| Title: | Extended Rasch Modeling |
|---|---|
| Description: | Fits Rasch models (RM), linear logistic test models (LLTM), rating scale model (RSM), linear rating scale models (LRSM), partial credit models (PCM), and linear partial credit models (LPCM). Missing values are allowed in the data matrix. Additional features are the ML estimation of the person parameters, Andersen's LR-test, item-specific Wald test, Martin-Loef-Test, nonparametric Monte-Carlo Tests, itemfit and personfit statistics including infit and outfit measures, ICC and other plots, automated stepwise item elimination, simulation module for various binary data matrices. |
| Authors: | Patrick Mair [cre, aut], Thomas Rusch [aut], Reinhold Hatzinger [aut], Marco J. Maier [aut], Rudolf Debelak [ctb] |
| Maintainer: | Patrick Mair <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0-6 |
| Built: | 2024-11-27 06:36:53 UTC |
| Source: | CRAN |
Performs likelihood ratio tests against the model with the largest number of parameters.
## S3 method for class 'eRm' anova(object, ...) ## S3 method for class 'eRm_anova' print(x, ...)## S3 method for class 'eRm' anova(object, ...) ## S3 method for class 'eRm_anova' print(x, ...)
object |
Gives the first object to be tested against others which follow, separated by commata. |
x |
An object of class |
... |
Further models to test with |
The anova method is quite flexible and, as long the used data are identical, every model except the LLRA can be tested against each other.
Regardless of the order that models are specified, they will always be sorted by the number of parameters in decreasing order.
If models are passed to the method, all models will be tested against the first model (i.e., the one with the largest amount of parameters).
anova.eRm returns a list object of class eRm_anova containing:
calls |
function calls of the different models (character). |
statistics |
the analysis of deviances table (columns are |
Although, there is a check for identical data matrices used, the models have to be nested for the likelihood ratio test to work. You have to ensure that this is the case, otherwise results will be invalid.
LLRAs cannot be tested with other models (RM, LLTM, RSM, ...); for more information see anova.llra.
Marco J. Maier
### dichotomous data dmod1 <- RM(lltmdat1) dmod2 <- LLTM(lltmdat1, mpoints = 2) anova(dmod1, dmod2) ### polytomous data pmod1 <- RSM(rsmdat) pmod2 <- PCM(rsmdat) anova(pmod1, pmod2) W <- cbind(rep(c(1,0), each=9), rep(c(0,1), each=9)) W pmod3 <- LPCM(rsmdat, W) anova(pmod3, pmod1, pmod2) # note that models are sorted by npar### dichotomous data dmod1 <- RM(lltmdat1) dmod2 <- LLTM(lltmdat1, mpoints = 2) anova(dmod1, dmod2) ### polytomous data pmod1 <- RSM(rsmdat) pmod2 <- PCM(rsmdat) anova(pmod1, pmod2) W <- cbind(rep(c(1,0), each=9), rep(c(0,1), each=9)) W pmod3 <- LPCM(rsmdat, W) anova(pmod3, pmod1, pmod2) # note that models are sorted by npar
Compute an analysis of deviance table for one or more LLRA.
## S3 method for class 'llra' anova(object, ...)## S3 method for class 'llra' anova(object, ...)
object, ...
|
Objects of class "llra", typically the result of a
call to |
An analysis of deviance table will be calculated. The models in rows are ordered from the smallest to the largest model. Each row shows the number of parameters (Npar) and the log-likelihood (logLik). For all but the first model, the parameter difference (df) and the difference in deviance or the likelihood ratio (-2LR) is given between two subsequent models (with increasing complexity). Please note that interpreting these values only makes sense if the models are nested.
The table also contains p-values comparing the reduction in the deviance to the df for each row based on the asymptotic Chi^2-Distribution of the Likelihood ratio test statistic.
An object of class "anova" inheriting from class "data.frame".
The comparison between two or more models by anova will only be valid
if they are fitted to the same dataset and if the models are nested. The
function does not check if that is the case.
Thomas Rusch
The model fitting function LLRA.
## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. #fit LLRA ex2 <- LLRA(llraDat2[,1:20],mpoints=4,groups=llraDat2[,21]) #Imposing a linear trend for items 2 and 3 using collapse_W collItems2 <- list(c(32,37,42),c(33,38,43)) newNames2 <- c("trend.I2","trend.I3") Wnew <- collapse_W(ex2$W,collItems2,newNames2) #Estimating LLRA with the linear trend for item 2 and 3 ex2new <- LLRA(llraDat2[1:20],W=Wnew,mpoints=4,groups=llraDat2[21]) #comparing models with likelihood ratio test anova(ex2,ex2new) ## End(Not run)## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. #fit LLRA ex2 <- LLRA(llraDat2[,1:20],mpoints=4,groups=llraDat2[,21]) #Imposing a linear trend for items 2 and 3 using collapse_W collItems2 <- list(c(32,37,42),c(33,38,43)) newNames2 <- c("trend.I2","trend.I3") Wnew <- collapse_W(ex2$W,collItems2,newNames2) #Estimating LLRA with the linear trend for item 2 and 3 ex2new <- LLRA(llraDat2[1:20],W=Wnew,mpoints=4,groups=llraDat2[21]) #comparing models with likelihood ratio test anova(ex2,ex2new) ## End(Not run)
Builds a design matrix for LLRA from scratch.
build_W(X, nitems, mpoints, grp_n, groupvec, itmgrps)build_W(X, nitems, mpoints, grp_n, groupvec, itmgrps)
X |
Data matrix as described in Hatzinger and Rusch (2009). It
must be of long format, e.g. for each person all item answers are written in subsequent rows. The columns correspond to time
points. Missing values are not allowed. It can easily be
constructed from data in wide format with
|
nitems |
The number of items. |
mpoints |
The number of time points. |
grp_n |
A vector of number of subjects per g+1 groups (e.g. g treatment or covariate groups and 1 control or baseline group. The sizes must be ordered like the corresponding groups. |
groupvec |
Assignment vector, i.e. which person belongs to which treatment/item group |
itmgrps |
Specifies how many groups of items there are. |
The function is designed to be modular and calls four internal function
build_effdes (for treatment/covariate effects), build_trdes (for trend
effects), build_catdes (for category parameter design matrix) and
get_item_cats (checks how many categories each item has). Those functions are not intended to be used by the user.
Labeling of effects also happens in the internal functions.
An LLRA design matrix as described by Hatzinger and Rusch
(2009). This can be passed as the W argument to LLRA or
LPCM.
The design matrix specifies every item to lie on its own dimension. Hence at every time point > 1, there are effects for each treatment or covariate group as well as trend effects for every item. Therefore overall there are items x (groups-1) x (time points-1) covariate effect parameters and items x (time points-1) trend parameters specified. For polytomous items there also are parameters for each category with the first and second category being equated for each item. They need not be equidistant. The number of parameters therefore increase quite rapidly for any additional time point, item or covariate group.
A warning is printed that the first two categories for polytomous items are equated.
Thomas Rusch
Hatzinger, R. and Rusch, T. (2009) IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51, pp. 87–120.
This function is used for automatic generation of the design matrix in LLRA.
##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. llraDat2a <- matrix(unlist(llraDat2[1:20]),ncol=4) groupvec <-rep(1:3*5,each=20) W <- build_W(llraDat2a,nitems=5,mpoints=4,grp_n=c(10,20,40),groupvec=groupvec,itmgrps=1:5) #There are 55 parameters dim(W) ## Not run: #Estimating LLRA by specifiying W ex2W <- LLRA(llraDat2[1:20],W=W,mpoints=4,groups=llraDat2[21]) ## End(Not run)##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. llraDat2a <- matrix(unlist(llraDat2[1:20]),ncol=4) groupvec <-rep(1:3*5,each=20) W <- build_W(llraDat2a,nitems=5,mpoints=4,grp_n=c(10,20,40),groupvec=groupvec,itmgrps=1:5) #There are 55 parameters dim(W) ## Not run: #Estimating LLRA by specifiying W ex2W <- LLRA(llraDat2[1:20],W=W,mpoints=4,groups=llraDat2[21]) ## End(Not run)
Collapses columns of a design matrix for LLRA to specify different
parameter restrictions in LLRA.
collapse_W(W, listItems, newNames)collapse_W(W, listItems, newNames)
W |
A design matrix (for LLRA), typically from a call to
|
listItems |
A list of numeric vectors. Each component of the list specifies columns to be collapsed together. |
newNames |
An (optional) character vector specifying the names of the collapsed effects. |
This function is a convenience function to collapse a design matrix,
i.e. to specify linear trend or treatment effects and so on. Collapsing
here means that effects in columns are summed up. For this, a list of numeric
vectors with the column indices of columns to be collapsed have to be
passed to the function. For example, if you want to collapse column 3, 6
and 8 into one new effect and 1, 4 and 9 into another it needs to be
passed with list(c(3,6,8),c(1,4,9)).
The new effects can be given names by passing a character vector to the function with equal length as the list.
An LLRA design matrix as described by Hatzinger and Rusch
(2009). This can be passed as the W argument to LLRA or
LPCM.
Thomas Rusch
Hatzinger, R. and Rusch, T. (2009) IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51, pp. 87–120.
The function to build design matrices from scratch, build_W.
##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. llraDat2a <- matrix(unlist(llraDat2[1:20]),ncol=4) groupvec <-rep(1:3*5,each=20) W <- build_W(llraDat2a, nitems=5, mpoints=4, grp_n=c(10,20,40), groupvec=groupvec,itmgrps=1:5) #There are 55 parameters to be estimated dim(W) #Imposing a linear trend for the second item ,i.e. parameters in #columns 32, 37 and 42 need to be collapsed into a single column. collItems1 <- list(c(32,37,42)) newNames1 <- c("trend.I2") Wstar1 <- collapse_W(W,collItems1) #53 parameters need to be estimated dim(Wstar1)##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. llraDat2a <- matrix(unlist(llraDat2[1:20]),ncol=4) groupvec <-rep(1:3*5,each=20) W <- build_W(llraDat2a, nitems=5, mpoints=4, grp_n=c(10,20,40), groupvec=groupvec,itmgrps=1:5) #There are 55 parameters to be estimated dim(W) #Imposing a linear trend for the second item ,i.e. parameters in #columns 32, 37 and 42 need to be collapsed into a single column. collItems1 <- list(c(32,37,42)) newNames1 <- c("trend.I2") Wstar1 <- collapse_W(W,collItems1) #53 parameters need to be estimated dim(Wstar1)
Artificial data sets for computing extended Rasch models.
raschdat1 raschdat2 raschdat3 raschdat4 lltmdat1 lltmdat2 rsmdat lrsmdat pcmdat pcmdat2 lpcmdat raschdat1_RM_fitted raschdat1_RM_plotDIF raschdat1_RM_lrres2raschdat1 raschdat2 raschdat3 raschdat4 lltmdat1 lltmdat2 rsmdat lrsmdat pcmdat pcmdat2 lpcmdat raschdat1_RM_fitted raschdat1_RM_plotDIF raschdat1_RM_lrres2
Numeric matrices with subjects as rows, items as columns, missing values as NA.
raschdat1_RM_fitted is the resulting object of RM(raschdat1) and used in examples to reduce computation time. For the generation of raschdat1_RM_plotDIF see the excluded example code of plotDIF. raschdat1_RM_lrres2 results from LRtest(RM(raschdat1), split = "mean")
This function computes various model tests and fit indices for objects of class ppar: Collapsed deviance, Casewise deviance, Rost's LR-test, Hosmer-Lemeshow test, R-Squared measures, confusion matrix, ROC analysis.
## S3 method for class 'ppar' gofIRT(object, groups.hl = 10, cutpoint = 0.5)## S3 method for class 'ppar' gofIRT(object, groups.hl = 10, cutpoint = 0.5)
object |
Object of class |
groups.hl |
Number of groups for Hosmer-Lemeshow test (see details). |
cutpoint |
Integer between 0 and 1 for computing the 0-1 model matrix from the estimated probabilities |
So far this test statistics are implemented only for dichotomous models without NA's. The Hosmer-Lemeshow test is computed by splitting the response vector into percentiles, e.g. groups.hl = 10 corresponds to decile splitting.
The function gofIRT returns an object of class gof containing:
test.table |
Ouput for model tests. |
R2 |
List with R-squared measures. |
classifier |
Confusion matrix, accuracy, sensitivity, specificity. |
AUC |
Area under ROC curve. |
Gini |
Gini coefficient. |
ROC |
FPR and TPR for different cutpoints. |
opt.cut |
Optimal cutpoint determined by ROC analysis. |
predobj |
Prediction output from ROC analysis ( |
Mair, P., Reise, S. P., and Bentler, P. M. (2008). IRT goodness-of-fit using approaches from logistic regression. UCLA Statistics Preprint Series.
itemfit.ppar,personfit.ppar,LRtest
#Goodness-of-fit for a Rasch model res <- RM(raschdat1) pres <- person.parameter(res) gof.res <- gofIRT(pres) gof.res summary(gof.res)#Goodness-of-fit for a Rasch model res <- RM(raschdat1) pres <- person.parameter(res) gof.res <- gofIRT(pres) gof.res summary(gof.res)
Computation of information criteria such as AIC, BIC, and cAIC based on unconditional (joint), marginal, and conditional log-likelihood
## S3 method for class 'ppar' IC(object)## S3 method for class 'ppar' IC(object)
object |
Object of class |
The joint log-likelihood is established by summation of the logarithms of the estimated solving probabilities. The marginal log-likelihood can be computed directly from the conditional log-likelihood (see vignette for details).
The function IC returns an object of class ICr containing:
ICtable |
Matrix containing log-likelihood values, number of parameters, AIC, BIC, and cAIC for the joint, marginal, and conditional log-likelihood. |
#IC's for Rasch model res <- RM(raschdat2) #Rasch model pres <- person.parameter(res) #Person parameters IC(pres) #IC's for RSM res <- RSM(rsmdat) pres <- person.parameter(res) IC(pres)#IC's for Rasch model res <- RM(raschdat2) #Rasch model pres <- person.parameter(res) #Person parameters IC(pres) #IC's for RSM res <- RSM(rsmdat) pres <- person.parameter(res) IC(pres)
Calculates Samejima's (1969) information for all items.
item_info(ermobject, theta = seq(-5, 5, 0.01)) i_info(hvec, itembeta, theta)item_info(ermobject, theta = seq(-5, 5, 0.01)) i_info(hvec, itembeta, theta)
ermobject |
An object of class 'eRm'. |
theta |
Supporting or sampling points on the latent trait. |
hvec |
Number of categories of a single item. |
itembeta |
Cumulative item category parameters for a single item. |
The function item_info calculates information of the
whole set of items in the 'eRm' object. The function i_info
does the same for a single item (and is called by item_info).
Returns a list (i_info) or a list of lists (where each list element
corresponds to an item, item_info) and contains
c.info |
Matrix of category information in columns for the different theta values in rows. |
i.info |
Vector of item information for the different theta values. |
Thomas Rusch
Samejima, F. (1969) Estimation of latent ability using a response pattern of graded scores. Psychometric Monographs, 17.
The function to calculate the test information, test_info
and the plot function plotINFO.
res <- PCM(pcmdat) info <- item_info(res) plotINFO(res,type="item")res <- PCM(pcmdat) info <- item_info(res) plotINFO(res,type="item")
pmat computes the theoretical person-item matrix with solving
probabilities for each category (except 0th). residuals computes the squared and standardized residuals based on
the observed and the expected person-item matrix. Chi-square based itemfit and personfit
statistics can be obtained by using itemfit and personfit. Corrected item-test correlations in itemfit are computed using the approach from Cureton (1966).
