simulpln {pln} | R Documentation |
Simulate data from polytomous logit-normit (graded logistic) model
simulpln(n,nitem,ncat,alphas,betas)
n |
Number of responses to generate. |
nitem |
Number of items. |
ncat |
Number of categories for the items. |
alphas |
A vector of length |
betas |
A vector of length |
Data from graded logistic models is generated under the following parameterization:
Pr(y_i = k_i| η) = { 1-Ψ (α_i,k + β_i*η) if k_i = 0, Ψ (α_i,k + β_i*η) - Ψ (α_i,k+1 + β_i*η) if 0 < k_i < m-1, Ψ (α_i,k+1 + β_i*η) if k_i = m-1}.
Where the items are y_i, i = 1, …, n, and response categories are k=0, …, m-1. η is the latent trait, Ψ is the logistic distribution function, α is an intercept (cutpoint) parameter, and β is a slope parameter. When the number of categories for the items is 2, this reduceds to the 2PL parameterization:
Pr(y_i = 1| η) = Ψ (α_1 + β_i η)
A data matrix in which each row represents a response pattern and the final column represents the frequency of each response pattern.
Carl F. Falk cffalk@gmail.com, Harry Joe
n<-500; ncat<-3; nitem<-5 alphas=c(0,-.5, .2,-1, .4,-.6, .3,-.2, .5,-.5) betas=c(1,1,1,.5,.5) set.seed(1234567) datfr<-simulpln(n,nitem,ncat,alphas,betas) nrmleplnout<-nrmlepln(datfr, ncat=ncat, nitem=nitem) nrmleplnout