, Jimmy de la Torre
[aut] , Jingping Du
[ctb]| Title: | Latent Transition Cognitive Diagnosis Model with Covariates |
|---|---|
| Description: | Implementation of the three-step approach of latent transition cognitive diagnosis model (CDM) with covariates. This approach can be used to assess changes in attribute mastery status and to evaluate the covariate effects on both the initial states and transition probabilities over time using latent logistic regression. Because stepwise approaches often yield biased estimates, correction for classification error probabilities (CEPs) is considered in this approach. The three-step approach for latent transition CDM with covariates involves the following steps: (1) fitting a CDM to the response data without covariates at each time point separately, (2) assigning examinees to latent states at each time point and computing the associated CEPs, and (3) estimating the latent transition CDM with the known CEPs and computing the regression coefficients. The method was proposed in Liang et al. (2023) <doi:10.3102/10769986231163320> and demonstrated using mental health data in Liang et al. (in press; annotated R code and data utilized in this example are available in Mendeley data) <doi:10.17632/kpjp3gnwbt.1>. |
| Authors: | Qianru Liang [aut, cre, cph]
, Jimmy de la Torre
[aut] , Jingping Du
[ctb] |
| Maintainer: | Qianru Liang <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.0 |
| Built: | 2024-12-12 06:49:03 UTC |
| Source: | CRAN |
The classification error probabilities (CEP) can be obtained in this data example.
cepcep
A list containing:
cep.matrixEach of the 4 lists includes two 2 by 2 matrices.
wEach of the 4 lists includes two 2005 by 2 matrices.
mpEach of the 4 lists includes two 2005 by 4 matrices.
eapEach of the 4 lists includes two 2005 by 4 matrices.
Function to compute classification error probabilities (CEP) for attributes at different time points. Only attribute-level CEP is available for the time being.
CEP_t(fit.object, t, K, N)CEP_t(fit.object, t, K, N)
fit.object |
a list of the G-DINA model objects return from |
t |
the number of time points. This package can only handle two time points can for the time being. |
K |
the number of attributes. |
N |
the number of examinees (observations). |
a list with elements
the CEP matrix
the correction weights
the estimated marginal posterior probabilities obtained from GDINA R package
the estimated EAP of attribute profiles obtained from GDINA R package
Liang, Q., de la Torre, J., & Law, N. (2023).Latent transition cognitive diagnosis model with covariates: A three-step approach. Journal of Educational and Behavioral Statistics. doi:10.3102/10769986231163320
Huebner, A., & Wang, C. (2011).A note on comparing examinee classification methods for cognitive diagnosis models. Educational and Psychological Measurement, 71, 407-419. doi:10.1177/0013164410388832
if(requireNamespace("GDINA")){ library(GDINA) # Assuming dat0, dat1, Q, and other necessary data and objects are predefined. rdmodel <- c("GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA", "GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA", "GDINA","GDINA","GDINA","GDINA","RRUM","GDINA","GDINA","GDINA", "GDINA","LLM","LLM","RRUM","ACDM","GDINA","GDINA","GDINA", "GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA") fitrd <- GDINA(dat = dat0, Q = Q, model= rdmodel, mono.constraint = TRUE, verbose=0) # Obtained the item parameters from Tan et al. (2022) itemparm.rd = GDINA::extract(fitrd,"catprob.parm") # Fit the response data at pre-test to the selected models fit.t1 = GDINA(dat = dat1[,3:42], Q = Q, mono.constraint = TRUE, model = rdmodel, catprob.parm = itemparm.rd, att.dist = "independent", control=list(maxitr = 0), verbose=0) # Fit the response data at post-test to the selected models fit.t2 = GDINA(dat = dat1[,43:82], Q = Q, mono.constraint = TRUE, model = rdmodel, catprob.parm = itemparm.rd, att.dist = "independent", control=list(maxitr = 0), verbose=0) fit.object = list() fit.object[[1]] <- fit.t1 fit.object[[2]] <- fit.t2 t = 2 # the number of time points K = ncol(Q) # the number of attributes N = nrow(dat1) # the number of observations cep = CEP_t(fit.object = fit.object, t = t, K = K, N = N) # The CEP matrices of the attributes cep$cep.matrix }if(requireNamespace("GDINA")){ library(GDINA) # Assuming dat0, dat1, Q, and other necessary data and objects are predefined. rdmodel <- c("GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA", "GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA", "GDINA","GDINA","GDINA","GDINA","RRUM","GDINA","GDINA","GDINA", "GDINA","LLM","LLM","RRUM","ACDM","GDINA","GDINA","GDINA", "GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA","GDINA") fitrd <- GDINA(dat = dat0, Q = Q, model= rdmodel, mono.constraint = TRUE, verbose=0) # Obtained the item parameters from Tan et al. (2022) itemparm.rd = GDINA::extract(fitrd,"catprob.parm") # Fit the response data at pre-test to the selected models fit.t1 = GDINA(dat = dat1[,3:42], Q = Q, mono.constraint = TRUE, model = rdmodel, catprob.parm = itemparm.rd, att.dist = "independent", control=list(maxitr = 0), verbose=0) # Fit the response data at post-test to the selected models fit.t2 = GDINA(dat = dat1[,43:82], Q = Q, mono.constraint = TRUE, model = rdmodel, catprob.parm = itemparm.rd, att.dist = "independent", control=list(maxitr = 0), verbose=0) fit.object = list() fit.object[[1]] <- fit.t1 fit.object[[2]] <- fit.t2 t = 2 # the number of time points K = ncol(Q) # the number of attributes N = nrow(dat1) # the number of observations cep = CEP_t(fit.object = fit.object, t = t, K = K, N = N) # The CEP matrices of the attributes cep$cep.matrix }
The dataset of time point 1 used in (Tan et al., 2023).
