastering an additional attribute lead to a lower probabilities of success, the monotonicity is violated.
monocheck(object, strict = FALSE)monocheck(object, strict = FALSE)
object |
object of class |
strict |
whether a strict monotonicity is checked? |
a logical vector for each item or category indicating whether
the monotonicity is violated (TRUE) or not (FALSE)
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") check <- monocheck(mod1) check mod2 <- GDINA(dat = dat, Q = Q, model = "GDINA",mono.constraint = check) check2 <- monocheck(mod2) check2 ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") check <- monocheck(mod1) check mod2 <- GDINA(dat = dat, Q = Q, model = "GDINA",mono.constraint = check) check2 <- monocheck(mod2) check2 ## End(Not run)
Calculate the number of parameters for GDINA estimates. Returned the total number of parameters, the number of item parameters and the number parameters of joint attribute distribution.
npar(object, ...)npar(object, ...)
object |
GDINA object |
... |
additional arguments |
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") npar(fit) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") npar(fit) ## End(Not run)
Function to calculate various person attribute parameters, including "EAP",
"MAP", and "MLE", for EAP, MAP and MLE estimates of
attribute patterns (see Huebner & Wang, 2011), "mp" for marginal mastery probabilities, and "HO"
for higher-order ability estimates if a higher-order model is fitted.
See GDINA for examples.
personparm(object, what = c("EAP", "MAP", "MLE", "mp", "HO"), digits = 4, ...)personparm(object, what = c("EAP", "MAP", "MLE", "mp", "HO"), digits = 4, ...)
object |
estimated GDINA object returned from |
what |
what to extract; It can be |
digits |
number of decimal places. |
... |
additional arguments |
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
Huebner, A., & Wang, C. (2011). A note on comparing examinee classification methods for cognitive diagnosis models. Educational and Psychological Measurement, 71, 407-419.
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") # EAP head(personparm(fit)) # MAP head(personparm(fit, what = "MAP")) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") # EAP head(personparm(fit)) # MAP head(personparm(fit, what = "MAP")) ## End(Not run)
Create various plots for GDINA estimates
## S3 method for class 'GDINA' plot( x, what = "IRF", item = "all", withSE = FALSE, SE.type = 2, person = 1, att.names = NULL, ... )## S3 method for class 'GDINA' plot( x, what = "IRF", item = "all", withSE = FALSE, SE.type = 2, person = 1, att.names = NULL, ... )
x |
model object of class |
what |
type of plot. Can be |
item |
A scalar or vector specifying the item(s) for IRF plots. |
withSE |
logical; Add error bar (estimate - SE, estimate + SE) to the IRF plots? |
SE.type |
How is SE estimated. By default, it's based on OPG using incomplete information. |
person |
A scalar or vector specifying the number of individuals for mastery plots. |
att.names |
Optional; a vector for attribute names. |
... |
additional arguments |
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") #plot item response functions for item 10 plot(mod1, item = 10) plot(mod1, what = "IRF", item = 10,withSE = TRUE) # plot mastery probabilities for individuals 4 and 10 plot(mod1, what = "mp", person = c(4,10)) plot(mod1, what = "mp", person = c(4,10,15), att.names = c("addition","subtraction","multiplication")) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") #plot item response functions for item 10 plot(mod1, item = 10) plot(mod1, what = "IRF", item = 10,withSE = TRUE) # plot mastery probabilities for individuals 4 and 10 plot(mod1, what = "mp", person = c(4,10)) plot(mod1, what = "mp", person = c(4,10,15), att.names = c("addition","subtraction","multiplication")) ## End(Not run)
Create plots of bivariate heatmap for item fit
## S3 method for class 'itemfit' plot(x, type = "all", adjusted = TRUE, ...)## S3 method for class 'itemfit' plot(x, type = "all", adjusted = TRUE, ...)
x |
model object of class |
type |
type of heatmap plot |
adjusted |
logical; plot adjusted or unadjusted p-values? |
... |
additional arguments |
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") ift <- itemfit(fit) # plot the adjusted p values for log odds or transformed correlation plot(ift) # plot unadjusted p values for log odds plot(ift,adjusted = FALSE, type = "logOR") ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") ift <- itemfit(fit) # plot the adjusted p values for log odds or transformed correlation plot(ift) # plot unadjusted p values for log odds plot(ift,adjusted = FALSE, type = "logOR") ## End(Not run)
The mesa plot was first proposed by de la Torre and Ma (2016) for graphically illustrating the best q-vector(s) for each item. The q-vector on the edge of the mesa is likely to be the best q-vector.
## S3 method for class 'Qval' plot( x, item, type = "best", no.qvector = 10, data.label = TRUE, eps = "auto", original.q.label = FALSE, auto.ylim = TRUE, ... )## S3 method for class 'Qval' plot( x, item, type = "best", no.qvector = 10, data.label = TRUE, eps = "auto", original.q.label = FALSE, auto.ylim = TRUE, ... )
x |
model object of class |
item |
a vector specifying which item(s) the plots are drawn for |
type |
types of the plot. It can be |
no.qvector |
the number of q vectors that need to be plotted when |
data.label |
logical; To show data label or not? |
eps |
the cutoff for PVAF. If not |
original.q.label |
logical; print the label showing the original q-vector or not? |
auto.ylim |
logical; create y range automatically or not? |
... |
additional arguments passed to |
de la Torre, J., & Ma, W. (2016, August). Cognitive diagnosis modeling: A general framework approach and its implementation in R. A Short Course at the Fourth Conference on Statistical Methods in Psychometrics, Columbia University, New York.
