sim.gdina.RdThe function sim.gdina.prepare creates necessary design matrices
Mj, Aj and necc.attr. In most cases, only the list
of item parameters delta must be modified by the user when
applying the simulation function sim.gdina. The distribution of latent
classes \(\alpha\) is represented by an underlying multivariate normal distribution
\(\alpha^\ast\) for which a mean vector thresh.alpha and a
covariance matrix cov.alpha must be specified.
Alternatively, a matrix of skill classes alpha
can be given as an input.
Note that this version of sim.gdina only works for dichotomous attributes.
sim.gdina(n, q.matrix, delta, link="identity", thresh.alpha=NULL, cov.alpha=NULL, alpha=NULL, Mj, Aj, necc.attr) sim.gdina.prepare( q.matrix )
| n | Number of persons |
|---|---|
| q.matrix | Q-matrix (see |
| delta | List with \(J\) entries where \(J\) is the number of items. Every list element corresponds to the parameter of an item. |
| link | Link function. Choices are |
| thresh.alpha | Vector of thresholds (means) of \(\alpha^\ast\) |
| cov.alpha | Covariance matrix of \(\alpha^\ast\) |
| alpha | Matrix of skill classes if they should not be simulated |
| Mj | Design matrix, see |
| Aj | Design matrix, see |
| necc.attr | List with \(J\) entries containing necessary attributes for each item |
The output of sim.gdina is a list with following entries:
Simulated item responses
Data frame with simulated attributes
Used Q-matrix
Used delta item parameters
Design matrices \(A_j\)
Design matrices \(M_j\)
Used link function
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179--199.
For estimating the GDINA model see gdina.
See the GDINA::simGDINA function in the
GDINA package for similar functionality.
See sim_model for a general simulation function.
############################################################################# # EXAMPLE 1: Simulating the GDINA model ############################################################################# n <- 50 # number of persons # define Q-matrix q.matrix <- matrix( c(1,1,0, 0,1,1, 1,0,1, 1,0,0, 0,0,1, 0,1,0, 1,1,1, 0,1,1, 0,1,1), ncol=3, byrow=TRUE) # thresholds for attributes alpha^\ast thresh.alpha <- c( .65, 0, -.30 ) # covariance matrix for alpha^\ast cov.alpha <- matrix(1,3,3) cov.alpha[1,2] <- cov.alpha[2,1] <- .4 cov.alpha[1,3] <- cov.alpha[3,1] <- .6 cov.alpha[3,2] <- cov.alpha[2,3] <- .8 # prepare design matrix by applying sim.gdina.prepare function rp <- CDM::sim.gdina.prepare( q.matrix ) delta <- rp$delta necc.attr <- rp$necc.attr Aj <- rp$Aj Mj <- rp$Mj # define delta parameters # intercept - main effects - second order interactions - ... str(delta) #=> modify the delta parameter list which contains only zeroes as default ## List of 9 ## $ : num [1:4] 0 0 0 0 ## $ : num [1:4] 0 0 0 0 ## $ : num [1:4] 0 0 0 0 ## $ : num [1:2] 0 0 ## $ : num [1:2] 0 0 ## $ : num [1:2] 0 0 ## $ : num [1:8] 0 0 0 0 0 0 0 0 ## $ : num [1:4] 0 0 0 0 ## $ : num [1:4] 0 0 0 0 delta[[1]] <- c( .2, .1, .15, .4 ) delta[[2]] <- c( .2, .3, .3, -.2 ) delta[[3]] <- c( .2, .2, .2, 0 ) delta[[4]] <- c( .15, .6 ) delta[[5]] <- c( .1, .7 ) delta[[6]] <- c( .25, .65 ) delta[[7]] <- c( .25, .1, .1, .1, 0, 0, 0, .25 ) delta[[8]] <- c( .2, 0, .3, -.1 ) delta[[9]] <- c( .2, .2, 0, .3 ) #****************************************** # Now, the "real simulation" starts sim.res <- CDM::sim.gdina( n=n, q.matrix=q.matrix, delta=delta, link="identity", thresh.alpha=thresh.alpha, cov.alpha=cov.alpha, Mj=Mj, Aj=Aj, necc.attr=necc.attr) # sim.res$data # simulated data # sim.res$alpha # simulated alpha if (FALSE) { ############################################################################# # EXAMPLE 2: Simulation based on already estimated GDINA model for data.ecpe ############################################################################# data(data.ecpe) dat <- data.ecpe$data q.matrix <- data.ecpe$q.matrix #*** # (1) estimate GDINA model mod <- CDM::gdina( data=dat[,-1], q.matrix=q.matrix ) #*** # (2) simulate data according to GDINA model set.seed(977) # prepare design matrix by applying sim.gdina.prepare function rp <- CDM::sim.gdina.prepare( q.matrix ) necc.attr <- rp$necc.attr # number of subjects to be simulated n <- 3000 # simulate attribute patterns probs <- mod$attribute.patt$class.prob # probabilities patt <- mod$attribute.patt.splitted # response patterns alpha <- patt[ sample( 1:(length(probs) ), n, prob=probs, replace=TRUE), ] # simulate data using estimated item parameters sim.res <- CDM::sim.gdina( n=n, q.matrix=q.matrix, delta=mod$delta, link="identity", alpha=alpha, Mj=mod$Mj, Aj=mod$Aj, necc.attr=rp$necc.attr) # extract data dat <- sim.res$data ############################################################################# # EXAMPLE 3: Simulation based on already estimated RRUM model for data.ecpe ############################################################################# dat <- CDM::data.ecpe$data q.matrix <- CDM::data.ecpe$q.matrix #*** # (1) estimate reduced RUM model mod <- CDM::gdina( data=dat[,-1], q.matrix=q.matrix, rule="RRUM" ) summary(mod) #*** # (2) simulate data according to RRUM model set.seed(977) # prepare design matrix by applying sim.gdina.prepare function rp <- CDM::sim.gdina.prepare( q.matrix ) necc.attr <- rp$necc.attr # number of subjects to be simulated n <- 5000 # simulate attribute patterns probs <- mod$attribute.patt$class.prob # probabilities patt <- mod$attribute.patt.splitted # response patterns alpha <- patt[ sample( 1:(length(probs) ), n, prob=probs, replace=TRUE), ] # simulate data using estimated item parameters sim.res <- CDM::sim.gdina( n=n, q.matrix=q.matrix, delta=mod$delta, link=mod$link, alpha=alpha, Mj=mod$Mj, Aj=mod$Aj, necc.attr=rp$necc.attr) # extract data dat <- sim.res$data }