dat0dat0
A data frame with 719 rows and 40 columns.
The longitudinal dataset used in this example. Items with a prefix "a" are for the pre-test, and items with a prefix "b" are for the post-test.
dat1dat1
A data frame with 2005 rows and 82 columns.
Function to estimate the latent logistic regression models at the initial state and transition
L_step3(par, z_t1, z_t2, weight, k)L_step3(par, z_t1, z_t2, weight, k)
par |
Coefficients of latent logistic regression to be estimated. |
z_t1 |
covariates at Time 1, which has already had the intercept column (1s). |
z_t2 |
covariates at Time 2, which has already had the intercept column (1s). |
weight |
Correction weight obtained from CEP. |
k |
The k-th attribute. |
log-likelihood value.
Liang, Q., de la Torre, J., & Law, N. (2023). Latent transition cognitive diagnosis model with covariates: A three-step approach. Journal of Educational and Behavioral Statistics.doi:10.3102/10769986231163320
The Q-matrix empirically validated by Tan et al.(2023).
QQ
A data frame with 40 rows and 4 columns.
Step 3 estimation for latent logistic regression coefficients
step3.est( cep, z_t1, z_t2, K, t, beta_in = matrix(0, ncol(z_t1), K), ga01_in = matrix(0, ncol(z_t2), K), ga10_in = matrix(0, ncol(z_t2)) )step3.est( cep, z_t1, z_t2, K, t, beta_in = matrix(0, ncol(z_t1), K), ga01_in = matrix(0, ncol(z_t2), K), ga10_in = matrix(0, ncol(z_t2)) )
cep |
estimated classification error probabilities returned from |
z_t1 |
covariates at Time 1, which has already had the intercept column (1s). |
z_t2 |
covariates at Time 2, which has already had the intercept column (1s). |
K |
the number of attributes. |
t |
the number of time points. This package can only handle two time points can for the time being. |
beta_in |
the initial values for the regression coefficients at Time 1 (initial state). Default are 0s. |
ga01_in |
the initial values for the regression coefficients of transition from absence (0) to presence (1) at Time 2. Default are 0s. |
ga10_in |
the initial values for the regression coefficients of transition from presence (1) to absence (0) at Time 2. Default are 0s. |
a list with elements
A data frame with 2 rows and 4 columns, representing the estimated regression coefficients at Time 1 (initial state)
A data frame with 4 rows and 4 columns, representing the estimated regression coefficients of transition from absence (0) to presence (1) at Time 2
A data frame with 4 rows and 4 columns, representing the estimated regression coefficients of transition from absence (0) to presence (1) at Time 2
A data frame with dimensions 40 by 9, containing the results of the estimation, including all regression coefficients and the corresponding odds ratios, Cohen's d, standard errors (SE), 95% confidence intervals, and p-values.