## S3 method for class 'ppar' pmat(object) ## S3 method for class 'ppar' residuals(object,...) ## S3 method for class 'ppar' itemfit(object) ## S3 method for class 'ppar' personfit(object) ## S3 method for class 'ifit' print(x, visible = TRUE, sort_by = c("none", "p", "outfit_MSQ", "infit_MSQ", "outfit_t", "infit_t", "discrim"), decreasing = FALSE, digits = 3,...) ## S3 method for class 'pfit' print(x, visible = TRUE, ...) ## S3 method for class 'resid' print(x, ...)## S3 method for class 'ppar' pmat(object) ## S3 method for class 'ppar' residuals(object,...) ## S3 method for class 'ppar' itemfit(object) ## S3 method for class 'ppar' personfit(object) ## S3 method for class 'ifit' print(x, visible = TRUE, sort_by = c("none", "p", "outfit_MSQ", "infit_MSQ", "outfit_t", "infit_t", "discrim"), decreasing = FALSE, digits = 3,...) ## S3 method for class 'pfit' print(x, visible = TRUE, ...) ## S3 method for class 'resid' print(x, ...)
object |
Object of class |
x |
Object of class |
visible |
If |
sort_by |
Optionally the itemfit output can be sorted by one of these criteria. |
decreasing |
If |
digits |
How many digits should be printed. |
... |
Further arguments passed to or from other methods. They are ignored in this function. |
pmat |
Matrix of theoretical probabilities for each category except 0th (from function |
i.fit |
Chi-squared itemfit statistics (from function |
i.df |
Degrees of freedom for itemfit statistics (from function |
st.res |
Standardized residuals (from function |
i.outfitMSQ |
Outfit mean-square statistics (from function |
i.infitMSQ |
Infit mean-square statistics (from function |
i.disc |
Corrected item-test correlations (from function |
p.fit |
Chi-squared personfit statistics (from function |
p.df |
Degrees of freedom for personfit statistics (from function |
st.res |
Standardized residuals (from function |
p.outfitMSQ |
Outfit mean-square statistics (from function |
p.infitMSQ |
Infit mean-square statistics (from function |
Patrick Mair, Reinhold Hatzinger, Moritz Heene
Smith Jr., E. V., and Smith, R. M. (2004). Introduction to Rasch Measurement. JAM press.
Wright, B.D., and Masters, G.N. Computation of OUTFIT and INFIT Statistics. Rasch Measurement Transactions, 1990, 3:4 p.84-85
Cureton, E. E. (1966). Corrected item-test correlations. Psychometrika, 31, 93-96
# Rasch model, estimation of item and person parameters res <- RM(raschdat2) p.res <- person.parameter(res) # Matrix with expected probabilities and corresponding residuals pmat(p.res) residuals(p.res) #Itemfit itemfit(p.res) #Personfit personfit(p.res)# Rasch model, estimation of item and person parameters res <- RM(raschdat2) p.res <- person.parameter(res) # Matrix with expected probabilities and corresponding residuals pmat(p.res) residuals(p.res) #Itemfit itemfit(p.res) #Personfit personfit(p.res)
Automatically builds design matrix and fits LLRA.
LLRA(X, W, mpoints, groups, baseline, itmgrps = NULL, ...) ## S3 method for class 'llra' print(x, ...)LLRA(X, W, mpoints, groups, baseline, itmgrps = NULL, ...) ## S3 method for class 'llra' print(x, ...)
X |
Data matrix as described in Hatzinger and Rusch (2009). It must be of wide format, e.g. for each person all item answers are written in columns for t1, t2, t3 etc. Hence each row corresponds to all observations for a single person. See llraDat1 for an example. Missing values are not allowed. |
W |
Design Matrix for LLRA to be passed to |
mpoints |
The number of time points. |
groups |
Vector, matrix or data frame with subject/treatment covariates. |
baseline |
An optional vector with the baseline values for the columns in group. |
itmgrps |
Specifies how many groups of items there are. Currently not functional but may be useful in the future. |
x |
For the print method, an object of class |
... |
Additional arguments to be passed to and from other methods. |
The function LLRA is a wrapper for LPCM to fit
Linear Logistic Models with Relaxed Assumptions (LLRA). LLRA
are extensions of the LPCM for the measurement of change over a number
of discrete time points for a set of
items. It can incorporate categorical covariate information. If no
design matrix W is passed as an argument, it is built automatically
from scratch.
Unless passed by the user, the baseline group is always the one with
the lowest (alpha-)numerical value for argument groups. All
other groups are labeled decreasingly according to the
(alpha)-numerical value, e.g. with 2 treatment groups (TG1 and TG2)
and one control group (CG), CG will be the baseline than TG1 and TG2.
Hence the group effects are ordered like
rev((unique(names(groupvec))) for naming.
Caution is advised as LLRA will fail if all changes for a group will be into a single direction (e.g. all subjects in the treatment group show improvement). Currently only data matrices are supported as arguments.
Returns an object of class 'llra' (also inheriting from class 'eRm') containing
loglik |
Conditional log-likelihood. |
iter |
Number of iterations. |
npar |
Number of parameters. |
convergence |
See code output in nlm. |
etapar |
Estimated basic item parameters. These are the LLRA effect parameters. |
se.eta |
Standard errors of the estimated basic item parameters. |
betapar |
Estimated item (easiness) parameters of the virtual items (not useful for interpretation here). |
se.beta |
Standard errors of virtual item parameters (not useful for interpretation here). |
hessian |
Hessian matrix if |
W |
Design matrix. |
X |
Data matrix in long format. The columns correspond to the measurement points and each persons item answers are listed susequently in rows. |
X01 |
Dichotomized data matrix. |
groupvec |
Assignment vector. |
call |
The matched call. |
itms |
The number of items. |
A warning is printed that the first two categories for polytomous items are equated to save parameters. See Hatzinger and Rusch (2009) for a justification why this is valid also from a substantive point of view.
Thomas Rusch
Fischer, G.H. (1995) Linear logistic models for change. In G.H. Fischer and I. W. Molenaar (eds.), Rasch models: Foundations, recent developments and applications (pp. 157–181), New York: Springer.
Glueck, J. and Spiel, C. (1997) Item response models for repeated measures designs: Application and limitations of four different approaches. Methods of Psychological Research, 2.
Hatzinger, R. and Rusch, T. (2009) IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51, pp. 87–120.
The function to build the design matrix build_W, and the
S3 methods summary.llra and plotTR and
plotGR for plotting.
##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) llra1 ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. dats <- llraDat2[1:20] groups <- llraDat2$group tps <- 4 #baseline CG ex2 <- LLRA(dats,mpoints=tps,groups=groups) #baseline TG1 ex2a <- LLRA(dats,mpoints=tps,groups=groups,baseline="TG1") #summarize results summary(ex2) summary(ex2a) #plotting plotGR(ex2) plotTR(ex2) ## End(Not run)##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) llra1 ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. dats <- llraDat2[1:20] groups <- llraDat2$group tps <- 4 #baseline CG ex2 <- LLRA(dats,mpoints=tps,groups=groups) #baseline TG1 ex2a <- LLRA(dats,mpoints=tps,groups=groups,baseline="TG1") #summarize results summary(ex2) summary(ex2a) #plotting plotGR(ex2) plotTR(ex2) ## End(Not run)
Converts wide data matrix in long format, sorts subjects according to groups and builds assigment vector.
llra.datprep(X, mpoints, groups, baseline)llra.datprep(X, mpoints, groups, baseline)
X |
Data matrix as described in Hatzinger and Rusch (2009). It must be of wide format, e.g. for each person all item answers are written in columns for t1, t2, t3 etc. Hence each row corresponds to all observations for a single person. Missing values are not allowed. |
mpoints |
The number of time points. |
groups |
Vector, matrix or data frame with subject/treatment covariates. |
baseline |
An optional vector with the baseline values for the columns in group. |
The function converts a data matrix from wide to long fromat as needed for LLRA. Additionally it sorts the subjects according to the different treatment/covariate groups. The group with the lowest (alpha-)numerical value will be the baseline.
Treatment and covariate groups are either defined by a vector, or by a matrix or data frame. The latter will be combined to a vector of groups corresponding to a combination of each factor level per column with the factor levels of the other column. The (constructed or passed) vector will then be used to create the assignment vector.
Returns a list with the components
X |
Data matrix in long format with subjects sorted by groups. |
assign.vec |
The assignment vector. |
grp_n |
A vector of the number of subjects in each group. |
Reinhold Hatzinger
The function that uses this is LLRA. The values from
llra.datprep can be passed to build_W.
# example 3 items, 3 timepoints, n=10, 2x2 treatments dat<-sim.rasch(10,9) tr1<-sample(c("a","b"),10,r=TRUE) tr2<-sample(c("x","y"),10,r=TRUE) # one treatment res<-llra.datprep(dat,mpoints=3,groups=tr1) res<-llra.datprep(dat,mpoints=3,groups=tr1,baseline="b") # two treatments res<-llra.datprep(dat,mpoints=3,groups=cbind(tr1,tr2)) res<-llra.datprep(dat,mpoints=3,groups=cbind(tr1,tr2),baseline=c("b","x")) # two treatments - data frame tr.dfr<-data.frame(tr1, tr2) res<-llra.datprep(dat,mpoints=3,groups=tr.dfr)# example 3 items, 3 timepoints, n=10, 2x2 treatments dat<-sim.rasch(10,9) tr1<-sample(c("a","b"),10,r=TRUE) tr2<-sample(c("x","y"),10,r=TRUE) # one treatment res<-llra.datprep(dat,mpoints=3,groups=tr1) res<-llra.datprep(dat,mpoints=3,groups=tr1,baseline="b") # two treatments res<-llra.datprep(dat,mpoints=3,groups=cbind(tr1,tr2)) res<-llra.datprep(dat,mpoints=3,groups=cbind(tr1,tr2),baseline=c("b","x")) # two treatments - data frame tr.dfr<-data.frame(tr1, tr2) res<-llra.datprep(dat,mpoints=3,groups=tr.dfr)
Artificial data set of 5 items, 5 time points and 5 groups for LLRA.
llraDat1llraDat1
A data frame with 150 observations of 26 variables.
t1.I1Answers to item 1 at time point 1
t1.I2Answers to item 2 at time point 1
t1.I3Answers to item 3 at time point 1
t1.I4Answers to item 4 at time point 1
t1.I5Answers to item 5 at time point 1
t2.I1Answers to item 1 at time point 2
t2.I2Answers to item 2 at time point 2
t2.I3Answers to item 3 at time point 2
t2.I4Answers to item 4 at time point 2
t2.I5Answers to item 5 at time point 2
t3.I1Answers to item 1 at time point 3
t3.I2Answers to item 2 at time point 3
t3.I3Answers to item 3 at time point 3
t3.I4Answers to item 4 at time point 3
t3.I5Answers to item 5 at time point 3
t4.I1Answers to item 1 at time point 4
t4.I2Answers to item 2 at time point 4
t4.I3Answers to item 3 at time point 4
t4.I4Answers to item 4 at time point 4
t4.I5Answers to item 5 at time point 4
t5.I1Answers to item 1 at time point 5
t5.I2Answers to item 2 at time point 5
t5.I3Answers to item 3 at time point 5
t5.I4Answers to item 4 at time point 5
t5.I5Answers to item 5 at time point 5
groupsThe group membership
This is a data set as described in Hatzinger and Rusch (2009). 5 items were measured at 5 time points (in columns). Each row corresponds to one person (P1 to P150). There are 4 treatment groups and a control group. Treatment group G5 has size 10 (the first ten subjects), treatment group G4 has size 20, treatment group G3 has size 30, treatment group G2 has size 40 and the control group CG has size 50 (the last 50 subjects). Item 1 is dichotomous, all others are polytomous. Item 2, 3, 4 and 5 have 3, 4, 5, 6 categories respectively.
Hatzinger, R. and Rusch, T. (2009) IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51, pp. 87–120.
llraDat1llraDat1
Artificial data set of 70 subjects with 5 items, 4 time points and 3 groups for LLRA.
llraDat2llraDat2
A data frame with 70 observations of 21 variables.
t1.I1Answers to item 1 at time point 1
t1.I2Answers to item 2 at time point 1
t1.I3Answers to item 3 at time point 1
t1.I4Answers to item 4 at time point 1
t1.I5Answers to item 5 at time point 1
t2.I1Answers to item 1 at time point 2
t2.I2Answers to item 2 at time point 2
t2.I3Answers to item 3 at time point 2
t2.I4Answers to item 4 at time point 2
t2.I5Answers to item 5 at time point 2
t3.I1Answers to item 1 at time point 3
t3.I2Answers to item 2 at time point 3
t3.I3Answers to item 3 at time point 3
t3.I4Answers to item 4 at time point 3
t3.I5Answers to item 5 at time point 3
t4.I1Answers to item 1 at time point 4
t4.I2Answers to item 2 at time point 4
t4.I3Answers to item 3 at time point 4
t4.I4Answers to item 4 at time point 4
t4.I5Answers to item 5 at time point 4
groupThe group membership
This is a data set as described in Hatzinger and Rusch (2009). 5 items were measured at 4 time points (in columns). Each persons answers to the items are recorded in the rows. There are 2 treatment groups and a control group. Treatment group 2 has size, 10, treatment group 1 has size 20 and the control group has size 40. Item 1 is dichotomous, all others are polytomous. Item 2, 3, 4 and 5 have 3, 4, 5, 6 categories respectively.
Hatzinger, R. and Rusch, T. (2009) IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51, pp. 87–120.
llraDat2llraDat2
Artificial data set of 3 items, 2 time points and 2 groups for LLRA. It is example 6 from Hatzinger and Rusch (2009).
llradat3llradat3
A data frame with 60 observations of 6 variables.
V1Answers to item 1 at time point 1
V2Answers to item 2 at time point 1
V3Answers to item 3 at time point 1
V4Answers to item 1 at time point 2
V5Answers to item 2 at time point 2
V6Answers to item 3 at time point 2
This is a data set as described in Hatzinger and Rusch (2009).
Hatzinger, R. and Rusch, T. (2009) IRT models with relaxed assumptions in eRm: A manual-like instruction. Psychology Science Quarterly, 51, pp. 87–120.
llradat3llradat3
This function computes the parameter estimates of a linear logistic test model (LLTM) for binary item responses by using CML estimation.
LLTM(X, W, mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE, etaStart)LLTM(X, W, mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE, etaStart)
X |
Input 0/1 data matrix or data frame; rows represent individuals (N in total),
columns represent items. Missing values have to be inserted as |
W |
Design matrix for the LLTM. If omitted, the function will compute W automatically. |
mpoints |
Number of measurement points. |
groupvec |
Vector of length N which determines the group membership of each subject,
starting from 1. If |
se |
If |
sum0 |
If |
etaStart |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |
Through appropriate definition of W the LLTM can be viewed as a more parsimonous
Rasch model, on the one hand, e.g. by imposing some cognitive base operations
to solve the items. One the other hand, linear extensions of the Rasch model
such as group comparisons and repeated measurement designs can be computed.
If more than one measurement point is examined, the item responses for the 2nd, 3rd, etc.
measurement point are added column-wise in X.
If W is user-defined, it is nevertheless necessary to
specify mpoints and groupvec. It is important that first the time contrasts and
then the group contrasts have to be imposed.
Available methods for LLTM-objects are:print, coef,
model.matrix, vcov,summary, logLik, person.parameters.
Returns on object of class eRm containing:
loglik |
Conditional log-likelihood. |
iter |
Number of iterations. |
npar |
Number of parameters. |
convergence |
See |
etapar |
Estimated basic item parameters. |
se.eta |
Standard errors of the estimated basic parameters. |
betapar |
Estimated item (easiness) parameters. |
se.beta |
Standard errors of item parameters. |
hessian |
Hessian matrix if |
W |
Design matrix. |
X |
Data matrix. |
X01 |
Dichotomized data matrix. |
groupvec |
Group membership vector. |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
#LLTM for 2 measurement points #100 persons, 2*15 items, W generated automatically res1 <- LLTM(lltmdat1, mpoints = 2) res1 summary(res1) #Reparameterized Rasch model as LLTM (more pasimonious) W <- matrix(c(1,2,1,3,2,2,2,1,1,1),ncol=2) #design matrix res2 <- LLTM(lltmdat2, W = W) res2 summary(res2)#LLTM for 2 measurement points #100 persons, 2*15 items, W generated automatically res1 <- LLTM(lltmdat1, mpoints = 2) res1 summary(res1) #Reparameterized Rasch model as LLTM (more pasimonious) W <- matrix(c(1,2,1,3,2,2,2,1,1,1),ncol=2) #design matrix res2 <- LLTM(lltmdat2, W = W) res2 summary(res2)
This function computes the parameter estimates of a linear partial credit model (LRSM) for polytomuous item responses by using CML estimation.
