Estimation of the Rasch Model with Variational Approximation
This function estimates the Rasch model by the estimation method of variational approximation (Rijmen & Vomlel, 2008).
rasch.va(dat, globconv=0.001, maxiter=1000)
dat |
Data frame with dichotomous item responses |
globconv |
Convergence criterion for item parameters |
maxiter |
Maximal number of iterations |
A list with following entries:
sig |
Standard deviation of the trait |
item |
Data frame with item parameters |
xsi.ij |
Data frame with variational parameters ξ_{ij} |
mu.i |
Vector with individual means μ_i |
sigma2.i |
Vector with individual variances σ_i^2 |
Rijmen, F., & Vomlel, J. (2008). Assessing the performance of variational methods for mixed logistic regression models. Journal of Statistical Computation and Simulation, 78, 765-779.
############################################################################# # EXAMPLE 1: Rasch model ############################################################################# set.seed(8706) N <- 5000 I <- 20 dat <- sirt::sim.raschtype( stats::rnorm(N,sd=1.3), b=seq(-2,2,len=I) ) # estimation via variational approximation mod1 <- sirt::rasch.va(dat) # estimation via marginal maximum likelihood mod2 <- sirt::rasch.mml2(dat) # estmation via joint maximum likelihood mod3 <- sirt::rasch.jml(dat) # compare sigma round( c( mod1$sig, mod2$sd.trait ), 3 ) ## [1] 1.222 1.314 # compare b round( cbind( mod1$item$b, mod2$item$b, mod3$item$itemdiff), 3 ) ## [,1] [,2] [,3] ## [1,] -1.898 -1.967 -2.090 ## [2,] -1.776 -1.841 -1.954 ## [3,] -1.561 -1.618 -1.715 ## [4,] -1.326 -1.375 -1.455 ## [5,] -1.121 -1.163 -1.228
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