t = 2 # the number of time points K = ncol(Q) # the number of attributes z_t1_test = matrix(sample(c(0, 1), size = 20, replace = TRUE), nrow = 10) z_t2_test = matrix(sample(c(0, 1), size = 40, replace = TRUE), nrow = 10) # Set appropriate initial values of the coefficients # Initial values of initial state's regression coefficients beta_in = matrix(0, ncol(z_t1_test), K) # Initial values of transition probability's regression coefficients # These were computed using the raw data. # When Gender coding is 1 = male, 0 = female: ga01_in = cbind(c(-2.15, 0.56, 0.09, -0.79), c(-1.6, 0.05, -0.01, -0.38), c(-1.25, 0.06, -0.25, 0.14), c(-1.18, -0.26, 0.04, 0.37)) #initial values of regression coefficients (for transition from 0 to 1) ga10_in = cbind(c(-0.84, -0.18, -0.14, 0.23), c(-0.18, 0.49, 0.44, -0.35), c(-0.22, 0.18, 0.37, -0.45), c(-0.49, 0.10, 0.43, 0.20)) cep_test = list() cep_test[["mp"]][[1]] = matrix(runif(40,min = 0,max=1),nrow = 10) cep_test[["mp"]][[2]] = matrix(runif(40,min = 0,max=1),nrow = 10) cep_test[["eap"]][[1]] = matrix(runif(40,min = 0,max=1),nrow = 10) cep_test[["eap"]][[2]] = matrix(runif(40,min = 0,max=1),nrow = 10) for (i in 1:4){ cep_test[["cep_matrix"]][[i]]=list() cep_test[["w"]][[i]]=list() for (k in 1:2) { cep_test[["cep_matrix"]][[i]][[k]]=matrix(c(1,0.02,0.06,1),nrow = 2) cep_test[["w"]][[i]][[k]] = matrix(runif(20,min = 0,max=1),nrow = 10) } } step3.output_test <- step3.est(cep = cep_test, z_t1 = z_t1_test, z_t2 = z_t2_test, K = K, t = t, beta_in, ga01_in, ga10_in) ## Not run: # The run is dependent on the output of the CEP_t() function # And the process time takes more than 5s. # It is not recommended to run it. # Covariates Z = dat1[, c(1,2)] # use intervention and gender as covariates z_t1 = cbind(1, Z$gender) # Covariate at time 1 z_t2 = cbind(1, Z$gender, Z$intervention, apply(Z,1,prod)) # Covariates at time 2 colnames(z_t1) <- c("intercept", "gender") colnames(z_t2) <- c("intercept", "gender", "intervention", "intervention_gender") t = 2 # the number of time points K = ncol(Q) # the number of attributes # Set appropriate initial values of the coefficients # Initial values of initial state's regression coefficients beta_in = matrix(0, ncol(z_t1), K) # Initial values of transition probability's regression coefficients # These were computed using the raw data. # When Gender coding is 1 = male, 0 = female: ga01_in = cbind(c(-2.15, 0.56, 0.09, -0.79), c(-1.6, 0.05, -0.01, -0.38), c(-1.25, 0.06, -0.25, 0.14), c(-1.18, -0.26, 0.04, 0.37)) #initial values of regression coefficients (for transition from 0 to 1) ga10_in = cbind(c(-0.84, -0.18, -0.14, 0.23), c(-0.18, 0.49, 0.44, -0.35), c(-0.22, 0.18, 0.37, -0.45), c(-0.49, 0.10, 0.43, 0.20)) #initial values of regression coefficients (for transition from 1 to 0) # Step 3 estimation (This will take a few minutes) step3.output <- step3.est(cep = cep, z_t1 = z_t1, z_t2 = z_t2, K = K, t = t, beta_in = beta_in, ga01_in = ga01_in, ga10_in = ga10_in) # Obtain estimation results step3.output$result # Latent logistic regression coefficients beta = step3.output$beta gamma_01 = step3.output$gamma_01 gamma_10 = step3.output$gamma_10 ## End(Not run)t = 2 # the number of time points K = ncol(Q) # the number of attributes z_t1_test = matrix(sample(c(0, 1), size = 20, replace = TRUE), nrow = 10) z_t2_test = matrix(sample(c(0, 1), size = 40, replace = TRUE), nrow = 10) # Set appropriate initial values of the coefficients # Initial values of initial state's regression