LPCM(X, W , mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE, etaStart)LPCM(X, W , mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE, etaStart)
X |
Input data matrix or data frame; rows represent individuals (N in total),
columns represent items. Missing values are inserted as |
W |
Design matrix for the LPCM. If omitted, the function will compute W automatically. |
mpoints |
Number of measurement points. |
groupvec |
Vector of length N which determines the group membership of each subject, starting from 1 |
se |
If |
sum0 |
If |
etaStart |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |
Through appropriate definition of W the LPCM can be viewed as a more parsimonous
PCM, on the one hand, e.g. by imposing some cognitive base operations
to solve the items. One the other hand, linear extensions of the Rasch model
such as group comparisons and repeated measurement designs can be computed.
If more than one measurement point is examined, the item responses for the 2nd, 3rd, etc.
measurement point are added column-wise in X.
If W is user-defined, it is nevertheless necessary to
specify mpoints and groupvec. It is important that first the time contrasts and
then the group contrasts have to be imposed.
Available methods for LPCM-objects are:print, coef,
model.matrix, vcov,summary, logLik, person.parameters.
Returns on object of class 'eRm' containing:
loglik |
Conditional log-likelihood. |
iter |
Number of iterations. |
npar |
Number of parameters. |
convergence |
See |
etapar |
Estimated basic item parameters. |
se.eta |
Standard errors of the estimated basic item parameters. |
betapar |
Estimated item (easiness) parameters. |
se.beta |
Standard errors of item parameters. |
hessian |
Hessian matrix if |
W |
Design matrix. |
X |
Data matrix. |
X01 |
Dichotomized data matrix. |
groupvec |
Group membership vector. |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
#LPCM for two measurement points and two subject groups #20 subjects, 2*3 items G <- c(rep(1,10),rep(2,10)) #group vector res <- LPCM(lpcmdat, mpoints = 2, groupvec = G) res summary(res)#LPCM for two measurement points and two subject groups #20 subjects, 2*3 items G <- c(rep(1,10),rep(2,10)) #group vector res <- LPCM(lpcmdat, mpoints = 2, groupvec = G) res summary(res)
This function computes the parameter estimates of a linear rating scale model (LRSM) for polytomuous item responses by using CML estimation.
LRSM(X, W , mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE, etaStart)LRSM(X, W , mpoints = 1, groupvec = 1, se = TRUE, sum0 = TRUE, etaStart)
X |
Input data matrix or data frame; rows represent individuals (N in total), columns represent items. Missing values are inserted as |
W |
Design matrix for the LRSM. If omitted, the function will compute W automatically. |
mpoints |
Number of measurement points. |
groupvec |
Vector of length N which determines the group membership of each subject, starting from 1 |
se |
If |
sum0 |
If |
etaStart |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |
Through appropriate definition of W the LRSM can be viewed as a more parsimonous
RSM, on the one hand, e.g. by imposing some cognitive base operations
to solve the items. One the other hand, linear extensions of the Rasch model
such as group comparisons and repeated measurement designs can be computed.
If more than one measurement point is examined, the item responses for the 2nd, 3rd, etc.
measurement point are added column-wise in X.
If W is user-defined, it is nevertheless necessary to
specify mpoints and groupvec. It is important that first the time contrasts and
then the group contrasts have to be imposed.
Available methods for LRSM-objects are:
print, coef,
model.matrix, vcov,summary, logLik, person.parameters.
Returns an object of class 'eRm' containing:
loglik |
Conditional log-likelihood. |
iter |
Number of iterations. |
npar |
Number of parameters. |
convergence |
See |
etapar |
Estimated basic item parameters (item and category parameters). |
se.eta |
Standard errors of the estimated basic item parameters. |
betapar |
Estimated item (easiness) parameters. |
se.beta |
Standard errors of item parameters. |
hessian |
Hessian matrix if |
W |
Design matrix. |
X |
Data matrix. |
X01 |
Dichotomized data matrix. |
groupvec |
Group membership vector. |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
#LRSM for two measurement points #20 subjects, 2*3 items, W generated automatically, #first parameter set to 0, no standard errors computed. res <- LRSM(lrsmdat, mpoints = 2, groupvec = 1, sum0 = FALSE, se = FALSE) res#LRSM for two measurement points #20 subjects, 2*3 items, W generated automatically, #first parameter set to 0, no standard errors computed. res <- LRSM(lrsmdat, mpoints = 2, groupvec = 1, sum0 = FALSE, se = FALSE) res
This LR-test is based on subject subgroup splitting.
## S3 method for class 'Rm' LRtest(object, splitcr = "median", se = TRUE) ## S3 method for class 'LR' plotGOF(x, beta.subset = "all", main = "Graphical Model Check", xlab, ylab, tlab = "item", xlim, ylim, type = "p", pos = 4, conf = NULL, ctrline = NULL, smooline = NULL, asp = 1, x_axis = TRUE, y_axis = TRUE, set_par = TRUE, reset_par = TRUE, ...)## S3 method for class 'Rm' LRtest(object, splitcr = "median", se = TRUE) ## S3 method for class 'LR' plotGOF(x, beta.subset = "all", main = "Graphical Model Check", xlab, ylab, tlab = "item", xlim, ylim, type = "p", pos = 4, conf = NULL, ctrline = NULL, smooline = NULL, asp = 1, x_axis = TRUE, y_axis = TRUE, set_par = TRUE, reset_par = TRUE, ...)
object |
Object of class |
splitcr |
Split criterion for subject raw score splitting.
|
se |
controls computation of standard errors in the submodels (default: |
x |
Object of class |
beta.subset |
If |
main |
Title of the plot. |
xlab |
Label on |
ylab |
Label on |
tlab |
Specification of item labels: |
xlim |
Limits on |
ylim |
Limits on |
type |
Plotting type (see |
pos |
Position of the item label (see |
conf |
for plotting confidence ellipses for the item parameters.
If |
ctrline |
for plotting confidence bands (control lines, cf. eg. Wright and Stone, 1999).
If |
smooline |
spline smoothed confidence bands; must be specified as a list with optional elements: |
asp |
sets the |
x_axis |
if |
y_axis |
if |
set_par |
if |
reset_par |
if |
... |
additional parameters. |
If the data set contains missing values and mean or median is specified as split criterion, means or medians are calculated for each missing value subgroup and consequently used for raw score splitting.
When using interactive selection for both labelling of single points (tlab = "identify" and drawing confidence ellipses at certain points (ia = TRUE) then first all plotted points are labelled and afterwards all ellipses are generated.
Both identification processes can be terminated by clicking the second (right) mouse button and selecting ‘Stop’ from the menu, or from the ‘Stop’ menu on the graphics window.
Using the specification which in allows for selectively drawing ellipses for certain items only, e.g., which = 1:3 draws ellipses for items 1 to 3 (as long as they are included in beta.subset).
The default is drawing ellipses for all items.
The element col in the conf list can either be a single color specification such as "blue" or a vector with color specifications for all items.
The length must be the same as the number of ellipses to be drawn.
For color specification a palette can be set up using standard palettes (e.g., rainbow) or palettes from the colorspace or RColorBrewer package.
An example is given below.
summary and print methods are available for objects of class LR.
LRtest returns an object of class LR containing:
LR |
LR-value. |
df |
Degrees of freedom of the test statistic. |
Chisq |
Chi-square value with corresponding df. |
pvalue |
P-value of the test. |
likgroup |
Log-likelihood values for the subgroups |
betalist |
List of beta parameters for the subgroups. |
selist |
List of standard errors of beta's. |
etalist |
List of eta parameters for the subgroups. |
spl.gr |
Names and levels for |
call |
The matched call. |
fitobj |
List containing model objects from subgroup fit. |
Patrick Mair, Reinhold Hatzinger, Marco J. Maier, Adrian Bruegger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
Wright, B.D., and Stone, M.H. (1999). Measurement essentials. Wide Range Inc., Wilmington. (https://www.rasch.org/measess/me-all.pdf 28Mb).
# the object used is the result of running ... RM(raschdat1) res <- raschdat1_RM_fitted # see ? raschdat1_RM_fitted # LR-test on dichotomous Rasch model with user-defined split splitvec <- sample(1:2, 100, replace = TRUE) lrres <- LRtest(res, splitcr = splitvec) lrres summary(lrres) ## Not run: # goodness-of-fit plot with interactive labelling of items w/o standard errors plotGOF(lrres, tlab = "identify") ## End(Not run) # LR-test with a full raw-score split X <- sim.rasch(1000, -2:2, seed = 5) res2 <- RM(X) full_lrt <- LRtest(res2, splitcr = "all.r") full_lrt ## Not run: # LR-test with mean split, standard errors for beta's lrres2 <- LRtest(res, split = "mean") ## End(Not run) # to save computation time, the results are loaded from raschdat1_RM_lrres2 lrres2 <- raschdat1_RM_lrres2 # see ?raschdat1_RM_lrres2 # goodness-of-fit plot # additional 95 percent control line with user specified style plotGOF(lrres2, ctrline = list(gamma = 0.95, col = "red", lty = "dashed")) # goodness-of-fit plot for items 1, 14, 24, and 25 # additional 95 percent confidence ellipses, default style plotGOF(lrres2, beta.subset = c(14, 25, 24, 1), conf = list()) ## Not run: # goodness-of-fit plot for items 1, 14, 24, and 25 # for items 1 and 24 additional 95 percent confidence ellipses # using colors for these 2 items from the colorspace package library("colorspace") my_colors <- rainbow_hcl(2) plotGOF(lrres2, beta.subset = c(14, 25, 24, 1), conf = list(which = c(1, 14), col = my_colors)) ## End(Not run) # first, save current graphical parameters in an object old_par <- par(mfrow = c(1, 2), no.readonly = TRUE) # plots plotGOF(lrres2, ctrline = list(gamma = 0.95, col = "red", lty = "dashed"), xlim = c(-3, 3), x_axis = FALSE, set_par = FALSE) axis(1, seq(-3, 3, .5)) plotGOF(lrres2, conf = list(), xlim = c(-3, 3), x_axis = FALSE, set_par = FALSE) axis(1, seq(-3, 3, .5)) text(-2, 2, labels = "Annotation") # reset graphical parameters par(old_par)# the object used is the result of running ... RM(raschdat1) res <- raschdat1_RM_fitted # see ? raschdat1_RM_fitted # LR-test on dichotomous Rasch model with user-defined split splitvec <- sample(1:2, 100, replace = TRUE) lrres <- LRtest(res, splitcr = splitvec) lrres summary(lrres) ## Not run: # goodness-of-fit plot with interactive labelling of items w/o standard errors plotGOF(lrres, tlab = "identify") ## End(Not run) # LR-test with a full raw-score split X <- sim.rasch(1000, -2:2, seed = 5) res2 <- RM(X) full_lrt <- LRtest(res2, splitcr = "all.r") full_lrt ## Not run: # LR-test with mean split, standard errors for beta's lrres2 <- LRtest(res, split = "mean") ## End(Not run) # to save computation time, the results are loaded from raschdat1_RM_lrres2 lrres2 <- raschdat1_RM_lrres2 # see ?raschdat1_RM_lrres2 # goodness-of-fit plot # additional 95 percent control line with user specified style plotGOF(lrres2, ctrline = list(gamma = 0.95, col = "red", lty = "dashed")) # goodness-of-fit plot for items 1, 14, 24, and 25 # additional 95 percent confidence ellipses, default style plotGOF(lrres2, beta.subset = c(14, 25, 24, 1), conf = list()) ## Not run: # goodness-of-fit plot for items 1, 14, 24, and 25 # for items 1 and 24 additional 95 percent confidence ellipses # using colors for these 2 items from the colorspace package library("colorspace") my_colors <- rainbow_hcl(2) plotGOF(lrres2, beta.subset = c(14, 25, 24, 1), conf = list(which = c(1, 14), col = my_colors)) ## End(Not run) # first, save current graphical parameters in an object old_par <- par(mfrow = c(1, 2), no.readonly = TRUE) # plots plotGOF(lrres2, ctrline = list(gamma = 0.95, col = "red", lty = "dashed"), xlim = c(-3, 3), x_axis = FALSE, set_par = FALSE) axis(1, seq(-3, 3, .5)) plotGOF(lrres2, conf = list(), xlim = c(-3, 3), x_axis = FALSE, set_par = FALSE) axis(1, seq(-3, 3, .5)) text(-2, 2, labels = "Annotation") # reset graphical parameters par(old_par)
This Likelihood-Ratio-Test is based on item subgroup splitting.
MLoef(robj, splitcr = "median")MLoef(robj, splitcr = "median")
robj |
An object of class |
splitcr |
Split criterion to define the item groups.
|
This function implements a generalization of the Martin-Löf test for polytomous items as proposed by Christensen, Bjørner, Kreiner & Petersen (2002), but does currently not allow for missing values.
If the split criterion is "median" or "mean" and one or more items' raw scores are equal the median resp. mean, MLoef will assign those items to the lower raw score group.
summary.MLoef gives detailed information about the allocation of all items.
summary and print methods are available for objects of class 'MLoef'.
An ‘exact’ version of the Martin-Löf test for binary items is implemented in the NPtest function.
MLoef returns an object of class MLoef containing:
LR |
LR-value |
df |
degrees of freedom |
p.value |
p-value of the test |
fullModel |
the overall Rasch model |
subModels |
a list containing the submodels |
Lf |
log-likelihood of the full model |
Ls |
list of the sub models' log-likelihoods |
i.groups |
a list of the item groups |
splitcr |
submitted split criterion |
split.vector |
binary allocation of items to groups |
warning |
items equalling median or mean for the respective split criteria |
call |
the matched call |
Marco J. Maier, Reinhold Hatzinger
Christensen, K. B., Bjørner, J. B., Kreiner S. & Petersen J. H. (2002). Testing unidimensionality in polytomous Rasch models. Psychometrika, (67)4, 563–574.
Fischer, G. H., and Molenaar, I. (1995). Rasch Models – Foundations, Recent Developements, and Applications. Springer.
Rost, J. (2004). Lehrbuch Testtheorie – Testkonstruktion. Bern: Huber.
# Martin-Löf-test on dichotomous Rasch model using "median" and a user-defined # split vector. Note that group indicators can be of character and/or numeric. splitvec <- c(1, 1, 1, "x", "x", "x", 0, 0, 1, 0) res <- RM(raschdat1[,1:10]) MLoef.1 <- MLoef(res, splitcr = "median") MLoef.2 <- MLoef(res, splitcr = splitvec) MLoef.1 summary(MLoef.2)# Martin-Löf-test on dichotomous Rasch model using "median" and a user-defined # split vector. Note that group indicators can be of character and/or numeric. splitvec <- c(1, 1, 1, "x", "x", "x", 0, 0, 1, 0) res <- RM(raschdat1[,1:10]) MLoef.1 <- MLoef(res, splitcr = "median") MLoef.2 <- MLoef(res, splitcr = splitvec) MLoef.1 summary(MLoef.2)
A variety of nonparametric tests as proposed by Ponocny (2001), Koller and Hatzinger (2012), and an ‘exact’ version of the Martin-Löf test are implemented. The function operates on random binary matrices that have been generated using an MCMC algorithm (Verhelst, 2008) from the RaschSampler package (Hatzinger, Mair, and Verhelst, 2009).
