vcov.RdComputes the asymptotic covariance matrix for
din objects. The covariance matrix is computed using the
empirical cross-product approach (see Paek & Cai, 2014).
In addition, an S3 method IRT.se is defined which produces
an extended output including vcov and confint.
# S3 method for din
vcov(object, extended=FALSE, infomat=FALSE,ind.item.skillprobs=TRUE,
ind.item=FALSE, diagcov=FALSE, h=.001,...)
# S3 method for din
confint(object, parm, level=.95, extended=FALSE,
ind.item.skillprobs=TRUE, ind.item=FALSE, diagcov=FALSE, h=.001, ... )
IRT.se(object, ...)
# S3 method for din
IRT.se( object, extended=FALSE, parm=NULL, level=.95,
infomat=FALSE, ind.item.skillprobs=TRUE, ind.item=FALSE,
diagcov=FALSE, h=.001, ... )An object inheriting from class din.
An optional logical indicating whether the covariance matrix should be calculated for an extended set of parameters (estimated and derived parameters).
An optional logical indicating whether the information matrix instead of the covariance matrix should be the output.
Optional logical indicating whether the covariance between item parameters and skill class probabilities are assumed to be zero.
Optional logical indicating whether covariances of item parameters between different items are zero.
Optional logical indicating whether all covariances between estimated parameters are set to zero.
Parameter used for numerical differentiation for computing the derivative of the log-likelihood function.
Vector of parameters. If it is missing, then for all estimated parameters a confidence interval is calculated.
Confidence level
Additional arguments to be passed.
coef: A vector of parameters.
vcov: A covariance matrix. The corresponding coefficients can be extracted
as the attribute coef from this object.
IRT.se: A data frame containing coefficients, standard errors
and confidence intervals for all parameters.
Paek, I., & Cai, L. (2014). A comparison of item parameter standard error estimation procedures for unidimensional and multidimensional item response theory modeling. Educational and Psychological Measurement, 74(1), 58-76.
if (FALSE) {
#############################################################################
# EXAMPLE 1: DINA model sim.dina
#############################################################################
data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")
dat <- sim.dina
q.matrix <- sim.qmatrix
#****** Model 1: DINA Model
mod1 <- CDM::din( dat, q.matrix=q.matrix, rule="DINA")
# look into parameter table of the model
mod1$partable
# covariance matrix
covmat1 <- vcov(mod1 )
# extract coefficients
coef(mod1)
# extract standard errors
sqrt( diag( covmat1))
# compute confidence intervals
confint( mod1, level=.90 )
# output table with standard errors
IRT.se( mod1, extended=TRUE )
#****** Model 2: Constrained DINA Model
# fix some slipping parameters
constraint.slip <- cbind( c(2,3,5), c(.15,.20,.25) )
# set some skill class probabilities to zero
zeroprob.skillclasses <- c(2,4)
# estimate model
mod2 <- CDM::din( dat, q.matrix=q.matrix, guess.equal=TRUE,
constraint.slip=constraint.slip, zeroprob.skillclasses=zeroprob.skillclasses)
# parameter table
mod2$partable
# freely estimated coefficients
coef(mod2)
# covariance matrix (estimated parameters)
vmod2a <- vcov(mod2)
sqrt( diag( vmod2a)) # standard errors
colnames( vmod2a )
names( attr( vmod2a, "coef") ) # extract coefficients
# covariance matrix (more parameters, extended=TRUE)
vmod2b <- vcov(mod2, extended=TRUE)
sqrt( diag( vmod2b))
attr( vmod2b, "coef")
# attach standard errors to parameter table
partable2 <- mod2$partable
partable2 <- partable2[ ! duplicated( partable2$parnames ), ]
partable2 <- data.frame( partable2, "se"=sqrt( diag( vmod2b)) )
partable2
# confidence interval for parameter "skill1" which is not in the model
# cannot be calculated!
confint(mod2, parm=c( "skill1", "all_guess" ) )
# confidence interval for only some parameters
confint(mod2, parm=paste0("prob_skill", 1:3 ) )
# compute only information matrix
infomod2 <- vcov(mod2, infomat=TRUE)
}