fit.gpcm {pleLMA}

Fits LMA model where category scale values equal a_im * x_j

Description

Function estimates the parameters of LMA models with fixed category scores multiplied by an item weight parameter. This function can be used to estimate the LMA model corresponding to is a generalized partial credit model for multi-category items and the 2 parameter logistic model for dichotomous items. The function sets up log objects and model formula. In the case of unidimensional models, the function iterates over item regressions; whereas, for multidimensional models, the function iterates between the item and phi regressions. This function is called from 'ple.lma', but can be run outside of 'ple.lma'.

Usage

fit.gpcm(
  Master,
  Phi.mat,
  PersonByItem,
  TraitByTrait,
  item.by.trait,
  tol,
  npersons,
  nitems,
  ncat,
  nless,
  ntraits,
  Maxnphi,
  pq.mat,
  starting.sv,
  ItemNames,
  LambdaName,
  LambdaNames,
  PhiNames
)

Arguments

Master

Master data set in long format

Phi.mat

Matrix of starting values of association parameters

PersonByItem

Person by item matrix of responses (same as inData)

TraitByTrait

Trait by trait adjacency matrix (same as inTraitAdj)

item.by.trait

Item by trait vector indicating trait item load on (same as inItemTraitAdj)

tol

Criterion used to determine convergence

npersons

Number of persons

nitems

Number of items

ncat

Number of categories per item

nless

Number of categories minus 1 (i.e., unique lambdas)

ntraits

Number of latent traits

Maxnphi

Number of phi parameters to be estimated

pq.mat

Used to compute rest-scores and totals

starting.sv

Fixed category scores

ItemNames

Names of items needed label output

LambdaName

Names of lambdas needed for formula of the item regressions

LambdaNames

Names of lambdas needed for formula of the stacked regression

PhiNames

Name of phi parameters (Null for uni-dimensional models)

Value

item.log History over iterations of the algorithm for items' log likelihood, lambda, and a parameter

phi.log History over iterations of the algorithm for log likelihood, lambdas nd phi parameters

criterion Current value of the convergence statistic which is the maximum of items' absolute differences between the current and previous value of the log likelihood

estimates An item by parameter matrix of estimated item parameter where the first column are items' log likelihood

Phi.mat Estimated matrix of association parameters

fitem Formula for item data

fstack Formula for stacked data

item.mlogit Summary from final run of mlogit for item regressions for each item

phi.mlogit Summary from final run mlogit for stacked regression

mlpl.item Value of maximum of log ple function from fitting items (i.e., sum of logLike)

mlpl.phi Value of maximum of log ple function from stacked regression to get phi estimates

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", "a1","a2","s1","s2")]
 #--- unidimensional
 inTraitAdj  <- matrix(1, nrow=1, ncol=1)
 inItemTraitAdj <- matrix(1, nrow=6, ncol=1)

# Need to set up data
s <- set.up(inData, model.type='gpcm', inTraitAdj, inItemTraitAdj, tol=1e-03)

g <- fit.gpcm(s$Master, s$Phi.mat, s$PersonByItem, s$TraitByTrait,
              s$item.by.trait, s$tol, s$npersons, s$nitems, s$ncat,
              s$nless, s$ntraits, s$Maxnphi, s$pq.mat, s$starting.sv,
              s$ItemNames, s$LambdaName, s$LambdaNames, s$PhiNames)