NPtest(obj, n = NULL, method = "T1", ...)NPtest(obj, n = NULL, method = "T1", ...)
obj |
A binary data matrix (or data frame) or an object containing the output from the RaschSampler package. |
n |
If |
method |
One of the test statistics. See Details below. |
... |
Further arguments according to |
The function uses the RaschSampler package, which is now packaged with eRm for convenience. It can, of course, still be accessed and downloaded separately via CRAN.
As an input the user has to supply either a binary data matrix or a RaschSampler output object.
If the input is a data matrix, the RaschSampler is called with default values (i.e., rsctrl(burn_in = 256, n_eff = n, step = 32), see rsctrl), where n corresponds to n_eff (the default number of sampled matrices is 500).
By default, the starting values for the random number generators (seed) are chosen randomly using system time.
Methods other than those listed below can easily be implemented using the RaschSampler package directly.
The currently implemented methods (following Ponocny's notation of -statistics) and their options are:
method = "T1"
Checks for local dependence via increased inter-item correlations.
For all item pairs, cases are counted with equal responses on both items.
method = "T1m"
Checks for multidimensionality via decreased inter-item correlations.
For all item pairs, cases are counted with equal responses on both items.
method = "T1l"
Checks for learning.
For all item pairs, cases are counted with response pattern (1,1).
method = "Tmd", idx1, idx2idx1 and idx2 are vectors of indices specifying items which define two subscales, e.g., idx1 = c(1, 5, 7) and idx2 = c(3, 4, 6)
Checks for multidimensionality based on correlations of person raw scores for the subscales.
method = "T2", idx = NULL, stat = "var"idx is a vector of indices specifying items which define a subscale, e.g., idx = c(1, 5, 7)stat defines the used statistic as a character object which can be: "var" (variance), "mad1" (mean absolute deviation), "mad2" (median absolute deviation), or "range" (range)
Checks for local dependence within model deviating subscales via increased dispersion of subscale person rawscores.
method = "T2m", idx = NULL, stat = "var"idx is a vector of indices specifying items which define a subscale, e.g., idx = c(1, 5, 7)stat defines the used statistic as a character object which can be: "var" (variance), "mad1" (mean absolute deviation), "mad2" (median absolute deviation), "range" (range)
Checks for multidimensionality within model deviating subscales via decreased dispersion of subscale person rawscores.
method = "T4", idx = NULL, group = NULL, alternative = "high"idx is a vector of indices specifying items which define a subscale, e.g., idx = c(1, 5, 7)group is a logical vector defining a subject group, e.g., group = ((age >= 20) & (age < 30))alternative specifies the alternative hypothesis and can be: "high" or "low".
Checks for group anomalies (DIF) via too high (low) raw scores on item(s) for specified group.
method = "T10", splitcr = "median"splitcr defines the split criterion for subject raw score splitting.
"median" uses the median as split criterion, "mean" performs a mean-split.
Optionally, splitcr can also be a vector which assigns each person to one of two subgroups (e.g., following an external criterion).
This vector can be numeric, character, logical, or a factor.
Global test for subgroup-invariance.
Checks for different item difficulties in two subgroups (for details see Ponocny, 2001).
method = "T11"
Global test for local dependence.
The statistic calculates the sum of absolute deviations between the observed inter-item correlations and the expected correlations.
method = "Tpbis", idxt, idxs
Test for discrimination.
The statistic calculates a point-biserial correlation for a test item (specified via idxt) with the person row scores for a subscale of the test sum (specified via idxs).
If the correlation is too low, the test item shows different discrimination compared to the items of the subscale.
The ‘exact’ version of the Martin-Löf statistic is specified via method = "MLoef" and optionally splitcr (see MLoef).
method = "Q3h"
Checks for local dependence by detecting an increased correlation of inter-item residuals. Low p-values correspond to a high ("h") correlation between two items.
method = "Q3l"
Checks for local dependence by detecting a decreased correlation of inter-item residuals. Low p-values correspond to a low ("l") correlation between two items.
Depending on the method argument, a list is returned which has one of the following classes:
'T1obj', 'T1mobj', 'T1lobj', 'Tmdobj', 'T2obj', 'T2mobj', 'T4obj', 'T10obj', 'T11obj', 'Tpbisobj', 'Q3hobj' or 'Q3lobj'.
The main output element is prop giving the one-sided -value, i.e., the number of statistics from the sampled matrices which are equal or exceed the statistic based on the observed data.
For , , and , prop is a vector.
For the Martin-Löf test, the returned object is of class 'MLobj'.
Besides other elements, it contains a prop vector and MLres, the output object from the asymptotic Martin-Löf test on the input data.
The RaschSampler package is no longer required to use NPtest since eRm version 0.15-0.
Reinhold Hatzinger
Ponocny, I. (2001). Nonparametric goodness-of-fit tests for the Rasch model. Psychometrika, 66(3), 437–459. doi:10.1007/BF02294444
Verhelst, N. D. (2008). An efficient MCMC algorithm to sample binary matrices with fixed marginals. Psychometrika, 73(4), 705–728. doi:10.1007/s11336-008-9062-3
Verhelst, N., Hatzinger, R., & Mair, P. (2007). The Rasch sampler. Journal of Statistical Software, 20(4), 1–14. https://www.jstatsoft.org/v20/i04
Koller, I., & Hatzinger, R. (2013). Nonparametric tests for the Rasch model: Explanation, development, and application of quasi-exact tests for small samples. Interstat, 11, 1–16. http://interstat.statjournals.net/YEAR/2013/abstracts/1311002.php
Koller, I., Maier, M. J., & Hatzinger, R. (2015). An Empirical Power Analysis of Quasi-Exact Tests for the Rasch Model: Measurement Invariance in Small Samples. Methodology, 11(2), 45–54. doi:10.1027/1614-2241/a000090
Debelak, R., & Koller, I. (2019). Testing the Local Independence Assumption of the Rasch Model With Q3-Based Nonparametric Model Tests. Applied Psychological Measurement doi:10.1177/0146621619835501
### Preparation: # data for examples below X <- as.matrix(raschdat1) # generate 100 random matrices based on original data matrix rmat <- rsampler(X, rsctrl(burn_in = 100, n_eff = 100, seed = 123)) ## the following examples can also directly be used by setting ## rmat <- as.matrix(raschdat1) ## without calling rsampler() first t1 <- NPtest(rmat, n = 100, method = "T1") ### Examples ################################################################### ###--- T1 ---------------------------------------------------------------------- t1 <- NPtest(rmat, method = "T1") # choose a different alpha for selecting displayed values print(t1, alpha = 0.01) ###--- T2 ---------------------------------------------------------------------- t21 <- NPtest(rmat, method = "T2", idx = 1:5, burn_in = 100, step = 20, seed = 7654321, RSinfo = TRUE) # default stat is variance t21 t22 <- NPtest(rmat, method = "T2", stat = "mad1", idx = c(1, 22, 5, 27, 6, 9, 11)) t22 ###--- T4 ---------------------------------------------------------------------- age <- sample(20:90, 100, replace = TRUE) # group MUST be a logical vector # (value of TRUE is used for group selection) age <- age < 30 t41 <- NPtest(rmat, method = "T4", idx = 1:3, group = age) t41 sex <- gl(2, 50) # group can also be a logical expression (generating a vector) t42 <- NPtest(rmat, method = "T4", idx = c(1, 4, 5, 6), group = sex == 1) t42 ###--- T10 --------------------------------------------------------------------- t101 <- NPtest(rmat, method = "T10") # default split criterion is "median" t101 ## Not run: split <- runif(100) t102 <- NPtest(rmat, method = "T10", splitcr = split > 0.5) t102 t103 <- NPtest(rmat, method = "T10", splitcr = sex) t103 ## End(Not run) ###--- T11 --------------------------------------------------------------------- t11 <- NPtest(rmat, method = "T11") t11 ###--- Tpbis ------------------------------------------------------------------- tpb <- NPtest(X[, 1:5], method = "Tpbis", idxt = 1, idxs = 2:5) tpb ###--- Martin-Löf -------------------------------------------------------------- ## Not run: # takes a while ... split <- rep(1:3, each = 10) NPtest(raschdat1, n = 100, method = "MLoef", splitcr = split) ## End(Not run)### Preparation: # data for examples below X <- as.matrix(raschdat1) # generate 100 random matrices based on original data matrix rmat <- rsampler(X, rsctrl(burn_in = 100, n_eff = 100, seed = 123)) ## the following examples can also directly be used by setting ## rmat <- as.matrix(raschdat1) ## without calling rsampler() first t1 <- NPtest(rmat, n = 100, method = "T1") ### Examples ################################################################### ###--- T1 ---------------------------------------------------------------------- t1 <- NPtest(rmat, method = "T1") # choose a different alpha for selecting displayed values print(t1, alpha = 0.01) ###--- T2 ---------------------------------------------------------------------- t21 <- NPtest(rmat, method = "T2", idx = 1:5, burn_in = 100, step = 20, seed = 7654321, RSinfo = TRUE) # default stat is variance t21 t22 <- NPtest(rmat, method = "T2", stat = "mad1", idx = c(1, 22, 5, 27, 6, 9, 11)) t22 ###--- T4 ---------------------------------------------------------------------- age <- sample(20:90, 100, replace = TRUE) # group MUST be a logical vector # (value of TRUE is used for group selection) age <- age < 30 t41 <- NPtest(rmat, method = "T4", idx = 1:3, group = age) t41 sex <- gl(2, 50) # group can also be a logical expression (generating a vector) t42 <- NPtest(rmat, method = "T4", idx = c(1, 4, 5, 6), group = sex == 1) t42 ###--- T10 --------------------------------------------------------------------- t101 <- NPtest(rmat, method = "T10") # default split criterion is "median" t101 ## Not run: split <- runif(100) t102 <- NPtest(rmat, method = "T10", splitcr = split > 0.5) t102 t103 <- NPtest(rmat, method = "T10", splitcr = sex) t103 ## End(Not run) ###--- T11 --------------------------------------------------------------------- t11 <- NPtest(rmat, method = "T11") t11 ###--- Tpbis ------------------------------------------------------------------- tpb <- NPtest(X[, 1:5], method = "Tpbis", idxt = 1, idxs = 2:5) tpb ###--- Martin-Löf -------------------------------------------------------------- ## Not run: # takes a while ... split <- rep(1:3, each = 10) NPtest(raschdat1, n = 100, method = "MLoef", splitcr = split) ## End(Not run)
This function computes the parameter estimates of a partial credit model for polytomous item responses by using CML estimation.
PCM(X, W, se = TRUE, sum0 = TRUE, etaStart)PCM(X, W, se = TRUE, sum0 = TRUE, etaStart)
X |
Input data matrix or data frame with item responses (starting from 0); rows represent individuals, columns represent items. Missing values are inserted as |
W |
Design matrix for the PCM. If omitted, the function will compute W automatically. |
se |
If |
sum0 |
If |
etaStart |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |
Through specification in W, the parameters of the categories with 0 responses
are set to 0 as well as the first category of the first item. Available methods
for PCM-objects are:print, coef, model.matrix,
vcov, plot, summary, logLik, person.parameters,
plotICC, LRtest.
Returns an object of class Rm, eRm containing.
loglik |
Conditional log-likelihood. |
iter |
Number of iterations. |
npar |
Number of parameters. |
convergence |
See |
etapar |
Estimated basic item difficulty parameters. |
se.eta |
Standard errors of the estimated basic item parameters. |
betapar |
Estimated item-category (easiness) parameters. |
se.beta |
Standard errors of item parameters. |
hessian |
Hessian matrix if |
W |
Design matrix. |
X |
Data matrix. |
X01 |
Dichotomized data matrix. |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
##PCM with 10 subjects, 3 items res <- PCM(pcmdat) res summary(res) #eta and beta parameters with CI thresholds(res) #threshold parameters##PCM with 10 subjects, 3 items res <- PCM(pcmdat) res summary(res) #eta and beta parameters with CI thresholds(res) #threshold parameters
Maximum likelihood estimation of the person parameters with spline interpolation for non-observed and 0/full responses. Extraction of information criteria such as AIC, BIC, and cAIC based on unconditional log-likelihood.
## S3 method for class 'eRm' person.parameter(object) ## S3 method for class 'ppar' summary(object, ...) ## S3 method for class 'ppar' print(x, ...) ## S3 method for class 'ppar' plot(x, xlab = "Person Raw Scores", ylab = "Person Parameters (Theta)", main = NULL, ...) ## S3 method for class 'ppar' coef(object, extrapolated = TRUE, ...) ## S3 method for class 'ppar' logLik(object, ...) ## S3 method for class 'ppar' confint(object, parm, level = 0.95, ...)## S3 method for class 'eRm' person.parameter(object) ## S3 method for class 'ppar' summary(object, ...) ## S3 method for class 'ppar' print(x, ...) ## S3 method for class 'ppar' plot(x, xlab = "Person Raw Scores", ylab = "Person Parameters (Theta)", main = NULL, ...) ## S3 method for class 'ppar' coef(object, extrapolated = TRUE, ...) ## S3 method for class 'ppar' logLik(object, ...) ## S3 method for class 'ppar' confint(object, parm, level = 0.95, ...)
object |
Object of class |
Arguments for print and plot methods:
x |
Object of class |
xlab |
Label of the x-axis. |
ylab |
Label of the y-axis. |
main |
Title of the plot. |
... |
Further arguments to be passed to or from other methods. They are ignored in this function. |
Arguments for the coef method:
extrapolated |
either returns extrapolated values for raw scores 0 and k or sets them |
Arguments for confint:
parm |
Parameter specification (ignored). |
level |
Alpha-level. |
If the data set contains missing values, person parameters are estimated for each missing value subgroup.
The function person.parameter returns an object of class ppar containing:
loglik |
Log-likelihood of the collapsed data (for faster estimation persons with the same raw score are collapsed). |
npar |
Number of parameters. |
niter |
Number of iterations. |
thetapar |
Person parameter estimates. |
se.theta |
Standard errors of the person parameters. |
hessian |
Hessian matrix. |
theta.table |
Matrix with person parameters (ordered according to original data) including NA pattern group. |
pers.ex |
Indices with persons excluded due to 0/full raw score |
X.ex |
Data matrix with persons excluded |
gmemb |
NA group membership vector (0/full persons excluded) |
The function coef returns a vector of the person parameter estimates for each person (i.e., the first column
of theta.table).
The function logLik returns an object of class loglik.ppar containing:
loglik |
Log-likelihood of the collapsed data (see above). |
df |
Degrees of freedom. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
#Person parameter estimation of a rating scale model res <- RSM(rsmdat) pres <- person.parameter(res) pres summary(pres) plot(pres) #Person parameter estimation for a Rasch model with missing values res <- RM(raschdat2, se = FALSE) #Rasch model without standard errors pres <- person.parameter(res) pres #person parameters summary(pres) logLik(pres) #log-likelihood of person parameter estimation#Person parameter estimation of a rating scale model res <- RSM(rsmdat) pres <- person.parameter(res) pres summary(pres) plot(pres) #Person parameter estimation for a Rasch model with missing values res <- RM(raschdat2, se = FALSE) #Rasch model without standard errors pres <- person.parameter(res) pres #person parameters summary(pres) logLik(pres) #log-likelihood of person parameter estimation
This function counts the number of persons who do not fit the Rasch model. More specifically, it returns the proportion and frequency of persons - or more generally cases - who exceed a Chi-square based Z-value of 1.96 (suggesting a statistically significant deviation from the predicted response pattern).
## S3 method for class 'ppar' PersonMisfit(object)## S3 method for class 'ppar' PersonMisfit(object)
object |
Object of class |
Returns the proportion and absolute number of persons who do not fit the Rasch model (Z-values > 1.96).