coefficients beta_in = matrix(0, ncol(z_t1_test), K) # Initial values of transition probability's regression coefficients # These were computed using the raw data. # When Gender coding is 1 = male, 0 = female: ga01_in = cbind(c(-2.15, 0.56, 0.09, -0.79), c(-1.6, 0.05, -0.01, -0.38), c(-1.25, 0.06, -0.25, 0.14), c(-1.18, -0.26, 0.04, 0.37)) #initial values of regression coefficients (for transition from 0 to 1) ga10_in = cbind(c(-0.84, -0.18, -0.14, 0.23), c(-0.18, 0.49, 0.44, -0.35), c(-0.22, 0.18, 0.37, -0.45), c(-0.49, 0.10, 0.43, 0.20)) cep_test = list() cep_test[["mp"]][[1]] = matrix(runif(40,min = 0,max=1),nrow = 10) cep_test[["mp"]][[2]] = matrix(runif(40,min = 0,max=1),nrow = 10) cep_test[["eap"]][[1]] = matrix(runif(40,min = 0,max=1),nrow = 10) cep_test[["eap"]][[2]] = matrix(runif(40,min = 0,max=1),nrow = 10) for (i in 1:4){ cep_test[["cep_matrix"]][[i]]=list() cep_test[["w"]][[i]]=list() for (k in 1:2) { cep_test[["cep_matrix"]][[i]][[k]]=matrix(c(1,0.02,0.06,1),nrow = 2) cep_test[["w"]][[i]][[k]] = matrix(runif(20,min = 0,max=1),nrow = 10) } } step3.output_test <- step3.est(cep = cep_test, z_t1 = z_t1_test, z_t2 = z_t2_test, K = K, t = t, beta_in, ga01_in, ga10_in) ## Not run: # The run is dependent on the output of the CEP_t() function # And the process time takes more than 5s. # It is not recommended to run it. # Covariates Z = dat1[, c(1,2)] # use intervention and gender as covariates z_t1 = cbind(1, Z$gender) # Covariate at time 1 z_t2 = cbind(1, Z$gender, Z$intervention, apply(Z,1,prod)) # Covariates at time 2 colnames(z_t1) <- c("intercept", "gender") colnames(z_t2) <- c("intercept", "gender", "intervention", "intervention_gender") t = 2 # the number of time points K = ncol(Q) # the number of attributes # Set appropriate initial values of the coefficients # Initial values of initial state's regression coefficients beta_in = matrix(0, ncol(z_t1), K) # Initial values of transition probability's regression coefficients # These were computed using the raw data. # When Gender coding is 1 = male, 0 = female: ga01_in = cbind(c(-2.15, 0.56, 0.09, -0.79), c(-1.6, 0.05, -0.01, -0.38), c(-1.25, 0.06, -0.25, 0.14), c(-1.18, -0.26, 0.04, 0.37)) #initial values of regression coefficients (for transition from 0 to 1) ga10_in = cbind(c(-0.84, -0.18, -0.14, 0.23), c(-0.18, 0.49, 0.44, -0.35), c(-0.22, 0.18, 0.37, -0.45), c(-0.49, 0.10, 0.43, 0.20)) #initial values of regression coefficients (for transition from 1 to 0) # Step 3 estimation (This will take a few minutes) step3.output <- step3.est(cep = cep, z_t1 = z_t1, z_t2 = z_t2, K = K, t = t, beta_in = beta_in, ga01_in = ga01_in, ga10_in = ga10_in) # Obtain estimation results step3.output$result # Latent logistic regression coefficients beta = step3.output$beta gamma_01 = step3.output$gamma_01 gamma_10 = step3.output$gamma_10 ## End(Not run)
The output of step 3 estimation can be obtained in this data example.
step3.outputstep3.output
A list containing:
betaA data frame with 2 rows and 4 columns.
gamma_01A data frame with 4 rows and 4 columns.
gamma_10A data frame with 4 rows and 4 columns.
resultA list containing the results of the estimation, with dimensions 40 by 9.
Function to compute transition matrix using classification results
trans.matrix(X)trans.matrix(X)
X |
a matrix containing the initial state (first column) and the transition state (second column). |
a 2 2 matrix where rows represent initial states (0 and 1) and the columns represent transition states (0 and 1).
