fit.rasch {pleLMA}

Fits an LMA using fixed category scores

Description

The LMA model with fixed category scores is fit by this function and the model corresponds to models in the Rasch family of item response models. The category scores can be set by either the user or the package defaults. The default category scores are equally spaced, sum to zero, and sum of squares equal 1. Scores can be set by user by specifying them in the item by category matrix of 'starting.sv'. The pseudo-likelihood algorithm only runs a single stacked regression. This functionis called from' ple.lma' but can also be run outside of the main wrapper function.

Usage

fit.rasch(
  Master,
  npersons,
  nitems,
  ncat,
  nless,
  Maxnphi,
  pq.mat,
  starting.sv,
  LambdaNames,
  PhiNames,
  ItemNames,
  LambdaName,
  ntraits
)

Arguments

Master

Master data set in long format

npersons

Number of persons

nitems

Number of items

ncat

Number of categories

nless

Number of unique Lambdas (i.e., ncat-1)

Maxnphi

Number of phi parameters

pq.mat

One dimensional array to compute rest-scores

starting.sv

Fixed category scores

LambdaNames

Names of lambda paramters in Master and formula for stacked regression

PhiNames

Names of association parameters

ItemNames

Names of items

LambdaName

Names of lambdas used in output

ntraits

Number of traits

Value

estimates An item by parameter matrix of the maximum of the log likelihood, estimated item parameters (i.e., Lambdas), and the values of the fixed category scores.

fstack Formula for stacked regression

phi.mlogit Results from mlogit for stacked regression

estimates An item x parameter estimate matrix and fixed category scores used

Phi.mat Estimated phi parameters

mlpl.phi Value of maximum of log pseudo-likelihood function from the stacked regression

AIC Akaike information criterion for pseudo-likelihood (smaller is better)

BIC Bayesian information criterion for pseudo-likelihood (smaller is better)

Examples

 #---  data(dass)
 inData <- dass[1:250,c("d1", "d2", "d3", "a1","a2","a3","s1","s2","s3")]
 #--- unidimensional
 inTraitAdj  <- matrix(1, nrow=1, ncol=1)
 inItemTraitAdj <- matrix(1, nrow=9, ncol=1)

 s <- set.up(inData, model.type='rasch', inTraitAdj, inItemTraitAdj)

 r <- fit.rasch(s$Master, s$npersons, s$nitems, s$ncat, s$nless, s$Maxnphi,
          s$pq.mat, s$starting.sv, s$LambdaNames, s$PhiNames, s$ItemNames,
          s$LambdaName, s$ntraits)