item.gpcm: Estimates item parameters of LMA with linear restrictions on category scores

Description

This function is internal to the function 'fit.gpcm' and performs the item regressions. It is a core function of the pseudo-likelihood algorithm for items of the GPCM. The function calls function 'itemGPCM.data' to create the data for input into 'mlogit', which is use to fit a conditional multinomial model for each item. The up-dated scale values are put into the Master data frame and the 'item.log' array. It generally would not run outside of 'fit.gpcm' or 'ple.lma'.

Usage

item.gpcm(
  Master,
  item.log,
  Phi.mat,
  fitem,
  TraitByTrait,
  PersonByItem,
  npersons,
  nitems,
  ncat,
  nless,
  ntraits,
  Maxnphi,
  pq.mat,
  starting.sv,
  LambdaName
)

Arguments

Master

Master data frame

item.log

History over iterations of items' log likelihood and estimates of lambda, and item parameters

Phi.mat

Starting value of matrix of association parameters (optional)

fitem

Formula for item regressions

TraitByTrait

Trait adjacency matrix (same as inTraitAdj)

PersonByItem

Same as inData

npersons

Number of persons

nitems

Number of items

ncat

Number of categories per item

nless

Number of unique lambdas and unique nus per item

ntraits

Number of latent traits

Maxnphi

Number of phi parameters to bet estimated (NULL for 1 dimensional)

pq.mat

Used to compute rest-scores and totals

starting.sv

Fixed category scores

LambdaName

Lambda names for formula for items item regressions

Value

Master Master data frame with up-dated category scores for items

item.log Up-dated history array over iterations of the algorithm of items' log likelihood and estimated lambda and alpha parameters