initial_states <- c(1, 2, 1, 2) final_states <- c(1, 1, 2, 2) transition_matrix <- trans.matrix(data.frame(initial_states, final_states)) print(transition_matrix) ## Not run: # transition probabilities (corrected and updated) t = 2 # the number of time points K = ncol(Q) # the number of attributes Z = dat1[, c(1,2)] z_t1 = cbind(1, Z$gender) # Covariate at time 1 z_t2 = cbind(1, Z$gender, Z$intervention, apply(Z,1,prod)) # Covariates at time 2 beta = step3.output$beta gamma_01 = step3.output$gamma_01 gamma_10 = step3.output$gamma_10 updated.class <- update.class(cep = cep, K = K, t = t, z_t1 = z_t1, z_t2 = z_t2, beta = beta, gamma_01 = gamma_01, gamma_10 = gamma_10) C.eap.t1 = updated.class$cor.profile[[1]] C.eap.t2 = updated.class$cor.profile[[2]] C.eap.t1t2 <- cbind(z_t2, C.eap.t1, C.eap.t2) t.A1.c = trans.matrix(as.matrix(C.eap.t1t2[,c("A1_t1","A1_t2")])) t.A1.c ## End(Not run)initial_states <- c(1, 2, 1, 2) final_states <- c(1, 1, 2, 2) transition_matrix <- trans.matrix(data.frame(initial_states, final_states)) print(transition_matrix) ## Not run: # transition probabilities (corrected and updated) t = 2 # the number of time points K = ncol(Q) # the number of attributes Z = dat1[, c(1,2)] z_t1 = cbind(1, Z$gender) # Covariate at time 1 z_t2 = cbind(1, Z$gender, Z$intervention, apply(Z,1,prod)) # Covariates at time 2 beta = step3.output$beta gamma_01 = step3.output$gamma_01 gamma_10 = step3.output$gamma_10 updated.class <- update.class(cep = cep, K = K, t = t, z_t1 = z_t1, z_t2 = z_t2, beta = beta, gamma_01 = gamma_01, gamma_10 = gamma_10) C.eap.t1 = updated.class$cor.profile[[1]] C.eap.t2 = updated.class$cor.profile[[2]] C.eap.t1t2 <- cbind(z_t2, C.eap.t1, C.eap.t2) t.A1.c = trans.matrix(as.matrix(C.eap.t1t2[,c("A1_t1","A1_t2")])) t.A1.c ## End(Not run)
Function to update classifications (attribute profiles) using the Bayes' Theorem
update_class(cep, K, t, z_t1, z_t2, beta, gamma_01, gamma_10)update_class(cep, K, t, z_t1, z_t2, beta, gamma_01, gamma_10)
cep |
estimated classification error probabilities returned from |
K |
the number of attributes. |
t |
the number of time points. This package can only handle two time points can for the time being. |
z_t1 |
covariates at Time 1, which has already had the intercept column (1s). |
z_t2 |
covariates at Time 2, which has already had the intercept column (1s). |
beta |
the estimated regression coefficients at Time 1 (initial state) |
gamma_01 |
the estimated regression coefficients of transition from absence (0) to presence (1) at Time 2 |
gamma_10 |
the estimated regression coefficients of transition from absence (0) to presence (1) at Time 2 |
a list with elements
the corrected and updated posterior probability
the corrected and updated attribute prevalance
the corrected and updated attribute profiles for different time points
Liang, Q., de la Torre, J., & Law, N. (2023). Latent transition cognitive diagnosis model with covariates: A three-step approach. Journal of Educational and Behavioral Statistics.doi:10.3102/10769986231163320
## Not run: #The run is dependent on the output of the step3.est() function and CEP_t() function #It is not recommended for run it. t = 2 # the number of time points K = ncol(Q) # the number of attributes Z = dat1[, c(1,2)] z_t1 = cbind(1, Z$gender) # Covariate at time 1 z_t2 = cbind(1, Z$gender, Z$intervention, apply(Z,1,prod)) # Covariates at time 2 beta = step3.output$beta gamma_01 = step3.output$gamma_01 gamma_10 = step3.output$gamma_10 # Update classifications using the Bayes' Theorem updated.class <- update.class(cep = cep, K = K, t = t, z_t1 = z_t1, z_t2 = z_t2, beta = beta, gamma_01 = gamma_01, gamma_10 = gamma_10) # The corrected and updated attribute prevalance updated.class$att.prevalance # The corrected and updated posterior probability updated.class$post.prob ## End(Not run)## Not run: #The run is dependent on the output of the step3.est() function and CEP_t() function #It is not recommended for run it. t = 2 # the number of time points K = ncol(Q) # the number of attributes Z = dat1[, c(1,2)] z_t1 = cbind(1, Z$gender) # Covariate at time 1 z_t2 = cbind(1, Z$gender, Z$intervention, apply(Z,1,prod)) # Covariates at time 2 beta = step3.output$beta gamma_01 = step3.output$gamma_01 gamma_10 = step3.output$gamma_10 # Update classifications using the Bayes' Theorem updated.class <- update.class(cep = cep, K = K, t = t, z_t1 = z_t1, z_t2 = z_t2, beta = beta, gamma_01 = gamma_01, gamma_10 = gamma_10) # The corrected and updated attribute prevalance updated.class$att.prevalance # The corrected and updated posterior probability updated.class$post.prob ## End(Not run)