PersonMisfit returns an object of class MisfittingPersons containing:
PersonMisfit |
the proportion of misfitting persons, |
count.misfit.Z |
the frequency of misfitting person, |
total.persons |
the number of persons for whom a fit value was estimated. |
Adrian Bruegger
rm1 <- RM(raschdat1) pers <- person.parameter(rm1) pmfit <- PersonMisfit(pers) pmfit summary(pmfit)rm1 <- RM(raschdat1) pers <- person.parameter(rm1) pmfit <- PersonMisfit(pers) pmfit summary(pmfit)
Calculates the statistic, i.e., the range of the inter-column correlations (-coefficients) for a binary matrix.
phi.range(mat)phi.range(mat)
mat |
a binary matrix |
The range of the inter-column correlations
ctr <- rsctrl(burn_in = 10, n_eff = 5, step=10, seed = 123, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) rso <- rsampler(mat, ctr) rso_st <- rstats(rso,phi.range) print(unlist(rso_st))ctr <- rsctrl(burn_in = 10, n_eff = 5, step=10, seed = 123, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) rso <- rsampler(mat, ctr) rso_st <- rstats(rso,phi.range) print(unlist(rso_st))
Performs an plot of item parameter conficence intervals based on LRtest subgroup splitting.
plotDIF(object, item.subset = NULL, gamma = 0.95, main = NULL, xlim = NULL, xlab = " ", ylab=" ", col = NULL, distance, splitnames=NULL, leg = FALSE, legpos="bottomleft", ...)plotDIF(object, item.subset = NULL, gamma = 0.95, main = NULL, xlim = NULL, xlab = " ", ylab=" ", col = NULL, distance, splitnames=NULL, leg = FALSE, legpos="bottomleft", ...)
object |
An object of class |
item.subset |
Subset of items to be plotted. Either a numeric vector indicating the items or a character vector indicating the itemnames. If nothing is defined (default), all items are plotted. |
gamma |
The level for the item parameter's confidence limits (default is gamma = 0.95). |
main |
Main title for the plot. |
xlim |
Numeric vector of length 2, giving the x coordinates ranges of the plot (the y coordinates depend on the number of depicted items). |
xlab |
Label for the x axis. |
ylab |
Label for the y axis. |
col |
By default the color for the drawn confidence lines is determined automatically whereas every group (split criterion) is depicted in the same color. |
distance |
Distance between each item's confidence lines – if omitted, the distance shrinks with increasing numbers of split criteria. Can be overriden using values in (0, 0.5). |
splitnames |
For labeling the splitobjects in the legend (returns a nicer output). |
leg |
If |
legpos |
Position of the legend with possible values |
... |
Further options to be passed to |
If there are items that cannot be estimated for some reasons, certainly these ones are not plotted.
For plotting several objects of class LR, the subgroup splitting by LRtest has to
be carried out for the same data set (or at least item subsets of it).
Plotting a certain subset of items could be useful if the objects of class LR contain a huge number
of estimated items.
The default level for the conficence limits is gamma = 0.95. (If the conficence limits should be corrected it is useful to use a correction, e.g., Bonferroni: 1 - (1 - gamma) / number of estimated items.)
plotCI returns a list containing the confidence limits of each group in each LRtest object.
Kathrin Gruber, Reinhold Hatzinger
LRtest, confint.threshold, thresholds
# the object used is the result of running RM(raschdat1) res <- raschdat1_RM_fitted # see ? raschdat1_RM_fitted ## Not run: # LR-test on dichotomous Rasch model with user-defined split splitvec <- rep(1:2, each = 50) lrres <- LRtest(res, splitcr = splitvec) # LR-test with mean split lrres2 <- LRtest(res, split = "mean") # combination of LRtest-objects in a list RMplotCI <- list(lrres, lrres2) ## End(Not run) # the object raschdat1_RM_plotDIF is the result of the computations outlined # above and is loaded to save computation time. see ?raschdat1_RM_plotDIF RMplotCI <- raschdat1_RM_plotDIF # Confidence intervals plot with default assumptions plotDIF(RMplotCI) # Confidence intervals plot with Bonferroni correction plotDIF(RMplotCI, gamma = (1 - (0.05/10))) # Confidence intervals plot for an item subset plotDIF(RMplotCI, item.subset = 1:6) # with user defined group color and legend plotDIF(RMplotCI, col = c("red", "blue"), leg = TRUE, legpos = "bottomright") # with names for the splitobjects plotDIF(RMplotCI, col = c("red", "blue"), leg = TRUE, legpos = "bottomright", splitnames = c(paste("User", 1:2), paste(rep("Mean", 2), 1:2)))# the object used is the result of running RM(raschdat1) res <- raschdat1_RM_fitted # see ? raschdat1_RM_fitted ## Not run: # LR-test on dichotomous Rasch model with user-defined split splitvec <- rep(1:2, each = 50) lrres <- LRtest(res, splitcr = splitvec) # LR-test with mean split lrres2 <- LRtest(res, split = "mean") # combination of LRtest-objects in a list RMplotCI <- list(lrres, lrres2) ## End(Not run) # the object raschdat1_RM_plotDIF is the result of the computations outlined # above and is loaded to save computation time. see ?raschdat1_RM_plotDIF RMplotCI <- raschdat1_RM_plotDIF # Confidence intervals plot with default assumptions plotDIF(RMplotCI) # Confidence intervals plot with Bonferroni correction plotDIF(RMplotCI, gamma = (1 - (0.05/10))) # Confidence intervals plot for an item subset plotDIF(RMplotCI, item.subset = 1:6) # with user defined group color and legend plotDIF(RMplotCI, col = c("red", "blue"), leg = TRUE, legpos = "bottomright") # with names for the splitobjects plotDIF(RMplotCI, col = c("red", "blue"), leg = TRUE, legpos = "bottomright", splitnames = c(paste("User", 1:2), paste(rep("Mean", 2), 1:2)))
Plots treatment or covariate group effects over time.
plotGR(object, ...)plotGR(object, ...)
object |
an object of class "llra". |
... |
Additional parameters to be passed to and from other methods. |
The plot is a lattice plot with each panel corresponding to an item. The effects are plotted for each groups (including baseline) over the different time points. The groups are given the same names as for the parameter estimates (derived from groupvec).
Please note that all effects are to be interpreted relative to the baseline.
Currently, this function only works for a full item x treatment x timepoints LLRA. Collapsed effects will not be displayed properly.
Objects of class "llra" that contain estimates from a collapsed
data matrix will not be displayed correctly.
Thomas Rusch
The plot method for trend effects plotTR.
##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) summary(llra1) plotGR(llra1) ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. ex2 <- LLRA(llraDat2[1:20],mpoints=4,groups=llraDat2[21]) plotGR(ex2) ## End(Not run)##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) summary(llra1) plotGR(llra1) ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. ex2 <- LLRA(llraDat2[1:20],mpoints=4,groups=llraDat2[21]) plotGR(ex2) ## End(Not run)
Plot functions for visualizing the item characteristic curves
## S3 method for class 'Rm' plotICC(object, item.subset = "all", empICC = NULL, empCI = NULL, mplot = NULL, xlim = c(-4, 4), ylim = c(0, 1), xlab = "Latent Dimension", ylab = "Probability to Solve", main=NULL, col = NULL, lty = 1, legpos = "left", ask = TRUE, ...) ## S3 method for class 'dRm' plotjointICC(object, item.subset = "all", legend = TRUE, xlim = c(-4, 4), ylim = c(0, 1), xlab = "Latent Dimension", ylab = "Probability to Solve", lty = 1, legpos = "topleft", main="ICC plot",col=NULL,...)## S3 method for class 'Rm' plotICC(object, item.subset = "all", empICC = NULL, empCI = NULL, mplot = NULL, xlim = c(-4, 4), ylim = c(0, 1), xlab = "Latent Dimension", ylab = "Probability to Solve", main=NULL, col = NULL, lty = 1, legpos = "left", ask = TRUE, ...) ## S3 method for class 'dRm' plotjointICC(object, item.subset = "all", legend = TRUE, xlim = c(-4, 4), ylim = c(0, 1), xlab = "Latent Dimension", ylab = "Probability to Solve", lty = 1, legpos = "topleft", main="ICC plot",col=NULL,...)
object |
object of class |
item.subset |
Subset of items to be plotted. Either a numeric vector indicating
the column in |
empICC |
Plotting the empirical ICCs for objects of class |
empCI |
Plotting confidence intervals for the the empirical ICCs.
If |
mplot |
if |
xlab |
Label of the x-axis. |
ylab |
Label of the y-axis. |
xlim |
Range of person parameters. |
ylim |
Range for probability to solve. |
legend |
If |
col |
If not specified or |
lty |
Line type. |
main |
Title of the plot. |
legpos |
Position of the legend with possible values |
ask |
If |
... |
Additional plot parameters. |
Empirical ICCs for objects of class dRm can be plotted using the option empICC, a
list where the first element specifies the type of calculation of the empirical values.
If empICC=list("raw", other specifications)
relative frequencies of the positive responses are calculated for each rawscore group and plotted
at the position of the corresponding person parameter. The other options use the default versions
of various smoothers: "tukey" (see smooth), "loess" (see loess),
and "kernel" (see ksmooth). For "loess" and "kernel" a further
element, smooth,
may be specified to control the span (default is 0.75) or the bandwith (default is 0.5),
respectively. For example, the specification could be empirical = list("loess", smooth=0.9)
or empirical = list("kernel",smooth=2).
Higher values result in smoother estimates of the empirical ICCs.
The optional confidence intervals are obtained by a procedure first given in
Clopper and Pearson (1934) based on the beta distribution (see binom.test).
For most of the plot options see plot and par.
Patrick Mair, Reinhold Hatzinger
## Not run: # Rating scale model, ICC plot for all items rsm.res <- RSM(rsmdat) thresholds(rsm.res) plotICC(rsm.res) # now items 1 to 4 in one figure without legends plotICC(rsm.res, item.subset = 1:4, mplot = TRUE, legpos = FALSE) # Rasch model for items 1 to 8 from raschdat1 # empirical ICCs displaying relative frequencies (default settings) rm8.res <- RM(raschdat1[,1:8]) plotICC(rm8.res, empICC=list("raw")) # the same but using different plotting styles plotICC(rm8.res, empICC=list("raw",type="b",col="blue",lty="dotted")) # kernel-smoothed empirical ICCs using bandwidth = 2 plotICC(rm8.res, empICC = list("kernel",smooth=3)) # raw empirical ICCs with confidence intervals # displaying only items 2,3,7,8 plotICC(rm8.res, item.subset=c(2,3,7,8), empICC=list("raw"), empCI=list()) # Joint ICC plot for items 2, 6, 8, and 15 for a Rasch model res <- RM(raschdat1) plotjointICC(res, item.subset = c(2,6,8,15), legpos = "left") ## End(Not run)## Not run: # Rating scale model, ICC plot for all items rsm.res <- RSM(rsmdat) thresholds(rsm.res) plotICC(rsm.res) # now items 1 to 4 in one figure without legends plotICC(rsm.res, item.subset = 1:4, mplot = TRUE, legpos = FALSE) # Rasch model for items 1 to 8 from raschdat1 # empirical ICCs displaying relative frequencies (default settings) rm8.res <- RM(raschdat1[,1:8]) plotICC(rm8.res, empICC=list("raw")) # the same but using different plotting styles plotICC(rm8.res, empICC=list("raw",type="b",col="blue",lty="dotted")) # kernel-smoothed empirical ICCs using bandwidth = 2 plotICC(rm8.res, empICC = list("kernel",smooth=3)) # raw empirical ICCs with confidence intervals # displaying only items 2,3,7,8 plotICC(rm8.res, item.subset=c(2,3,7,8), empICC=list("raw"), empCI=list()) # Joint ICC plot for items 2, 6, 8, and 15 for a Rasch model res <- RM(raschdat1) plotjointICC(res, item.subset = c(2,6,8,15), legpos = "left") ## End(Not run)
'eRm' objects
Calculates and plots the individual item-category information (type='category'), item information (type='item') or test/scale information (i.e., summed item information, type='scale' or 'test') ) as defined by Samejima (1969)
plotINFO(ermobject, type = "both", theta = seq(-6, 6, length.out = 1001L), legpos = "topright", ...)plotINFO(ermobject, type = "both", theta = seq(-6, 6, length.out = 1001L), legpos = "topright", ...)
ermobject |
An object of class |
type |
A string denoting the type of information to be
plotted. Currently supports |
theta |
Supporting or sampling points on the latent trait. |
legpos |
Defines the positioning of the legend, as in |
... |
Further arguments.
|
Thomas Rusch
Samejima, F. (1969) Estimation of latent ability using a response pattern of graded scores. Psychometric Monographs, 17.
The function to calculate the item or test information, item_info and test_info.
res <- PCM(pcmdat) plotINFO(res)res <- PCM(pcmdat) plotINFO(res)
A person-item map displays the location of item (and threshold) parameters as well as the distribution of person parameters.along the latent dimension. Person-item maps are useful to compare the range and position of the item measure distribution (lower panel) to the range and position of the person measure distribution (upper panel). Items should ideally be located along the whole scale to meaningfully measure the ‘ability’ of all persons.
plotPImap(object, item.subset = "all", sorted = FALSE, main = "Person-Item Map", latdim = "Latent Dimension", pplabel = "Person\nParameter\nDistribution", cex.gen = 0.7, xrange = NULL, warn.ord = TRUE, warn.ord.colour = "black", irug = TRUE, pp = NULL)plotPImap(object, item.subset = "all", sorted = FALSE, main = "Person-Item Map", latdim = "Latent Dimension", pplabel = "Person\nParameter\nDistribution", cex.gen = 0.7, xrange = NULL, warn.ord = TRUE, warn.ord.colour = "black", irug = TRUE, pp = NULL)
object |
Object of class |
item.subset |
Subset of items to be plotted. Either a numeric vector indicating
the column in |
sorted |
If |
main |
Main title of the plot. |
latdim |
Label of the x-axis, i.e., the latent dimension. |
pplabel |
Title for the upper panel displaying the person parameter distribution |
cex.gen |
|
xrange |
Range for the x-axis |
warn.ord |
If |
warn.ord.colour |
Nonordinal threshold locations for polytomous
items are coloured with this colour to make them more visible. This
is especially useful when there are many items so that the plot is
quite dense. The default is |
irug |
If |
pp |
If non- |
Item locations are displayed with bullets, threshold locations with circles.
Patrick Mair, Reinhold Hatzinger, patches from Julian Gilbey and Marco J. Maier
Bond, T.G., and Fox Ch.M. (2007) Applying the Rasch Model. Fundamental Measurement in the Human Sciences. 2nd Edition. Lawrence Erlbaum Associates.
res <- PCM(pcmdat) plotPImap(res, sorted=TRUE)res <- PCM(pcmdat) plotPImap(res, sorted=TRUE)
A Bond-and-Fox Pathway Map displays the location of each item or each person against its infit t-statistic. Pathway maps are useful for identifying misfitting items or misfitting persons. Items or people should ideally have a infit t-statistic lying between about -2 and +2, and these values are marked.
plotPWmap(object, pmap = FALSE, imap=TRUE, item.subset = "all", person.subset = "all", mainitem = "Item Map", mainperson = "Person Map", mainboth="Item/Person Map", latdim = "Latent Dimension", tlab = "Infit t statistic", pp = NULL, cex.gen = 0.6, cex.pch=1, person.pch = 1, item.pch = 16, personCI = NULL, itemCI = NULL, horiz=FALSE)plotPWmap(object, pmap = FALSE, imap=TRUE, item.subset = "all", person.subset = "all", mainitem = "Item Map", mainperson = "Person Map", mainboth="Item/Person Map", latdim = "Latent Dimension", tlab = "Infit t statistic", pp = NULL, cex.gen = 0.6, cex.pch=1, person.pch = 1, item.pch = 16, personCI = NULL, itemCI = NULL, horiz=FALSE)
object |
Object of class |
pmap |
Plot a person map if |
imap |
Plot an item map if |
item.subset |
Subset of items to be plotted for an item map.
Either a numeric vector indicating the item numbers or a character
vector indicating the item names. If |
person.subset |
Subset of persons to be plotted for a person map.
