fit.rasch: Fits an LMA using fixed category scores
In pleLMA: Pseudo-Likelihood Estimation of Log-Multiplicative Association Models

Description Usage Arguments Value Examples

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.

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

`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

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)

 #---  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)