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ Q[1,] <- c(0,1,0) mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") out <- Qval(mod1,eps = 0.9) item <- c(1,2,10) plot(out,item=item,data.label=FALSE,type="all") plot(out,item=10,type="best",eps=0.95) plot(out,item=10,type="all",no.qvector=6) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ Q[1,] <- c(0,1,0) mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") out <- Qval(mod1,eps = 0.9) item <- c(1,2,10) plot(out,item=item,data.label=FALSE,type="all") plot(out,item=10,type="best",eps=0.95) plot(out,item=10,type="all",no.qvector=6) ## End(Not run)
Q-matrix validation for the (sequential) G-DINA model based on PVAF (de la Torre & Chiu, 2016; Najera, Sorrel, & Abad, 2019; Najera et al., 2020), stepwise Wald test (Ma & de la Torre, 2020) or mesa plot (de la Torre & Ma, 2016). All these methods are suitable for dichotomous and ordinal response data. If too many modifications are suggested based on the default PVAF method, you are suggested to try the stepwise Wald test method, iterative procedures or predicted cutoffs. You should always check the mesa plots for further examination.
Qval( GDINA.obj, method = "PVAF", iter = "none", eps = 0.95, digits = 4, wald.args = list(), iter.args = list(empty.att = FALSE, max.iter = 150, verbose = FALSE) ) ## S3 method for class 'Qval' extract(object, what = c("sug.Q", "varsigma", "PVAF", "eps", "Q"), ...) ## S3 method for class 'Qval' summary(object, ...)Qval( GDINA.obj, method = "PVAF", iter = "none", eps = 0.95, digits = 4, wald.args = list(), iter.args = list(empty.att = FALSE, max.iter = 150, verbose = FALSE) ) ## S3 method for class 'Qval' extract(object, what = c("sug.Q", "varsigma", "PVAF", "eps", "Q"), ...) ## S3 method for class 'Qval' summary(object, ...)
GDINA.obj |
an estimated model object of class |
method |
which Q-matrix validation method is used? Can be either |
iter |
implement the method iteratively? Can be |
eps |
cutoff value for PVAF from 0 to 1. Default = 0.95. Note that it can also be -1, indicating the predicted cutoff based on Najera, Sorrel, and Abad (2019). |
digits |
how many decimal places in each number? The default is 4. |
wald.args |
a list of arguments for the stepwise Wald test method.
|
iter.args |
a list of arguments for the iterative implementation.
|
object |
|
what |
argument for S3 method |
... |
additional arguments |
An object of class Qval. Elements that can be
extracted using extract method include:
suggested Q-matrix
original Q-matrix
varsigma index
PVAF
extract(Qval): extract various elements from Qval objects
summary(Qval): print summary information
Wenchao Ma, The University of Alabama, [email protected],
Miguel A. Sorrel, Universidad Autónoma de Madrid,
Jimmy de la Torre, The University of Hong Kong
de la Torre, J. & Chiu, C-Y. (2016). A General Method of Empirical Q-matrix Validation. Psychometrika, 81, 253-273.
de la Torre, J., & Ma, W. (2016, August). Cognitive diagnosis modeling: A general framework approach and its implementation in R. A Short Course at the Fourth Conference on Statistical Methods in Psychometrics, Columbia University, New York.
Ma, W., & de la Torre, J. (2020). An empirical Q-matrix validation method for the sequential G-DINA model. British Journal of Mathematical and Statistical Psychology, 73, 142-163.
Najera, P., Sorrel, M. A., & Abad, F.J. (2019). Reconsidering cutoff points in the general method of empirical Q-matrix validation. Educational and Psychological Measurement, 79, 727-753.
Najera, P., Sorrel, M. A., de la Torre, J., & Abad, F. J. (2020). Improving robustness in Q-matrix validation using an iterative and dynamic procedure. Applied Psychological Measurement.
## Not run: ################################ # # Binary response # ################################ dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ Q[10,] <- c(0,1,0) # Fit the G-DINA model mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") # Q-validation using de la Torre and Chiu's method pvaf <- Qval(mod1,method = "PVAF",eps = 0.95) pvaf extract(pvaf,what = "PVAF") #See also: extract(pvaf,what = "varsigma") extract(pvaf,what = "sug.Q") # Draw mesa plots using the function plot plot(pvaf,item=10) #The stepwise Wald test stepwise <- Qval(mod1,method = "wald") stepwise extract(stepwise,what = "PVAF") #See also: extract(stepwise,what = "varsigma") extract(stepwise,what = "sug.Q") #Set eps = -1 to determine the cutoff empirically pvaf2 <- Qval(mod1,method = "PVAF",eps = -1) pvaf2 #Iterative procedure (test-attribute level) pvaf3 <- Qval(mod1, method = "PVAF", eps = -1, iter = "test.att", iter.args = list(verbose = 1)) pvaf3 ################################ # # Ordinal response # ################################ seq.est <- GDINA(sim20seqGDINA$simdat,sim20seqGDINA$simQ, sequential = TRUE) stepwise <- Qval(seq.est, method = "wald") ## End(Not run)## Not run: ################################ # # Binary response # ################################ dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ Q[10,] <- c(0,1,0) # Fit the G-DINA model mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA") # Q-validation using de la Torre and Chiu's method pvaf <- Qval(mod1,method = "PVAF",eps = 0.95) pvaf extract(pvaf,what = "PVAF") #See also: extract(pvaf,what = "varsigma") extract(pvaf,what = "sug.Q") # Draw mesa plots using the function plot plot(pvaf,item=10) #The stepwise Wald test stepwise <- Qval(mod1,method = "wald") stepwise extract(stepwise,what = "PVAF") #See also: extract(stepwise,what = "varsigma") extract(stepwise,what = "sug.Q") #Set eps = -1 to determine the cutoff empirically pvaf2 <- Qval(mod1,method = "PVAF",eps = -1) pvaf2 #Iterative procedure (test-attribute level) pvaf3 <- Qval(mod1, method = "PVAF", eps = -1, iter = "test.att", iter.args = list(verbose = 1)) pvaf3 ################################ # # Ordinal response # ################################ seq.est <- GDINA(sim20seqGDINA$simdat,sim20seqGDINA$simQ, sequential = TRUE) stepwise <- Qval(seq.est, method = "wald") ## End(Not run)
Count the frequency of a row vector in a data frame
rowMatch(df, vec = NULL)rowMatch(df, vec = NULL)
df |
a data frame or matrix |
vec |
the vector for matching |
count the number of vector vec in the data frame
row.no row numbers of the vector vec in the data frame
df <- data.frame(V1=c(1L,2L),V2=LETTERS[1:3],V3=rep(1,12)) rowMatch(df,c(2,"B",1))df <- data.frame(V1=c(1L,2L),V2=LETTERS[1:3],V3=rep(1,12)) rowMatch(df,c(2,"B",1))
Calculate score function for each dichotomous item or each nonzero category for polytomous items Only applicable to saturated model ofr joint attribute distribution
score(object, parm = "delta")score(object, parm = "delta")
object |
an object of class GDINA |
parm |
Either |
a list where elements give the score functions for each item or category
## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") score(fit) ## End(Not run)## Not run: dat <- sim10GDINA$simdat Q <- sim10GDINA$simQ fit <- GDINA(dat = dat, Q = Q, model = "GDINA") score(fit) ## End(Not run)
Simulated data, Q-matrix and item parameters for a 10-item test with 3 attributes.