Either a numeric vector indicating the person numbers or a character
vector indicating the person names. If |
mainitem |
Main title of an item plot. |
mainperson |
Main title of a person plot. |
mainboth |
Main title of a person/item joint plot. |
latdim |
Label of the y-axis, i.e., the latent dimension. |
tlab |
Label of the x-axis, i.e., the t-statistic dimension. |
pp |
If non- |
cex.gen |
|
cex.pch |
applies to all plotting symbols. The default is 1. |
person.pch, item.pch
|
Specifies the symbol used for plotting
person data and item data respectively; the defaults are 1 and 16
respectively. See |
personCI, itemCI
|
Plotting confidence intervals for the the
person abilities and item difficulties. If The same goes for |
horiz |
if |
This code uses vertical(horizontal) error bars rather than circles or boxes to indicate standard errors. It also offers the possibility of plotting item or person data on its own; this can considerably simplify the reading of the plots for large datasets.
Julian Gilbey
Bond T.G., Fox C.M. (2007) Applying the Rasch Model: Fundamental Measurement in the Human Sciences (2nd ed.) chapter 3, Lawrence Erlbaum Associates, Inc.
Linacre J.M., Wright B.D. (1994) Dichotomous Infit and Outfit Mean-Square Fit Statistics / Chi-Square Fit Statistics. Rasch Measurement Transactions 8:2 p. 350, https://www.rasch.org/rmt/rmt82a.htm
Linacre J.M. (2002) What do Infit and Outfit, Mean-square and Standardized mean? Rasch Measurement Transactions 16:2 p. 878, https://www.rasch.org/rmt/rmt162f.htm
Wright B.D., Masters G.N. (1990) Computation of OUTFIT and INFIT Statistics. Rasch Measurement Transactions 3:4 p. 84–85, https://www.rasch.org/rmt/rmt34e.htm
res <- PCM(pcmdat) pparm <- person.parameter(res) plotPWmap(res, pp = pparm) plotPWmap(res, pp = pparm, pmap = TRUE)res <- PCM(pcmdat) pparm <- person.parameter(res) plotPWmap(res, pp = pparm) plotPWmap(res, pp = pparm, pmap = TRUE)
Plots trend effects over time.
plotTR(object, ...)plotTR(object, ...)
object |
an object of class |
... |
Additional parameters to be passed to and from other methods |
The plot is a lattice plot with one panel. The effects for each items are plotted over the different time points.
Please note that all effects are to be interpreted relative to the baseline (i.e. t1).
Currently, this function only works for a full item x treatment x timepoints LLRA. Collapsed effects will not be displayed properly.
Objects of class "llra" that contain estimates from a collapsed
data matrix will not be displayed correctly.
Thomas Rusch
The plot method for treatment effects "plotGR".
##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) summary(llra1) plotTR(llra1) ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. ex2 <- LLRA(llraDat2[1:20],mpoints=4,groups=llraDat2[21]) plotTR(ex2) ## End(Not run)##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) summary(llra1) plotTR(llra1) ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. ex2 <- LLRA(llraDat2[1:20],mpoints=4,groups=llraDat2[21]) plotTR(ex2) ## End(Not run)
Returns data matrix based on model probabilites. So far implemented for dichotomous models only.
## S3 method for class 'ppar' predict(object, cutpoint = "randomized", ...)## S3 method for class 'ppar' predict(object, cutpoint = "randomized", ...)
object |
Object of class |
cutpoint |
Either single integer value between 0 and 1 or |
... |
Additional arguments ignored |
A randomized assignment implies that for each cell an additional random number is drawn. If the model probability is larger than this value, the person gets 1 on this particular item, if smaller, 0 is assigned. Alternatively, a numeric probability cutpoint can be assigned and the 0-1 scoring is carried out according to the same rule.
Returns data matrix based on model probabilities
Patrick Mair, Reinhold Hatzinger
#Model-based data matrix for RSM res <- RM(raschdat2) pres <- person.parameter(res) predict(pres)#Model-based data matrix for RSM res <- RM(raschdat2) pres <- person.parameter(res) predict(pres)
Several methods for objects of class 'eRm'.
## S3 method for class 'eRm' print(x, ...) ## S3 method for class 'eRm' summary(object, ...) ## S3 method for class 'eRm' coef(object, parm="beta", ...) ## S3 method for class 'eRm' model.matrix(object, ...) ## S3 method for class 'eRm' vcov(object, ...) ## S3 method for class 'eRm' logLik(object, ...) ## S3 method for class 'eRm' confint(object, parm = "beta", level = 0.95, ...)## S3 method for class 'eRm' print(x, ...) ## S3 method for class 'eRm' summary(object, ...) ## S3 method for class 'eRm' coef(object, parm="beta", ...) ## S3 method for class 'eRm' model.matrix(object, ...) ## S3 method for class 'eRm' vcov(object, ...) ## S3 method for class 'eRm' logLik(object, ...) ## S3 method for class 'eRm' confint(object, parm = "beta", level = 0.95, ...)
x |
Object of class |
object |
Object of class |
parm |
Either |
level |
Alpha-level. |
... |
Further arguments to be passed to or from other methods. They are ignored in this function. |
The print method displays the value of
the log-likelihood, parameter estimates (basic parameters eta) and their standard errors.
For RM, RSM, and PCM models, the etas are difficulty parameters, for the LLTM, LRSM,
LPCM the sign of the parameters depend on the design matrix and are easiness effects by default.
The summary method additionally gives the full set of item parameters beta as
easiness parameters for all models.
Print methods are also available for the functions logLik and confint
(see below).
The methods below are extractor functions and return various quantities:
vcov returns the variance-covariance matrix of the parameter estimates,
coef a vector of estimates of the eta or beta basic parameters,
model.matrix the design matrix,
logLik an object with elements loglik and df containing
the log-likelihood value and df.
confint a matrix of confidence interval values for eta or beta.
Patrick Mair, Reinhold Hatzinger
res <- RM(raschdat1) res summary(res) coef(res) vcov(res) model.matrix(res) logLik(res)res <- RM(raschdat1) res summary(res) coef(res) vcov(res) model.matrix(res) logLik(res)
The package implements an MCMC algorithm for sampling of
binary matrices with fixed margins complying to the Rasch model.
Its stationary distribution is uniform. The algorithm also allows
for square matrices with fixed diagonal.
Parameter estimates in the Rasch model only depend on the marginal totals of
the data matrix that is used for the estimation. From this it follows that, if the
model is valid, all binary matrices with the same marginals as the observed one
are equally likely. For any statistic of the data matrix, one can approximate
the null distribution, i.e., the distribution if the Rasch model is valid, by taking
a random sample from the collection of equally likely data matrices and constructing
the observed distribution of the statistic.
One can then simply determine the exceedence probability of the statistic in the
observed sample, and thus construct a non-parametric test of the Rasch model.
The main purpose of this package is the implementation of a methodology to build nonparametric
tests for the Rasch model.
In the context of social network theories, where the structure of binary asymmetric
relations is studied, for example,
person esteems person , which correponds to a 1 in cell
of the associated adjacency matrix. If one wants to study
the distribution of a statistic defined on the adjacency matrix and conditional
on the marginal totals, one has to exclude the diagonal cells from consideration, i.e.,
by keeping the diagonal cells fixed at an arbitrary value. The RaschSampler package
has implemented an appropriate option, thus it can be also used for sampling random adjacency
matrices with given marginal totals.
| Package: | RaschSampler |
| Type: | Package |
| Version: | 0.8-6 |
| Date: | 2012-07-03 |
| License: | GNU GPL 2, June 1991 |
The user has to supply a binary input matrix. After defining appropriate control
parameters using rsctrl the sampling function rsampler
may be called to obtain an object of class RSmpl which contains the
generated random matrices in encoded form. After defining an appropriate function
to operate on a binary matrix (e.g., calculate a statistic such as phi.range)
the application of this function to the sampled matrices is performed
using rstats. Prior to applying the user defined function, rstats
decodes the matrices packed in the RSmpl-object.
The package also defines a utility function rsextrobj for extracting certains parts from
the RSmpl-object resulting in an object of class RSmplext.
Both types of objects can be saved and reloaded for later use.
Summary methods are available to print information on these objects, as well as
on the control object RSctr which is obtained from using
rsctrl containing the specification for the sampling routine.
The current implementation allows for data matrices up to 4096 rows and 128 columns.
This can be changed by setting nmax and kmax in RaschSampler.f90
to values which are a power of 2. These values should also be changed in rserror.R.
For convenience, we reuse the Fortran code of package version 0.8-1 which cicumvents the
compiler bug in Linux distributions of GCC 4.3. The following note from package version 0.8-3
is thus obsolete:
In case of compilation errors (due to a bug in Linux distributions of GCC 4.3) please use
RaschSampler.f90 from package version 0.8-1 and change nmax and kmax
accordingly (or use GCC 4.4).
Reinhold Hatzinger, Patrick Mair, Norman D. Verhelst
Verhelst, N. D. (2008) An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals. Psychometrika, Volume 73, Number 4
Verhelst, N. D., Hatzinger, R., and Mair, P. (2007) The Rasch Sampler, Journal of Statistical Software, Vol. 20, Issue 4, Feb 2007
This function computes the parameter estimates of a Rasch model for binary item responses by using CML estimation.
RM(X, W, se = TRUE, sum0 = TRUE, etaStart)RM(X, W, se = TRUE, sum0 = TRUE, etaStart)
X |
Input 0/1 data matrix or data frame; rows represent individuals, columns represent items. Missing values are inserted as |
W |
Design matrix for the Rasch model. If omitted, the function will compute W automatically. |
se |
If |
sum0 |
If |
etaStart |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |
For estimating the item parameters the CML method is used.
Available methods for RM-objects are:print, coef, model.matrix,
vcov, summary, logLik, person.parameter, LRtest,
Waldtest, plotICC, plotjointICC.
Returns an object of class dRm, Rm, eRm and contains the log-likelihood value, the parameter estimates and their standard errors.
loglik |
Conditional log-likelihood. |
iter |
Number of iterations. |
npar |
Number of parameters. |
convergence |
See |
etapar |
Estimated basic item difficulty parameters. |
se.eta |
Standard errors of the estimated basic item parameters. |
betapar |
Estimated item (easiness) parameters. |
se.beta |
Standard errors of item parameters. |
hessian |
Hessian matrix if |
W |
Design matrix. |
X |
Data matrix. |
X01 |
Dichotomized data matrix. |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
# Rasch model with beta.1 restricted to 0 res <- RM(raschdat1, sum0 = FALSE) res summary(res) res$W #generated design matrix # Rasch model with sum-0 beta restriction; no standard errors computed res <- RM(raschdat1, se = FALSE, sum0 = TRUE) res summary(res) res$W #generated design matrix #Rasch model with missing values res <- RM(raschdat2) res summary(res)# Rasch model with beta.1 restricted to 0 res <- RM(raschdat1, sum0 = FALSE) res summary(res) res$W #generated design matrix # Rasch model with sum-0 beta restriction; no standard errors computed res <- RM(raschdat1, se = FALSE, sum0 = TRUE) res summary(res) res$W #generated design matrix #Rasch model with missing values res <- RM(raschdat2) res summary(res)
The function implements an MCMC algorithm for sampling of binary matrices with fixed margins complying to the Rasch model. Its stationary distribution is uniform. The algorithm also allows for square matrices with fixed diagonal.
rsampler(inpmat, controls = rsctrl())rsampler(inpmat, controls = rsctrl())
inpmat |
A binary (data) matrix with |
controls |
An object of class |
rsampler is a wrapper function for a Fortran routine to generate binary random matrices based
on an input matrix.
On output the generated binary matrices are integer encoded. For further
processing of the generated matrices use the function rstats.
A list of class RSmpl with components
n |
number of rows of the input matrix |
k |
number of columns of the input matrix |
inpmat |
the input matrix |
tfixed |
|
burn_in |
length of the burn in process |
n_eff |
number of generated matrices (effective matrices) |
step |
controls the number number of void matrices generated in the the burn in
process and when effective matrices are generated (see note
in |
seed |
starting value for the random number generator |
n_tot |
number of matrices in |
outvec |
vector of encoded random matrices |
ier |
error code |
An element of outvec is a four byte (or 32 bits) integer.
The matrices to be output are stored bitwise (some bits are unused, since a integer is used for every row of a matrix).
So the number of integers per row needed equals (integer division), which is one to four in the present implementation since the number of columns and rows must not exceed 128 and 4096, respectively.
The summary method (summary.RSmpl) prints information on the content of the output object.
Reinhold Hatzinger, Norman Verhelst
Verhelst, N. D. (2008). An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals. Psychometrika, 73 (4)
data(xmpl) ctr<-rsctrl(burn_in=10, n_eff=5, step=10, seed=0, tfixed=FALSE) res<-rsampler(xmpl,ctr) summary(res)data(xmpl) ctr<-rsctrl(burn_in=10, n_eff=5, step=10, seed=0, tfixed=FALSE) res<-rsampler(xmpl,ctr) summary(res)
The object of class RSctr represents the control parameter
specification for the sampling function rsampler.
A legitimate RSctr object is a list with components
burn_in |
the number of matrices to be sampled to come close to a stationary distribution. |
n_eff |
the number of effective matrices, i.e.,
the number of matrices
to be generated by the sampling function |
step |
controls the number number of void matrices generated in the the burn in
process and when effective matrices are generated (see note
in |
seed |
is the indicator for the seed of the random number generator.
If the value of seed at equals zero, a seed is generated
by the sampling function |
tfixed |
|
This object is returned from function
rsctrl.
This class has a method for the generic summary
function.
Various parameters that control aspects of the random generation of binary matrices.
rsctrl(burn_in = 100, n_eff = 100, step = 16, seed = 0, tfixed = FALSE)rsctrl(burn_in = 100, n_eff = 100, step = 16, seed = 0, tfixed = FALSE)
burn_in |
the number of sampled matrices to
come close to a stationary distribution.
The default is |
n_eff |
the number of effective matrices, i.e., the number of matrices to be generated by the sampling function |
step |
controls the number number of void matrices generated in the the burn in
process and when effective matrices are generated (see note
below). The default is |
seed |
is the indicator for the seed of the random number generator.
Its value must be in the range 0 and 2147483646 (2**31-2).
If the value of seed equals zero, a seed is generated
by the sampling function |
tfixed |
logical, – specifies if in case of a quadratic input
matrix the diagonal is considered fixed (see note below).
The default is |
A list of class RSctr with components
burn_in, n_eff, step,
seed, tfixed.,
If one of the components is incorrectly specified
the error function rserror
is called and some informations are printed. The ouput object
will not be defined.
The specification of step controls the sampling algorithm as follows:
If , e.g., burn_in = 10, n_eff = 5, and step = 2,
then during the burn in period step * burn_in = 2 * 10
matrices are generated. After that, n_eff * step = 5 * 2 matrices
are generated and every second matrix of these last ten is returned from
link{rsampler}.tfixed has no effect if the input matrix is not quadratic,
i.e., all matrix elements are considered free (unrestricted).
If the input matrix is quadratic, and tfixed = TRUE,
the main diagonal of the matrix is considered as fixed.
On return from link{rsampler} all diagonal elements
of the generated matrices are set to zero.
This specification applies, e.g.,
to analyzing square incidence matrices
representing binary asymmetric relation
in social network theory.
