pln (version 0.2-3)

simulpln: Simulate data from polytomous logit-normit (graded logistic) model

Description

Simulate data from polytomous logit-normit (graded logistic) model

Usage

simulpln(n, nitem, ncat, alphas, betas)

Value

A data matrix in which each row represents a response pattern and the final column represents the frequency of each response pattern.

Arguments

n

Number of responses to generate.

nitem

Number of items.

ncat

Number of categories for the items.

alphas

A vector of length nitem\(\times\)(ncat-1) corresponding to true values for the (decreasing) cutpoints for the items.

betas

A vector of length nitem corresponding to values for the beta vectors of slopes.

Author

Carl F. Falk , Harry Joe

Details

Data from graded logistic models is generated under the following parameterization: $$Pr(y_i = k_i| \eta) = \left\{ \begin{array}{ll} 1-\Psi (\alpha_{i,k} + \beta_i \eta) & \mbox{if } k_i = 0\\ \Psi (\alpha_{i,k} + \beta_i \eta) - \Psi (\alpha_{i,k+1} + \beta_i \eta) & \mbox{if } 0 < k_i < m-1\\ \Psi (\alpha_{i,k+1} + \beta_i \eta) & \mbox{if } k_i = m-1 \end{array} \right. $$ Where the items are \(y_i, i = 1, \dots, n\), and response categories are \(k=0, \dots, m-1\). \(\eta\) is the latent trait, \(\Psi\) is the logistic distribution function, \(\alpha\) is an intercept (cutpoint) parameter, and \(\beta\) is a slope parameter. When the number of categories for the items is 2, this reduces to the 2PL parameterization: $$Pr(y_i = 1| \eta) = \Psi (\alpha_1 + \beta_i \eta)$$

See Also

nrmlepln nrmlerasch nrbcpln

Examples

   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