sim10GDINAsim10GDINA
A list with components:
simdatsimulated responses of 1000 examinees
simQartificial Q-matrix
simItemparartificial item parameters (probability of success for each latent group)
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Simulated data, Q-matrix and item parameters for a 10-item test measuring 3 attributes.
sim10MCDINAsim10MCDINA
A list with components:
simdatsimulated responses of 3000 examinees
simQartificial Q-matrix
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Simulated data, Q-matrix and item parameters for a 10-item test measuring 5 attributes.
sim10MCDINA2sim10MCDINA2
A list with components:
simdatsimulated responses of 3000 examinees
simQartificial Q-matrix
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Simulated data, Qc-matrix and item parameters for a 20-item test measuring 5 attributes.
sim20seqGDINAsim20seqGDINA
A list with components:
simdatsimulated polytomous responses of 2000 examinees
simQartificial Qc-matrix
simItemparartificial item parameters (category level probability of success for each latent group)
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Simulated data, and Qc-matrix for a 21-item test measuring 5 attributes.
sim21seqDINAsim21seqDINA
A list with components:
simdatsimulated responses of 2000 examinees
simQartificial Qc-matrix
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Simulated data, Q-matrix and item parameters for a 30-item test measuring 5 attributes.
sim30DINAsim30DINA
A list with components:
simdatsimulated responses of 1000 examinees
simQartificial Q-matrix
simItemparartificial item parameters (probability of success for each latent group)
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Simulated data, Q-matrix and item parameters for a 30-item test measuring 5 attributes.
sim30GDINAsim30GDINA
A list with components:
simdatsimulated responses of 1000 examinees
simQartificial Q-matrix
simItemparartificial item parameters(probability of success for each latent group)
Wenchao Ma, The University of Alabama, [email protected]
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Simulated data, Q-matrix and item parameters for a 30-item test measuring 5 attributes.
sim30pGDINAsim30pGDINA
A list with components:
simdatsimulated responses of 3000 examinees
simQartificial Q-matrix
simItemparartificial item parameters(probability of success for each latent group)
Data generation for diagnostic tree model
simDTM(N, Qc, gs.parm, Tmatrix, red.delta = NULL, att.gr = NULL)simDTM(N, Qc, gs.parm, Tmatrix, red.delta = NULL, att.gr = NULL)
N |
sample size |
Qc |
Association matrix between attributes (column) and PSEUDO items (row); The first column is item number and the second column is the pseudo item number for each item. If a pseudo item has more than one nonzero categories, more than one rows are needed. |
gs.parm |
the same as the gs.parm in simGDINA function in the GDINA package. It is a list with the same number of elements as the number of rows in the Qc matrix |
Tmatrix |
mapping matrix showing the relation between the OBSERVED responses (rows) and the PSEDUO items (columns); The first column gives the observed responses. |
red.delta |
reduced delta parameters using logit link function |
att.gr |
attribute group indicator |
## Not run: K=5 g=0.2 item.no <- rep(1:6,each=4) # the first node has three response categories: 0, 1 and 2 node.no <- rep(c(1,1,2,3),6) Q1 <- matrix(0,length(item.no),K) Q2 <- cbind(7:(7+K-1),rep(1,K),diag(K)) for(j in 1:length(item.no)) { Q1[j,sample(1:K,sample(3,1))] <- 1 } Qc <- rbind(cbind(item.no,node.no,Q1),Q2) Tmatrix.set <- list(cbind(c(0,1,2,3,3),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1,2,3,4),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1),c(0,1))) Tmatrix <- Tmatrix.set[c(1,1,1,1,1,1,rep(3,K))] sim <- simDTM(N=2000,Qc=Qc,gs.parm=matrix(0.2,nrow(Qc),2),Tmatrix=Tmatrix) est <- DTM(dat=sim$dat,Qc=Qc,Tmatrix = Tmatrix) ## End(Not run)## Not run: K=5 g=0.2 item.no <- rep(1:6,each=4) # the first node has three response categories: 0, 1 and 2 node.no <- rep(c(1,1,2,3),6) Q1 <- matrix(0,length(item.no),K) Q2 <- cbind(7:(7+K-1),rep(1,K),diag(K)) for(j in 1:length(item.no)) { Q1[j,sample(1:K,sample(3,1))] <- 1 } Qc <- rbind(cbind(item.no,node.no,Q1),Q2) Tmatrix.set <- list(cbind(c(0,1,2,3,3),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1,2,3,4),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)), cbind(c(0,1),c(0,1))) Tmatrix <- Tmatrix.set[c(1,1,1,1,1,1,rep(3,K))] sim <- simDTM(N=2000,Qc=Qc,gs.parm=matrix(0.2,nrow(Qc),2),Tmatrix=Tmatrix) est <- DTM(dat=sim$dat,Qc=Qc,Tmatrix = Tmatrix) ## End(Not run)
Simulate responses based on the G-DINA model (de la Torre, 2011) and sequential G-DINA model
(Ma & de la Torre, 2016), or CDMs subsumed by them, including the DINA model, DINO model, ACDM,
LLM and R-RUM. Attributes can be simulated from uniform, higher-order or multivariate normal
distributions, or be supplied by users. See Examples and Details for
how item parameter specifications. See the help page of GDINA
for model parameterizations.