The summary method (summary.RSctr) prints
the current definitions.
ctr <- rsctrl(n_eff = 1, seed = 987654321) # specify new controls summary(ctr) ## Not run: # incorrect specifications will lead to an error ctr2 <- rsctrl(step = -3, n_eff = 10000) ## End(Not run)ctr <- rsctrl(n_eff = 1, seed = 987654321) # specify new controls summary(ctr) ## Not run: # incorrect specifications will lead to an error ctr2 <- rsctrl(step = -3, n_eff = 10000) ## End(Not run)
Convenience function to extract a matrix.
rsextrmat(RSobj, mat.no = 1)rsextrmat(RSobj, mat.no = 1)
RSobj |
object as obtained from using |
mat.no |
number of the matrix to extract from the sample object. |
One of the matrices (either the original or a sampled matrix)
ctr <- rsctrl(burn_in = 10, n_eff = 3, step=10, seed = 0, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) all_m <- rsampler(mat, ctr) summary(all_m) # extract the third sampled matrix (here the fourth) third_m <- rsextrmat(all_m, 4) head(third_m)ctr <- rsctrl(burn_in = 10, n_eff = 3, step=10, seed = 0, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) all_m <- rsampler(mat, ctr) summary(all_m) # extract the third sampled matrix (here the fourth) third_m <- rsextrmat(all_m, 4) head(third_m)
Utility function to extract some of the generated matrices, still in encoded form.
rsextrobj(RSobj, start = 1, end = 8192)rsextrobj(RSobj, start = 1, end = 8192)
RSobj |
object as obtained from using |
start |
number of the matrix to start with. When specifying 1 (the default value) the original input matrix is included in the output object. |
end |
last matrix to be extracted. If |
A list of class RSmpl with components
n |
number of rows of the input matrix |
k |
number of columns of the input matrix |
inpmat |
the input matrix |
tfixed |
|
burn_in |
length of the burn in process |
n_eff |
number of generated matrices (effective matrices) |
step |
controls the number number of void matrices generated in the burn in
process and when effective matrices are generated (see note
in |
seed |
starting value for the random number generator |
n_tot |
number of matrices in |
outvec |
vector of encoded random matrices |
ier |
error code |
By default, all generated matrices plus
the original matrix (in position 1) are contained in
outvec, thus n_tot = n_eff + 1. If
the original matrix is not in outvec then
n_tot = n_eff.
For saving and loading objects
of class RSobj see the example below.
For extracting a decoded (directly usable) matrix use rsextrmat.
ctr <- rsctrl(burn_in = 10, n_eff = 3, step=10, seed = 0, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) all_m <- rsampler(mat, ctr) summary(all_m) some_m <- rsextrobj(all_m, 1, 2) summary(some_m) ## Not run: save(some_m, file = "some.RSobj.RData") rm(some_m) ls() load("some.RSobj.RData") summary(some_m) ## End(Not run)ctr <- rsctrl(burn_in = 10, n_eff = 3, step=10, seed = 0, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) all_m <- rsampler(mat, ctr) summary(all_m) some_m <- rsextrobj(all_m, 1, 2) summary(some_m) ## Not run: save(some_m, file = "some.RSobj.RData") rm(some_m) ls() load("some.RSobj.RData") summary(some_m) ## End(Not run)
This function computes the parameter estimates of a rating scale model for polytomous item responses by using CML estimation.
RSM(X, W, se = TRUE, sum0 = TRUE, etaStart)RSM(X, W, se = TRUE, sum0 = TRUE, etaStart)
X |
Input data matrix or data frame with item responses (starting from 0); rows represent individuals, columns represent items. Missing values are inserted as |
W |
Design matrix for the RSM. If omitted, the function will compute W automatically. |
se |
If |
sum0 |
If |
etaStart |
A vector of starting values for the eta parameters can be specified. If missing, the 0-vector is used. |
The design matrix approach transforms the RSM into a partial credit model
and estimates the corresponding basic parameters by using CML.
Available methods for RSM-objects are print, coef, model.matrix,
vcov, summary, logLik, person.parameters, plotICC, LRtest.
Returns an object of class 'Rm', 'eRm' and contains the log-likelihood value,
the parameter estimates and their standard errors.
loglik |
Conditional log-likelihood. |
iter |
Number of iterations. |
npar |
Number of parameters. |
convergence |
See |
etapar |
Estimated basic item difficulty parameters (item and category parameters). |
se.eta |
Standard errors of the estimated basic item parameters. |
betapar |
Estimated item-category (easiness) parameters. |
se.beta |
Standard errors of item parameters. |
hessian |
Hessian matrix if |
W |
Design matrix. |
X |
Data matrix. |
X01 |
Dichotomized data matrix. |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Mair, P., and Hatzinger, R. (2007). Extended Rasch modeling: The eRm package for the application of IRT models in R. Journal of Statistical Software, 20(9), 1-20.
Mair, P., and Hatzinger, R. (2007). CML based estimation of extended Rasch models with the eRm package in R. Psychology Science, 49, 26-43.
##RSM with 10 subjects, 3 items res <- RSM(rsmdat) res summary(res) #eta and beta parameters with CI thresholds(res) #threshold parameters##RSM with 10 subjects, 3 items res <- RSM(rsmdat) res summary(res) #eta and beta parameters with CI thresholds(res) #threshold parameters
The objects of class RSmpl and RSmplext contain
the original input matrix, the generated (encoded) random matrices, and
some information about the sampling process.
A list of class RSmpl or RSmplext with components
n |
number of rows of the input matrix |
k |
number of columns of the input matrix |
inpmat |
the input matrix |
tfixed |
|
burn_in |
length of the burn in process |
n_eff |
number of generated matrices (effective matrices) |
step |
controls the number number of void matrices generated in the the burn in
process and when effective matrices are generated (see note
in |
seed |
starting value for the random number generator |
n_tot |
number of matrices in |
outvec |
vector of encoded random matrices |
ier |
error code (see below) |
These classes of objects are returned from
rsampler and rsextrobj.
Both classes have methods for the generic summary
function.
By default, all generated matrices plus
the original matrix (in position 1) are contained in
outvec, thus n_tot = n_eff + 1. If
the original matrix is not in outvec then
n_tot = n_eff.
If ier is 0, no error was detected. Otherwise use
the error function rserror(ier) to obtain some informations.
For saving and loading objects
of class RSmpl or RSmplext
see the example in rsextrobj.
This function is used to calculate user defined statistics for the (original and) sampled matrices. A user defined function has to be provided.
rstats(RSobj, userfunc, ...)rstats(RSobj, userfunc, ...)
RSobj |
|
userfunc |
a user defined function which performs operations on the (original and) sampled matrices. The first argument in the definition of the user function must be an object of type matrix. |
... |
further arguments, that are passed to the user function |
A list of objects as specified in the user supplied function
The encoded matrices that are contained in the
input object RSobj are decoded and passed to the user function in turn.
If RSobj is not an object obtained from either rsampler
or rsextrobj or
no user function is specified an error message is printed.
A simple user function, phi.range, is included in
the RaschSampler package for demonstration purposes.
rstats can be used to obtain the 0/1 values for any
of the sampled matrices (see second example below). Please note,
that the output from the user function is stored in a list where
the number of components corresponds to the number of matrices passed
to the user function (see third example).
ctr <- rsctrl(burn_in = 10, n_eff = 5, step=10, seed = 12345678, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) rso <- rsampler(mat, ctr) rso_st <- rstats(rso,phi.range) unlist(rso_st) # extract the third generated matrix # (here, the first is the input matrix) # and decode it into rsmat rso2 <- rsextrobj(rso,4,4) summary(rso2) rsmat <- rstats(rso2, function(x) matrix(x, nr = rso2$n)) print(rsmat[[1]]) # extract only the first r rows of the third generated matrix mat<-function(x, nr = nr, r = 3){ m <- matrix(x, nr = nr) m[1:r,] } rsmat2 <- rstats(rso2, mat, nr=rso$n, r = 3) print(rsmat2[[1]]) # apply a user function to the decoded object print(phi.range(rsmat[[1]]))ctr <- rsctrl(burn_in = 10, n_eff = 5, step=10, seed = 12345678, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) rso <- rsampler(mat, ctr) rso_st <- rstats(rso,phi.range) unlist(rso_st) # extract the third generated matrix # (here, the first is the input matrix) # and decode it into rsmat rso2 <- rsextrobj(rso,4,4) summary(rso2) rsmat <- rstats(rso2, function(x) matrix(x, nr = rso2$n)) print(rsmat[[1]]) # extract only the first r rows of the third generated matrix mat<-function(x, nr = nr, r = 3){ m <- matrix(x, nr = nr) m[1:r,] } rsmat2 <- rstats(rso2, mat, nr=rso$n, r = 3) print(rsmat2[[1]]) # apply a user function to the decoded object print(phi.range(rsmat[[1]]))
This function calculates the proportion of person variance that is not due to error.
The concept of person separation reliability is very similar to reliability indices such as Cronbach's .
SepRel(pobject) ## S3 method for class 'eRm_SepRel' print(x, ...) ## S3 method for class 'eRm_SepRel' summary(object, ...)SepRel(pobject) ## S3 method for class 'eRm_SepRel' print(x, ...) ## S3 method for class 'eRm_SepRel' summary(object, ...)
pobject |
Object of class |
x |
Object of class |
object |
Object of class |
... |
Further arguments. |
Returns the person separation reliability where SSD is the squared standard deviation and MSE the mean squared error. Note that persons with raw scores of 0 or k are ignored in the computation.
Please note that the concept of reliability and associated problems are fundamentally different between IRT and CTT (Classical Test Theory). Separation reliability is more like a workaround to make the “change” from CTT to IRT easier for users by providing something “familiar.” Hence, we recommend not to put too much emphasis on this particular measure and use it with caution.
If you compare the separation reliability obtained using eRm with values by other software, you will find that they are most likely not equal. This has a couple of reasons, one of the most important is the employed estimation method.
eRm uses a conditional maximum likelihood (CML) framework and handles missing values as separate groups during the estimation of item parameters. Person parameters are computed in a second step using unconditional or joint maximum likelihood (UML or JML) estimation with item parameters assumed to be known from the first step. Other programs might do JML to estimate item and person parameters at the same time, or employ marginal maximum likelihood MML to estimate item parameters, assuming a certain distribution for person parameters. In the latter case person parameters might be obtained by various methods like EAP, MAP, .... Even CML-based programs yield different values, for example, if they use Warm's weighted maximum likelihood estimation WLE to compute person parameters in the second step.
The bottom line is that, since there is not “definite” solution for this problem, you will end up with different values under different circumstances. This is another reason to take results and implications with a grain of salt.
SepRel returns a list object of class eRm_SepRel containing:
sep.rel |
the person separation reliability, |
SSD.PS |
the squared standard deviation (i.e., total person variability), |
MSE |
the mean square measurement error (i.e., model error variance). |
Original code by Adrian Brügger ([email protected]), adapted by Marco J. Maier
Wright, B.D., and Stone, M.H. (1999). Measurement essentials. Wide Range Inc., Wilmington. (https://www.rasch.org/measess/me-all.pdf 28Mb).
# Compute Separation Reliability for a Rasch Model: pers <- person.parameter(RM(raschdat1)) res <- SepRel(pers) res summary(res)# Compute Separation Reliability for a Rasch Model: pers <- person.parameter(RM(raschdat1)) res <- SepRel(pers) res summary(res)
This utility function returns a 0-1 matrix violating the parallel ICC assumption in the Rasch model.
sim.2pl(persons, items, discrim = 0.25, seed = NULL, cutpoint = "randomized")sim.2pl(persons, items, discrim = 0.25, seed = NULL, cutpoint = "randomized")
persons |
Either a vector of person parameters or an integer indicating the number of persons (see details). |
items |
Either a vector of item parameters or an integer indicating the number of items (see details). |
discrim |
Standard deviation on the log scale. |
seed |
A seed for the random number generated can be set. |
cutpoint |
Either |
If persons and/or items (using single integers) are specified to determine the number of subjects or items, the corresponding parameter vector is drawn from N(0,1).
The cutpoint argument refers to the transformation of the theoretical probabilities into a 0-1 data matrix.
A randomized assingment implies that for each cell an additional random number is drawn.
If the model probability is larger than this value, the person gets 1 on this particular item, if smaller, 0 is assigned.
Alternatively, a numeric probability cutpoint can be assigned and the 0-1 scoring is carried out according to the same rule.
The discrim argument can be specified either as a vector of length items defining the item discrimination parameters in the 2-PL (e.g., c(1,1,0.5,1,1.5)), or as a single value.
In that case, the discrimination parameters are drawn from a lognormal distribution with meanlog = 0, where the specified value in discrim refers to the standard deviation on the log-scale.
The larger the values, the stronger the degree of Rasch violation.
Reasonable values are up to 0.5.
If 0, the data are Rasch homogeneous.
Su\'arez-Falc\'on, J. C., & Glas, C. A. W. (2003). Evaluation of global testing procedures for item fit to the Rasch model. British Journal of Mathematical and Statistical Society, 56, 127-143.
sim.rasch, sim.locdep, sim.xdim
#simulating 2-PL data #500 persons, 10 items, sdlog = 0.30, randomized cutpoint X <- sim.2pl(500, 10, discrim = 0.30) #item and discrimination parameters from uniform distribution, #cutpoint fixed dpar <- runif(50, 0, 2) ipar <- runif(50, -1.5, 1.5) X <- sim.2pl(500, ipar, dpar, cutpoint = 0.5)#simulating 2-PL data #500 persons, 10 items, sdlog = 0.30, randomized cutpoint X <- sim.2pl(500, 10, discrim = 0.30) #item and discrimination parameters from uniform distribution, #cutpoint fixed dpar <- runif(50, 0, 2) ipar <- runif(50, -1.5, 1.5) X <- sim.2pl(500, ipar, dpar, cutpoint = 0.5)
This utility function returns a 0-1 matrix violating the local independence assumption.
sim.locdep(persons, items, it.cor = 0.25, seed = NULL, cutpoint = "randomized")sim.locdep(persons, items, it.cor = 0.25, seed = NULL, cutpoint = "randomized")
persons |
Either a vector of person parameters or an integer indicating the number of persons (see details). |
items |
Either a vector of item parameters or an integer indicating the number of items (see details). |
it.cor |
Either a single correlation value between 0 and 1 or a positive semi-definite VC matrix. |
seed |
A seed for the random number generated can be set. |
cutpoint |
Either |
If persons or items is an integer value, the corresponding parameter vector
is drawn from N(0,1). The cutpoint argument refers to the transformation of the theoretical
probabilities into a 0-1 data matrix. A randomized assingment implies that for each cell an
additional random number is drawn. If the model probability is larger than this value,
the person gets 1 on this particular item, if smaller, 0 is assigned. Alternatively, a numeric probability cutpoint can be assigned and the 0-1 scoring is carried out according to the same rule.
The argument it.cor reflects the pair-wise inter-item correlation. If this should be constant
across the items, a single value between 0 (i.e. Rasch model) and 1 (strong violation) can be specified.
Alternatively, a symmetric VC-matrix of dimension number of items can be defined.
Jannarone, R. J. (1986). Conjunctive item response theory kernels. Psychometrika, 51, 357-373.
Su\'arez-Falc\'on, J. C., & Glas, C. A. W. (2003). Evaluation of global testing procedures for item fit to the Rasch model. British Journal of Mathematical and Statistical Society, 56, 127-143.
#simulating locally-dependent data #500 persons, 10 items, inter-item correlation of 0.5 X <- sim.locdep(500, 10, it.cor = 0.5) #500 persons, 4 items, correlation matrix specified sigma <- matrix(c(1,0.2,0.2,0.3,0.2,1,0.4,0.1,0.2,0.4,1,0.8,0.3,0.1,0.8,1), ncol = 4) X <- sim.locdep(500, 4, it.cor = sigma)#simulating locally-dependent data #500 persons, 10 items, inter-item correlation of 0.5 X <- sim.locdep(500, 10, it.cor = 0.5) #500 persons, 4 items, correlation matrix specified sigma <- matrix(c(1,0.2,0.2,0.3,0.2,1,0.4,0.1,0.2,0.4,1,0.8,0.3,0.1,0.8,1), ncol = 4) X <- sim.locdep(500, 4, it.cor = sigma)
This utility function returns a 0-1 matrix which fits the Rasch model.
sim.rasch(persons, items, seed = NULL, cutpoint = "randomized")sim.rasch(persons, items, seed = NULL, cutpoint = "randomized")
persons |
Either a vector of person parameters or an integer indicating the number of persons (see details) |
items |
Either a vector of item parameters or an integer indicating the number of items (see details) |
seed |
A seed for the random number generated can be set. |
cutpoint |
Either |
If persons or items is an integer value, the corresponding parameter vector is drawn from N(0,1). The cutpoint argument refers to the transformation of the theoretical probabilities into a 0-1 data matrix. A randomized assingment implies that for each cell an additional random number is drawn. If the model probability is larger than this value, the person gets 1 on this particular item, if smaller, 0 is assigned. Alternatively, a numeric probability cutpoint can be assigned and the 0-1 scoring is carried out according to the same rule.
