Simulate data from polytomous logitnormit (graded logistic) model
1  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) = { 1Ψ (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 < m1, Ψ (α_i,k+1 + β_i*η) if k_i = m1}.
Where the items are y_i, i = 1, …, n, and response categories are k=0, …, m1. 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
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