simGDINA( N, Q, gs.parm = NULL, delta.parm = NULL, catprob.parm = NULL, model = "GDINA", sequential = FALSE, no.bugs = 0, gs.args = list(type = "random", mono.constraint = TRUE), design.matrix = NULL, linkfunc = NULL, att.str = NULL, attribute = NULL, att.dist = "uniform", item.names = NULL, higher.order.parm = list(theta = NULL, lambda = NULL), mvnorm.parm = list(mean = NULL, sigma = NULL, cutoffs = NULL), att.prior = NULL, digits = 4 ) ## S3 method for class 'simGDINA' extract( object, what = c("dat", "Q", "attribute", "catprob.parm", "delta.parm", "higher.order.parm", "mvnorm.parm", "LCprob.parm"), ... )simGDINA( N, Q, gs.parm = NULL, delta.parm = NULL, catprob.parm = NULL, model = "GDINA", sequential = FALSE, no.bugs = 0, gs.args = list(type = "random", mono.constraint = TRUE), design.matrix = NULL, linkfunc = NULL, att.str = NULL, attribute = NULL, att.dist = "uniform", item.names = NULL, higher.order.parm = list(theta = NULL, lambda = NULL), mvnorm.parm = list(mean = NULL, sigma = NULL, cutoffs = NULL), att.prior = NULL, digits = 4 ) ## S3 method for class 'simGDINA' extract( object, what = c("dat", "Q", "attribute", "catprob.parm", "delta.parm", "higher.order.parm", "mvnorm.parm", "LCprob.parm"), ... )
N |
Sample size. |
Q |
A required matrix; The number of rows occupied by a single-strategy dichotomous item is 1, by a polytomous item is
the number of nonzero categories, and by a mutiple-strategy dichotomous item is the number of strategies.
The number of column is equal to the number of attributes if all items are single-strategy dichotomous items, but
the number of attributes + 2 if any items are polytomous or have multiple strategies.
For a polytomous item, the first column represents the item number and the second column indicates the nonzero category number.
For a multiple-strategy dichotomous item, the first column represents the item number and the second column indicates the strategy number.
For binary attributes, 1 denotes the attributes are measured by the items and 0 means the attributes are not
measured. For polytomous attributes, non-zero elements indicate which level
of attributes are needed. See |
gs.parm |
A matrix or data frame for guessing and slip parameters. The number of rows occupied by a dichotomous item is 1, and by a polytomous item is
the number of nonzero categories. The number of columns must be 2, where the first column represents the guessing parameters (or |
delta.parm |
A list of delta parameters of each latent group for each item or category. This may need to be used in conjunction with
the argument |
catprob.parm |
A list of success probabilities of each latent group for each non-zero category of each item. See |
model |
A character vector for each item or nonzero category, or a scalar which will be used for all
items or nonzero categories to specify the CDMs. The possible options
include |
sequential |
logical; |
no.bugs |
the number of bugs (or misconceptions) for the |
gs.args |
a list of options when
|
design.matrix |
a list of design matrices; Its length must be equal to the number of items (or nonzero categories for sequential models). |
linkfunc |
a vector of link functions for each item/category; It can be |
att.str |
attribute structure. |
attribute |
optional user-specified person attributes. It is a |
att.dist |
A string indicating the distribution for attribute simulation. It can be |
item.names |
A vector giving the name of items or categories. If it is |
higher.order.parm |
A list specifying parameters for higher-order distribution for attributes
if |
mvnorm.parm |
a list of parameters for multivariate normal attribute distribution. |
att.prior |
probability for each attribute pattern. Order is the same as that returned from |
digits |
How many decimal places in each number? The default is 4. |
object |
object of class |
what |
argument for S3 method |
... |
additional arguments |
Item parameter specifications in simGDINA:
Item parameters can be specified in one of three different ways.
The first and probably the easiest way is to specify the guessing and slip parameters for each item or nonzero category using
gs.parm, which is a matrix or data frame for and
for all items for dichotomous items and and
for all nonzero categories for polytomous items. Note that or
must be greater than 0.
For generating ACDM, LLM, and RRUM, delta parameters are generated randomly if type="random",
or in a way that each required attribute contributes equally, as in
Ma, Iaconangelo, & de la Torre (2016) if type="equal". For ACDM, LLM and RRUM, generated
delta parameters are always positive, which implies that monotonicity constraints are always satisfied.
If the generating model is the G-DINA model, mono.constraint can be used to specify whether monotonicity
constraints should be satisfied.
The second way of simulating responses is to specify success probabilities (i.e.,
or ) for each nonzero category of each item directly
using the argument catprob.parm. If an item or category requires attributes, success probabilities
need to be provided. catprob.parm must be a list, where each element gives the success probabilities for nonzero category of each item.
Note that success probabilities cannot be negative or greater than one.
The third way is to specify delta parameters for data simulation. For DINA and DINO model, each nonzero category requires two
delta parameters. For ACDM, LLM and RRUM, if a nonzero category requires attributes, delta parameters
need to be specified. For the G-DINA model, a nonzero category requiring attributes has delta parameters.
It should be noted that specifying delta parameters needs to ascertain the derived success probabilities are within the interval.
