Simulation of the GDINA model
The 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 α is represented by an underlying multivariate normal distribution
α^\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 α^\ast |
cov.alpha |
Covariance matrix of α^\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:
data |
Simulated item responses |
alpha |
Data frame with simulated attributes |
q.matrix |
Used Q-matrix |
delta |
Used delta item parameters |
Aj |
Design matrices A_j |
Mj |
Design matrices M_j |
link |
Used link function |
The function sim.gdina.prepare possesses the following values as output
in a list: delta, necc.attr, Aj and Mj.
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
## Not run:
#############################################################################
# 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
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.