Su\'arez-Falc\'on, J. C., & Glas, C. A. W. (2003). Evaluation of global testing procedures for item fit to the Rasch model. British Journal of Mathematical and Statistical Society, 56, 127-143.
#simulating Rasch homogenous data #100 persons, 10 items, parameter drawn from N(0,1) X <- sim.rasch(100, 10) #person parameters drawn from uniform distribution, fixed cutpoint ppar <- runif(100,-2,2) X <- sim.rasch(ppar, 10, cutpoint = 0.5)#simulating Rasch homogenous data #100 persons, 10 items, parameter drawn from N(0,1) X <- sim.rasch(100, 10) #person parameters drawn from uniform distribution, fixed cutpoint ppar <- runif(100,-2,2) X <- sim.rasch(ppar, 10, cutpoint = 0.5)
This utility function simulates a 0-1 matrix violating the unidimensionality assumption in the Rasch model.
sim.xdim(persons, items, Sigma, weightmat, seed = NULL, cutpoint = "randomized")sim.xdim(persons, items, Sigma, weightmat, seed = NULL, cutpoint = "randomized")
persons |
Either a matrix (each column corresponds to a dimension) of person parameters or an integer indicating the number of persons (see details). |
items |
Either a vector of item parameters or an integer indicating the number of items (see details). |
Sigma |
A positive-definite symmetric matrix specifying the covariance matrix of the variables. |
weightmat |
Matrix for item-weights for each dimension (columns). |
seed |
A seed for the random number generated can be set. |
cutpoint |
Either |
If persons is specified as matrix, Sigma is ignored. If items is
an integer value, the corresponding parameter vector is drawn from N(0,1).
The cutpoint argument refers to the transformation of the theoretical probabilities
into a 0-1 data matrix. A randomized assingment implies that for each cell an additional random
number is drawn. If the model probability is larger than this value, the person gets 1 on
this particular item, if smaller, 0 is assigned. Alternatively, a numeric probability
cutpoint can be assigned and the 0-1 scoring is carried out according to the same rule.
If weightmat is not specified, a random indicator matrix is generated where each item is a measurement
of only one dimension. For instance, the first row for a 3D-model could be (0,1,0) which means
that the first item measures the second dimension only. This corresponds to the between-item
multidimensional model presented by Adams et al. (1997).
Sigma reflects the VC-structure for the person parameters drawn from a multivariate
standard normal distribution. Thus, the diagonal elements are typically 1 and the lower the
covariances in the off-diagonal, the stronger the model violation.
Adams, R. J., Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21, 1-23.
Glas, C. A. W. (1992). A Rasch model with a multivariate distribution of ability. In M. Wilson (Ed.), Objective Measurement: Foundations, Recent Developments, and Applications (pp. 236-258). Norwood, NJ: Ablex.
sim.rasch, sim.locdep, sim.2pl
# 500 persons, 10 items, 3 dimensions, random weights. Sigma <- matrix(c(1, 0.01, 0.01, 0.01, 1, 0.01, 0.01, 0.01, 1), 3) X <- sim.xdim(500, 10, Sigma) #500 persons, 10 items, 2 dimensions, weights fixed to 0.5 itemvec <- runif(10, -2, 2) Sigma <- matrix(c(1, 0.05, 0.05, 1), 2) weights <- matrix(0.5, ncol = 2, nrow = 10) X <- sim.xdim(500, itemvec, Sigma, weightmat = weights)# 500 persons, 10 items, 3 dimensions, random weights. Sigma <- matrix(c(1, 0.01, 0.01, 0.01, 1, 0.01, 0.01, 0.01, 1), 3) X <- sim.xdim(500, 10, Sigma) #500 persons, 10 items, 2 dimensions, weights fixed to 0.5 itemvec <- runif(10, -2, 2) Sigma <- matrix(c(1, 0.05, 0.05, 1), 2) weights <- matrix(0.5, ncol = 2, nrow = 10) X <- sim.xdim(500, itemvec, Sigma, weightmat = weights)
This function eliminates items stepwise according to one of the following criteria: itemfit, Wald test, Andersen's LR-test
## S3 method for class 'eRm' stepwiseIt(object, criterion = list("itemfit"), alpha = 0.05, verbose = TRUE, maxstep = NA)## S3 method for class 'eRm' stepwiseIt(object, criterion = list("itemfit"), alpha = 0.05, verbose = TRUE, maxstep = NA)
object |
Object of class |
criterion |
List with either |
alpha |
Significance level. |
verbose |
If |
maxstep |
Maximum number of elimination steps. If |
If criterion = list("itemfit") the elimination stops when none of the p-values
in itemfit is significant. Within each step the item with the largest chi-squared
itemfit value is excluded.
If criterion = list("Waldtest") the elimination stops when none of the p-values
resulting from the Wald test is significant. Within each step the item with the largest z-value in
Wald test is excluded.
If criterion = list("LRtest") the elimination stops when Andersen's LR-test is not
significant. Within each step the item with the largest z-value in Wald test is excluded.
The function returns an object of class step containing:
X |
Reduced data matrix (bad items eliminated) |
fit |
Object of class |
it.elim |
Vector contaning the names of the eliminated items |
res.wald |
Elimination results for Wald test criterion |
res.itemfit |
Elimination results for itemfit criterion |
res.LR |
Elimination results for LR-test criterion |
nsteps |
Number of elimination steps |
LRtest.Rm, Waldtest.Rm, itemfit.ppar
## 2pl-data, 100 persons, 10 items set.seed(123) X <- sim.2pl(500, 10, 0.4) res <- RM(X) ## elimination according to itemfit stepwiseIt(res, criterion = list("itemfit")) ## Wald test based on mean splitting stepwiseIt(res, criterion = list("Waldtest","mean")) ## Andersen LR-test based on random split set.seed(123) groupvec <- sample(1:3, 500, replace = TRUE) stepwiseIt(res, criterion = list("LRtest",groupvec))## 2pl-data, 100 persons, 10 items set.seed(123) X <- sim.2pl(500, 10, 0.4) res <- RM(X) ## elimination according to itemfit stepwiseIt(res, criterion = list("itemfit")) ## Wald test based on mean splitting stepwiseIt(res, criterion = list("Waldtest","mean")) ## Andersen LR-test based on random split set.seed(123) groupvec <- sample(1:3, 500, replace = TRUE) stepwiseIt(res, criterion = list("LRtest",groupvec))
summary method for class "llra"
## S3 method for class 'llra' summary(object, level, ...) ## S3 method for class 'summary.llra' print(x, ...)## S3 method for class 'llra' summary(object, level, ...) ## S3 method for class 'summary.llra' print(x, ...)
object |
an object of class "llra", typically result of a call to
|
x |
an object of class "summary.llra", usually, a result of a call
to |
level |
The level of confidence for the confidence intervals. Default is 0.95. |
... |
further arguments passed to or from other methods. |
Objects of class "summary.llra" contain all parameters of interest plus the confidence intervals.
print.summary.llra rounds the values to 3 digits and displays
them nicely.
The function summary.lllra computes and returns a list of
summary statistics of the fitted LLRA given in object, reusing the
components (list elements) call, etapar,
iter, loglik, model, npar and se.etapar from its argument, plus
ci |
The upper and lower confidence interval borders. |
Thomas Rusch
The model fitting function LLRA.
##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) summary(llra1) ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. ex2 <- LLRA(llraDat2[1:20],mpoints=4,llraDat2[21]) sumEx2 <- summary(ex2, level=0.95) #print a summary sumEx2 #get confidence intervals sumEx2$ci ## End(Not run)##Example 6 from Hatzinger & Rusch (2009) groups <- c(rep("TG",30),rep("CG",30)) llra1 <- LLRA(llradat3,mpoints=2,groups=groups) summary(llra1) ## Not run: ##An LLRA with 2 treatment groups and 1 baseline group, 5 items and 4 ##time points. Item 1 is dichotomous, all others have 3, 4, 5, 6 ##categories respectively. ex2 <- LLRA(llraDat2[1:20],mpoints=4,llraDat2[21]) sumEx2 <- summary(ex2, level=0.95) #print a summary sumEx2 #get confidence intervals sumEx2$ci ## End(Not run)
Prints the current definitions for the sampling function.
## S3 method for class 'RSctr' summary(object, ...)## S3 method for class 'RSctr' summary(object, ...)
object |
object of class |
... |
potential further arguments (ignored) |
ctr <- rsctrl(n_eff = 1, seed = 123123123) # specify controls summary(ctr)ctr <- rsctrl(n_eff = 1, seed = 123123123) # specify controls summary(ctr)
Prints a summary list for sample objects of class RSmpl
and RSmplext.
## S3 method for class 'RSmpl' summary(object, ...) ## S3 method for class 'RSmplext' summary(object, ...)## S3 method for class 'RSmpl' summary(object, ...) ## S3 method for class 'RSmplext' summary(object, ...)
object |
object as obtained from |
... |
potential further arguments (ignored) |
Describes the status of an sample object.
ctr <- rsctrl(burn_in = 10, n_eff = 3, step=10, seed = 0, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) all_m <- rsampler(mat, ctr) summary(all_m) some_m <- rsextrobj(all_m, 1, 2) summary(some_m)ctr <- rsctrl(burn_in = 10, n_eff = 3, step=10, seed = 0, tfixed = FALSE) mat <- matrix(sample(c(0,1), 50, replace = TRUE), nr = 10) all_m <- rsampler(mat, ctr) summary(all_m) some_m <- rsextrobj(all_m, 1, 2) summary(some_m)
eRm objects
Calculates the information of a test or a scale as the sum of Samejima's (1969) information for all items.
test_info(ermobject, theta=seq(-5,5,0.01))test_info(ermobject, theta=seq(-5,5,0.01))
ermobject |
An object of class |
theta |
Supporting or sampling points on the latent trait. |
The function test_info calculates the test or scale information of the
whole set of items in the 'eRm' object.
Returns the vector of test information for all values of theta.
Thomas Rusch
Samejima, F. (1969) Estimation of latent ability using a response pattern of graded scores. Psychometric Monographs, 17.
The function to calculate the item information, item_info
and the plot function plotINFO.
res <- PCM(pcmdat) tinfo <- test_info(res) plotINFO(res, type="test")res <- PCM(pcmdat) tinfo <- test_info(res) plotINFO(res, type="test")
This function transforms the beta parameters into threshold parameters. These can be interpreted by means of log-odds as visualized in ICC plots.
## S3 method for class 'eRm' thresholds(object) ## S3 method for class 'threshold' print(x, ...) ## S3 method for class 'threshold' summary(object, ...) ## S3 method for class 'threshold' confint(object, parm, level = 0.95, ...)## S3 method for class 'eRm' thresholds(object) ## S3 method for class 'threshold' print(x, ...) ## S3 method for class 'threshold' summary(object, ...) ## S3 method for class 'threshold' confint(object, parm, level = 0.95, ...)
Arguments for thresholds:
object |
Object of class |
Arguments for print, summary, and confint methods:
x |
Object of class |
parm |
Parameter specification (ignored). |
level |
Alpha-level. |
... |
Further arguments to be passed to methods. They are ignored. |
For dichotomous models (i.e., RM and LLTM) threshold parameters are not computed.
The print method returns a location parameter for each item which is the
mean of the corresponding threshold parameters. For LPCM and LRSM the thresholds are
computed for each design matrix block (i.e., measurement point/group) separately
(PCM and RSM have only 1 block).
The function thresholds returns an object of class threshold containing:
threshpar |
Vector with threshold parameters. |
se.thresh |
Vector with standard errors. |
threshtable |
Data frame with location and threshold parameters. |
Andrich, D. (1978). Application of a psychometric rating model to ordered categories which are scored with successive integers. Applied Psychological Measurement, 2, 581-594.
#Threshold parameterization for a rating scale model res <- RSM(rsmdat) th.res <- thresholds(res) th.res confint(th.res) summary(th.res) #Threshold parameters for a PCM with ICC plot res <- PCM(pcmdat) th.res <- thresholds(res) th.res plotICC(res) #Threshold parameters for a LPCM: #Block 1: t1, g1; Block 2: t1, g2; ...; Block 6: t2,g3 G <- c(rep(1,7),rep(2,7),rep(3,6)) # group vector for 3 groups res <- LPCM(lpcmdat, mpoints = 2, groupvec = G) th.res <- thresholds(res) th.res#Threshold parameterization for a rating scale model res <- RSM(rsmdat) th.res <- thresholds(res) th.res confint(th.res) summary(th.res) #Threshold parameters for a PCM with ICC plot res <- PCM(pcmdat) th.res <- thresholds(res) th.res plotICC(res) #Threshold parameters for a LPCM: #Block 1: t1, g1; Block 2: t1, g2; ...; Block 6: t2,g3 G <- c(rep(1,7),rep(2,7),rep(3,6)) # group vector for 3 groups res <- LPCM(lpcmdat, mpoints = 2, groupvec = G) th.res <- thresholds(res) th.res
Performs a Wald test on item-level by splitting subjects into subgroups.
## S3 method for class 'Rm' Waldtest(object, splitcr = "median") ## S3 method for class 'wald' print(x,...)## S3 method for class 'Rm' Waldtest(object, splitcr = "median") ## S3 method for class 'wald' print(x,...)
object |
Object of class |
splitcr |
Split criterion for subject raw score splitting. |
x |
Object of class |
... |
Further arguments passed to or from other methods. They are ignored in this function. |
Items are eliminated if they not have the same number of categories in each subgroup.
To avoid this problem, for RSM and PCM it is considered to use a random or another user-defined split.
If the data set contains missing values and mean or median is specified as splitcriterion,
means or medians are calculated for each missing value subgroup and consequently used for raw score splitting.
Returns an object of class wald containing:
coef.table |
Data frame with test statistics, z- and p-values. |
betapar1 |
Beta parameters for first subgroup |
se.beta1 |
Standard errors for first subgroup |
betapar2 |
Beta parameters for second subgroup |
se.beta2 |
Standard errors for second subgroup |
se.beta2 |
Standard errors for second subgroup |
spl.gr |
Names and levels for |
call |
The matched call. |
Patrick Mair, Reinhold Hatzinger
Fischer, G. H., and Molenaar, I. (1995). Rasch Models - Foundations, Recent Developements, and Applications. Springer.
Fischer, G. H., and Scheiblechner, H. (1970). Algorithmen und Programme fuer das probabilistische Testmodell von Rasch [Algorithms and programs for Rasch's probabilistic test model]. Psychologische Beitraege, 12, 23-51.
#Wald test for Rasch model with user-defined subject split res <- RM(raschdat2) splitvec <- sample(1:2,25,replace=TRUE) Waldtest(res, splitcr = splitvec)#Wald test for Rasch model with user-defined subject split res <- RM(raschdat2) splitvec <- sample(1:2,25,replace=TRUE) Waldtest(res, splitcr = splitvec)
Ficitious data sets - matrices with binary responses
data(xmpl)data(xmpl)
The format of xmpl is:
300 rows (referring to subjects)
30 columns (referring to items)
The format of xmplbig is:
4096 rows (referring to subjects)
128 columns (referring to items) xmplbig has the maximum dimensions that the RaschSampler package
can handle currently.
data(xmpl) print(head(xmpl))data(xmpl) print(head(xmpl))