Please note that you need to specify item parameters in ONLY one of these three ways. If gs.parm is specified, it will be used regardless of
the inputs in catprob.parm and delta.parm. If gs.parm is not specified, simGDINA will check
if delta.parm is specified; if yes, it will be used for data generation. if both gs.parm and delta.parm are not specified,
catprob.parm is used for data generation.
an object of class simGDINA. Elements that can be extracted using method extract
include:
simulated item response matrix
Q-matrix
A matrix for inviduals' attribute patterns
a list of non-zero category success probabilities for each latent group
a list of delta parameters
Higher-order parameters
multivariate normal distribution parameters
A matrix of item/category success probabilities for each latent class
Wenchao Ma, The University of Alabama, [email protected]
Jimmy de la Torre, The University of Hong Kong
Chiu, C.-Y., Douglas, J. A., & Li, X. (2009). Cluster analysis for cognitive diagnosis: Theory and applications. Psychometrika, 74, 633-665.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.
de la Torre, J., & Douglas, J. A. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333-353.
Haertel, E. H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 301-321.
Hartz, S. M. (2002). A bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality (Unpublished doctoral dissertation). University of Illinois at Urbana-Champaign.
Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258-272.
Ma, W., & de la Torre, J. (2016). A sequential cognitive diagnosis model for polytomous responses. British Journal of Mathematical and Statistical Psychology. 69, 253-275.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification. Applied Psychological Measurement, 40, 200-217.
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 187-212.
Templin, J. L., & Henson, R. A. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11, 287-305.
## Not run: #################################################### # Example 1 # # Data simulation (DINA) # #################################################### N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated DINA model; to simulate G-DINA model # and other CDMs, change model argument accordingly sim <- simGDINA(N,Q,gs.parm = gs,model = "DINA") # True item success probabilities extract(sim,what = "catprob.parm") # True delta parameters extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 2 # # Data simulation (RRUM) # #################################################### N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.2,J),slip=rep(0.2,J)) # Simulated RRUM # deltas except delta0 for each item will be simulated # randomly subject to the constraints of RRUM sim <- simGDINA(N,Q,gs.parm = gs,model = "RRUM") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 3 # # Data simulation (LLM) # #################################################### N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated LLM # By specifying type="equal", each required attribute is # assumed to contribute to logit(P) equally sim <- simGDINA(N,Q,gs.parm = gs,model = "LLM",gs.args = list (type="equal")) #check below for what the equal contribution means extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 4 # # Data simulation (all CDMs) # #################################################### set.seed(12345) N <- 500 Q <- sim10GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated different CDMs for different items models <- c("GDINA","DINO","DINA","ACDM","LLM","RRUM","GDINA","LLM","RRUM","DINA") sim <- simGDINA(N,Q,gs.parm = gs,model = models,gs.args = list(type="random")) # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 5a # # Data simulation (all CDMs) # # using probability of success in list format # #################################################### # success probabilities for each item need to be provided in list format as follows: # if item j requires Kj attributes, 2^Kj success probabilities # need to be specified # e.g., item 1 only requires 1 attribute # therefore P(0) and P(1) should be specified; # similarly, item 10 requires 3 attributes, # P(000),P(100),P(010)...,P(111) should be specified; # the latent class represented by each element can be obtained # by calling attributepattern(Kj) itemparm.list <- list(item1=c(0.2,0.9), item2=c(0.1,0.8), item3=c(0.1,0.9), item4=c(0.1,0.3,0.5,0.9), item5=c(0.1,0.1,0.1,0.8), item6=c(0.2,0.9,0.9,0.9), item7=c(0.1,0.45,0.45,0.8), item8=c(0.1,0.28,0.28,0.8), item9=c(0.1,0.4,0.4,0.8), item10=c(0.1,0.2,0.3,0.4,0.4,0.5,0.7,0.9)) set.seed(12345) N <- 500 Q <- sim10GDINA$simQ # When simulating data using catprob.parm argument, # it is not necessary to specify model and type sim <- simGDINA(N,Q,catprob.parm = itemparm.list) #################################################### # Example 5b # # Data simulation (all CDMs) # # using probability of success in list format # # attribute has a linear structure # #################################################### est <- GDINA(sim10GDINA$simdat,sim10GDINA$simQ,att.str = list(c(1,2),c(2,3))) # design matrix # link function # item probabilities ip <- extract(est,"itemprob.parm") sim <- simGDINA(N=500,sim10GDINA$simQ,catprob.parm = ip, design.matrix = dm,linkfunc = lf,att.str = list(c(1,2),c(2,3))) #################################################### # Example 6a # # Data simulation (all CDMs) # # using delta parameters in list format # #################################################### delta.list <- list(c(0.2,0.7), c(0.1,0.7), c(0.1,0.8), c(0.1,0.7), c(0.1,0.8), c(0.2,0.3,0.2,0.1), c(0.1,0.35,0.35), c(-1.386294,0.9808293,1.791759), c(-1.609438,0.6931472,0.6), c(0.1,0.1,0.2,0.3,0.0,0.0,0.1,0.1)) model <- c("GDINA","GDINA","GDINA","DINA","DINO","GDINA","ACDM","LLM","RRUM","GDINA") N <- 500 Q <- sim10GDINA$simQ sim <- simGDINA(N,Q,delta.parm = delta.list, model = model) #################################################### # Example 6b # # Data simulation (all CDMs) # # using delta parameters in list format # # attribute has a linear structure # #################################################### est <- GDINA(sim10GDINA$simdat,sim10GDINA$simQ,att.str = list(c(1,2),c(2,3))) # design matrix # link function # item probabilities ip <- extract(est,"delta.parm") sim <- simGDINA(N=500,sim10GDINA$simQ,delta.parm = d, design.matrix = dm,linkfunc = lf,att.str = list(c(1,2),c(2,3))) #################################################### # Example 7 # # Data simulation (higher order DINA model) # #################################################### Q <- sim30GDINA$simQ gs <- matrix(0.1,nrow(Q),2) N <- 500 set.seed(12345) theta <- rnorm(N) K <- ncol(Q) lambda <- data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)) sim <- simGDINA(N,Q,gs.parm = gs, model="DINA", att.dist = "higher.order", higher.order.parm = list(theta = theta,lambda = lambda)) #################################################### # Example 8 # # Data simulation (higher-order CDMs) # #################################################### Q <- sim30GDINA$simQ gs <- matrix(0.1,nrow(Q),2) models <- c(rep("GDINA",5), rep("DINO",5), rep("DINA",5), rep("ACDM",5), rep("LLM",5), rep("RRUM",5)) N <- 500 set.seed(12345) theta <- rnorm(N) K <- ncol(Q) lambda <- data.frame(a=runif(K,0.7,1.3),b=seq(-2,2,length.out=K)) sim <- simGDINA(N,Q,gs.parm = gs, model=models, att.dist = "higher.order", higher.order.parm = list(theta = theta,lambda = lambda)) #################################################### # Example 9 # # Data simulation (higher-order model) # # using the multivariate normal threshold model # #################################################### # See Chiu et al., (2009) N <- 500 Q <- sim10GDINA$simQ K <- ncol(Q) gs <- matrix(0.1,nrow(Q),2) cutoffs <- qnorm(c(1:K)/(K+1)) m <- rep(0,K) vcov <- matrix(0.5,K,K) diag(vcov) <- 1 simMV <- simGDINA(N,Q,gs.parm = gs, att.dist = "mvnorm", mvnorm.parm=list(mean = m, sigma = vcov,cutoffs = cutoffs)) #################################### # Example 10 # # Simulation using # # user-specified att structure# #################################### # --- User-specified attribute structure ----# Q <- sim30GDINA$simQ K <- ncol(Q) # divergent structure A1->A2->A3;A1->A4->A5;A1->A4->A6 diverg <- list(c(1,2), c(2,3), c(1,4), c(4,5)) struc <- att.structure(diverg,K) # data simulation N <- 1000 # data simulation gs <- matrix(0.1,nrow(Q),2) simD <- simGDINA(N,Q,gs.parm = gs, model = "DINA",att.dist = "categorical",att.prior = struc$att.prob) #################################################### # Example 11 # # Data simulation # # (GDINA with monotonicity constraints) # #################################################### set.seed(12345) N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated different CDMs for different items sim <- simGDINA(N,Q,gs.parm = gs,model = "GDINA",gs.args=list(mono.constraint=TRUE)) # True item success probabilities extract(sim,what = "catprob.parm") # True delta parameters extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 12 # # Data simulation # # (Sequential G-DINA model - polytomous responses) # #################################################### set.seed(12345) N <- 2000 # restricted Qc matrix Qc <- sim20seqGDINA$simQ #total number of categories J <- nrow(Qc) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # simulate sequential DINA model simseq <- simGDINA(N, Qc, sequential = TRUE, gs.parm = gs, model = "GDINA") # True item success probabilities extract(simseq,what = "catprob.parm") # True delta parameters extract(simseq,what = "delta.parm") # simulated data extract(simseq,what = "dat") # simulated attributes extract(simseq,what = "attribute") #################################################### # Example 13 # DINA model Attribute generated using # categorical distribution #################################################### Q <- sim10GDINA$simQ gs <- matrix(0.1,nrow(Q),2) N <- 5000 set.seed(12345) prior <- c(0.1,0.2,0,0,0.2,0,0,0.5) sim <- simGDINA(N,Q,gs.parm = gs, model="DINA", att.dist = "categorical",att.prior = prior) # check latent class sizes table(sim$att.group)/N #################################################### # Example 14 # MS-DINA model #################################################### Q <- matrix(c(1,1,1,1,0, 1,2,0,1,1, 2,1,1,0,0, 3,1,0,1,0, 4,1,0,0,1, 5,1,1,0,0, 5,2,0,0,1),ncol = 5,byrow = TRUE) d <- list( item1=c(0.2,0.7), item2=c(0.1,0.6), item3=c(0.2,0.6), item4=c(0.2,0.7), item5=c(0.1,0.8)) set.seed(12345) sim <- simGDINA(N=1000,Q = Q, delta.parm = d, model = c("MSDINA","MSDINA","DINA","DINA","DINA","MSDINA","MSDINA")) # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") ############################################################## # Example 15 # reparameterized SISM model (Kuo, Chen, & de la Torre, 2018) # see GDINA function for more details ############################################################### # The Q-matrix used in Kuo, et al (2018) # The first four columns are for Attributes 1-4 # The last three columns are for Bugs 1-3 Q <- matrix(c(1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,0,0,0,0, 0,0,0,1,0,0,0, 0,0,0,0,1,0,0, 0,0,0,0,0,1,0, 0,0,0,0,0,0,1, 1,0,0,0,1,0,0, 0,1,0,0,1,0,0, 0,0,1,0,0,0,1, 0,0,0,1,0,1,0, 1,1,0,0,1,0,0, 1,0,1,0,0,0,1, 1,0,0,1,0,0,1, 0,1,1,0,0,0,1, 0,1,0,1,0,1,1, 0,0,1,1,0,1,1, 1,0,1,0,1,1,0, 1,1,0,1,1,1,0, 0,1,1,1,1,1,0),ncol = 7,byrow = TRUE) J <- nrow(Q) N <- 500 gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) sim <- simGDINA(N,Q,gs.parm = gs,model = "SISM",no.bugs=3) # True item success probabilities extract(sim,what = "catprob.parm") # True delta parameters extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") ## End(Not run)## Not run: #################################################### # Example 1 # # Data simulation (DINA) # #################################################### N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated DINA model; to simulate G-DINA model # and other CDMs, change model argument accordingly sim <- simGDINA(N,Q,gs.parm = gs,model = "DINA") # True item success probabilities extract(sim,what = "catprob.parm") # True delta parameters extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 2 # # Data simulation (RRUM) # #################################################### N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.2,J),slip=rep(0.2,J)) # Simulated RRUM # deltas except delta0 for each item will be simulated # randomly subject to the constraints of RRUM sim <- simGDINA(N,Q,gs.parm = gs,model = "RRUM") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 3 # # Data simulation (LLM) # #################################################### N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated LLM # By specifying type="equal", each required attribute is # assumed to contribute to logit(P) equally sim <- simGDINA(N,Q,gs.parm = gs,model = "LLM",gs.args = list (type="equal")) #check below for what the equal contribution means extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 4 # # Data simulation (all CDMs) # #################################################### set.seed(12345) N <- 500 Q <- sim10GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated different CDMs for different items models <- c("GDINA","DINO","DINA","ACDM","LLM","RRUM","GDINA","LLM","RRUM","DINA") sim <- simGDINA(N,Q,gs.parm = gs,model = models,gs.args = list(type="random")) # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 5a # # Data simulation (all CDMs) # # using probability of success in list format # #################################################### # success probabilities for each item need to be provided in list format as follows: # if item j requires Kj attributes, 2^Kj success probabilities # need to be specified # e.g., item 1 only requires 1 attribute # therefore P(0) and P(1) should be specified; # similarly, item 10 requires 3 attributes, # P(000),P(100),P(010)...,P(111) should be specified; # the latent class represented by each element can be obtained # by calling attributepattern(Kj) itemparm.list <- list(item1=c(0.2,0.9), item2=c(0.1,0.8), item3=c(0.1,0.9), item4=c(0.1,0.3,0.5,0.9), item5=c(0.1,0.1,0.1,0.8), item6=c(0.2,0.9,0.9,0.9), item7=c(0.1,0.45,0.45,0.8), item8=c(0.1,0.28,0.28,0.8), item9=c(0.1,0.4,0.4,0.8), item10=c(0.1,0.2,0.3,0.4,0.4,0.5,0.7,0.9)) set.seed(12345) N <- 500 Q <- sim10GDINA$simQ # When simulating data using catprob.parm argument, # it is not necessary to specify model and type sim <- simGDINA(N,Q,catprob.parm = itemparm.list) #################################################### # Example 5b # # Data simulation (all CDMs) # # using probability of success in list format # # attribute has a linear structure # #################################################### est <- GDINA(sim10GDINA$simdat,sim10GDINA$simQ,att.str = list(c(1,2),c(2,3))) # design matrix # link function # item probabilities ip <- extract(est,"itemprob.parm") sim <- simGDINA(N=500,sim10GDINA$simQ,catprob.parm = ip, design.matrix = dm,linkfunc = lf,att.str = list(c(1,2),c(2,3))) #################################################### # Example 6a # # Data simulation (all CDMs) # # using delta parameters in list format # #################################################### delta.list <- list(c(0.2,0.7), c(0.1,0.7), c(0.1,0.8), c(0.1,0.7), c(0.1,0.8), c(0.2,0.3,0.2,0.1), c(0.1,0.35,0.35), c(-1.386294,0.9808293,1.791759), c(-1.609438,0.6931472,0.6), c(0.1,0.1,0.2,0.3,0.0,0.0,0.1,0.1)) model <- c("GDINA","GDINA","GDINA","DINA","DINO","GDINA","ACDM","LLM","RRUM","GDINA") N <- 500 Q <- sim10GDINA$simQ sim <- simGDINA(N,Q,delta.parm = delta.list, model = model) #################################################### # Example 6b # # Data simulation (all CDMs) # # using delta parameters in list format # # attribute has a linear structure # #################################################### est <- GDINA(sim10GDINA$simdat,sim10GDINA$simQ,att.str = list(c(1,2),c(2,3))) # design matrix # link function # item probabilities ip <- extract(est,"delta.parm") sim <- simGDINA(N=500,sim10GDINA$simQ,delta.parm = d, design.matrix = dm,linkfunc = lf,att.str = list(c(1,2),c(2,3))) #################################################### # Example 7 # # Data simulation (higher order DINA model) # #################################################### Q <- sim30GDINA$simQ gs <- matrix(0.1,nrow(Q),2) N <- 500 set.seed(12345) theta <- rnorm(N) K <- ncol(Q) lambda <- data.frame(a=rep(1,K),b=seq(-2,2,length.out=K)) sim <- simGDINA(N,Q,gs.parm = gs, model="DINA", att.dist = "higher.order", higher.order.parm = list(theta = theta,lambda = lambda)) #################################################### # Example 8 # # Data simulation (higher-order CDMs) # #################################################### Q <- sim30GDINA$simQ gs <- matrix(0.1,nrow(Q),2) models <- c(rep("GDINA",5), rep("DINO",5), rep("DINA",5), rep("ACDM",5), rep("LLM",5), rep("RRUM",5)) N <- 500 set.seed(12345) theta <- rnorm(N) K <- ncol(Q) lambda <- data.frame(a=runif(K,0.7,1.3),b=seq(-2,2,length.out=K)) sim <- simGDINA(N,Q,gs.parm = gs, model=models, att.dist = "higher.order", higher.order.parm = list(theta = theta,lambda = lambda)) #################################################### # Example 9 # # Data simulation (higher-order model) # # using the multivariate normal threshold model # #################################################### # See Chiu et al., (2009) N <- 500 Q <- sim10GDINA$simQ K <- ncol(Q) gs <- matrix(0.1,nrow(Q),2) cutoffs <- qnorm(c(1:K)/(K+1)) m <- rep(0,K) vcov <- matrix(0.5,K,K) diag(vcov) <- 1 simMV <- simGDINA(N,Q,gs.parm = gs, att.dist = "mvnorm", mvnorm.parm=list(mean = m, sigma = vcov,cutoffs = cutoffs)) #################################### # Example 10 # # Simulation using # # user-specified att structure# #################################### # --- User-specified attribute structure ----# Q <- sim30GDINA$simQ K <- ncol(Q) # divergent structure A1->A2->A3;A1->A4->A5;A1->A4->A6 diverg <- list(c(1,2), c(2,3), c(1,4), c(4,5)) struc <- att.structure(diverg,K) # data simulation N <- 1000 # data simulation gs <- matrix(0.1,nrow(Q),2) simD <- simGDINA(N,Q,gs.parm = gs, model = "DINA",att.dist = "categorical",att.prior = struc$att.prob) #################################################### # Example 11 # # Data simulation # # (GDINA with monotonicity constraints) # #################################################### set.seed(12345) N <- 500 Q <- sim30GDINA$simQ J <- nrow(Q) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # Simulated different CDMs for different items sim <- simGDINA(N,Q,gs.parm = gs,model = "GDINA",gs.args=list(mono.constraint=TRUE)) # True item success probabilities extract(sim,what = "catprob.parm") # True delta parameters extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") #################################################### # Example 12 # # Data simulation # # (Sequential G-DINA model - polytomous responses) # #################################################### set.seed(12345) N <- 2000 # restricted Qc matrix Qc <- sim20seqGDINA$simQ #total number of categories J <- nrow(Qc) gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) # simulate sequential DINA model simseq <- simGDINA(N, Qc, sequential = TRUE, gs.parm = gs, model = "GDINA") # True item success probabilities extract(simseq,what = "catprob.parm") # True delta parameters extract(simseq,what = "delta.parm") # simulated data extract(simseq,what = "dat") # simulated attributes extract(simseq,what = "attribute") #################################################### # Example 13 # DINA model Attribute generated using # categorical distribution #################################################### Q <- sim10GDINA$simQ gs <- matrix(0.1,nrow(Q),2) N <- 5000 set.seed(12345) prior <- c(0.1,0.2,0,0,0.2,0,0,0.5) sim <- simGDINA(N,Q,gs.parm = gs, model="DINA", att.dist = "categorical",att.prior = prior) # check latent class sizes table(sim$att.group)/N #################################################### # Example 14 # MS-DINA model #################################################### Q <- matrix(c(1,1,1,1,0, 1,2,0,1,1, 2,1,1,0,0, 3,1,0,1,0, 4,1,0,0,1, 5,1,1,0,0, 5,2,0,0,1),ncol = 5,byrow = TRUE) d <- list( item1=c(0.2,0.7), item2=c(0.1,0.6), item3=c(0.2,0.6), item4=c(0.2,0.7), item5=c(0.1,0.8)) set.seed(12345) sim <- simGDINA(N=1000,Q = Q, delta.parm = d, model = c("MSDINA","MSDINA","DINA","DINA","DINA","MSDINA","MSDINA")) # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") ############################################################## # Example 15 # reparameterized SISM model (Kuo, Chen, & de la Torre, 2018) # see GDINA function for more details ############################################################### # The Q-matrix used in Kuo, et al (2018) # The first four columns are for Attributes 1-4 # The last three columns are for Bugs 1-3 Q <- matrix(c(1,0,0,0,0,0,0, 0,1,0,0,0,0,0, 0,0,1,0,0,0,0, 0,0,0,1,0,0,0, 0,0,0,0,1,0,0, 0,0,0,0,0,1,0, 0,0,0,0,0,0,1, 1,0,0,0,1,0,0, 0,1,0,0,1,0,0, 0,0,1,0,0,0,1, 0,0,0,1,0,1,0, 1,1,0,0,1,0,0, 1,0,1,0,0,0,1, 1,0,0,1,0,0,1, 0,1,1,0,0,0,1, 0,1,0,1,0,1,1, 0,0,1,1,0,1,1, 1,0,1,0,1,1,0, 1,1,0,1,1,1,0, 0,1,1,1,1,1,0),ncol = 7,byrow = TRUE) J <- nrow(Q) N <- 500 gs <- data.frame(guess=rep(0.1,J),slip=rep(0.1,J)) sim <- simGDINA(N,Q,gs.parm = gs,model = "SISM",no.bugs=3) # True item success probabilities extract(sim,what = "catprob.parm") # True delta parameters extract(sim,what = "delta.parm") # simulated data extract(sim,what = "dat") # simulated attributes extract(sim,what = "attribute") ## End(Not run)
An interactive Shiny application for running GDINA function. See Ma and de la Torre (2019) and de la Torre and Akbay (2019) for tutorials.
startGDINA()startGDINA()
Wenchao Ma, The University of Alabama, [email protected]
de la Torre, J & Akbay, L. (2019). Implementation of Cognitive Diagnosis Modeling using the GDINA R Package. Eurasian Journal of Educational Research, 80, 171-192.
Ma, W., & de la Torre, J. (2019). Digital Module 05: Diagnostic measurement-The G-DINA framework. Educational Measurement: Issues and Practice, 39, 114-115.
Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.
## Not run: library(shiny) library(shinydashboard) startGDINA() ## End(Not run)## Not run: library(shiny) library(shinydashboard) startGDINA() ## End(Not run)
Unique values in a vector
unique_only(vec)unique_only(vec)
vec |
a vector |
sorted unique values
vec <- c(4,2,3,5,4,4,4) unique_only(vec) # see the difference from unique unique(vec) vec <- letters[1:5] unique_only(vec)vec <- c(4,2,3,5,4,4,4) unique_only(vec) # see the difference from unique unique(vec) vec <- letters[1:5] unique_only(vec)
Generate unrestricted Qc matrix from an restricted Qc matrix
unrestrQ(Qc)unrestrQ(Qc)
Qc |
an restricted Qc matrix |
an unrestricted Qc matrix
Qc <- sim21seqDINA$simQc Qc unrestrQ(Qc)Qc <- sim21seqDINA$simQc Qc unrestrQ(Qc)