fit.nominal {pleLMA}

Fits the nominal model

Description

Function estimates the parameters of LMA models where the category scale are estimated. The function can be used to estimate the parameters of the LMA model corresponding the nominal model (for multi-category items) and the 2 parameter logistic model for dichotomous items. The function sets up log object(s) 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.nominal(
  Master,
  Phi.mat,
  starting.sv,
  pq.mat,
  tol,
  PersonByItem,
  TraitByTrait,
  ItemByTrait,
  item.by.trait,
  ItemNames,
  LambdaNames,
  NuNames,
  LambdaName,
  NuName,
  PhiNames,
  npersons,
  nitems,
  ncat,
  nless,
  ntraits,
  Maxnphi
)

Arguments

Master

Master data set in long format

Phi.mat

Matrix of starting values of the association parameters

starting.sv

Matrix starting values category scale values

pq.mat

Array used compute rest scores and total scores

tol

Value used to determine convergence of algorithm

PersonByItem

Same as inData (rows are response patterns)

TraitByTrait

Same as inTraitAdj (trait x trait adjacency)

ItemByTrait

Same as inItemTraitAdj (item x trait adjacency)

item.by.trait

One dimensional array indicating trait item loads on

ItemNames

Names of items in inData (i.e. columns names of categorical variables)

LambdaNames

Lambda names used in the Master and stacked data frames

NuNames

Nu names in Master data frame

LambdaName

Lambda names in formula for items

NuName

Nu names in formula for item regressions

PhiNames

Association parameter names for stacked regression

npersons

Number of persons

nitems

Number of items

ncat

Number of categories per item

nless

ncat-1 = number unique lambda and unique nus

ntraits

Number of traits

Maxnphi

Number of association parametets

Value

item.log Iteration history of LogLike, lambda, and item parameters

phi.log Iteration history of LogLike, lambdas and phi parameters

criterion Current value of the convergence statistic

estimates Item x parameter matrix: LogLike, lambda and scale values

Phi.mat Estimated conditional correlation matrix

fitem Formula for item data

fstack Formula for stacked data

item.mlogit Summaries from final run of mlogit for item regressions

phi.mlogit Summary from final run of mlogit for stacked regression

mlpl.item Max log pseudo-likelihood function from item regressions

mlpl.phi Maximum of log pseudo-likelihood function from 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='nominal', inTraitAdj, inItemTraitAdj,
           tol=1e-02)

 n1 <- fit.nominal(s$Master, s$Phi.mat, s$starting.sv, s$pq.mat, s$tol,
       s$PersonByItem, s$TraitByTrait, s$ItemByTrait, s$item.by.trait,
       s$ItemNames, s$LambdaNames,  s$NuNames, s$LambdaName, s$NuName,
       s$PhiNames, s$npersons, s$nitems, s$ncat,s$ nless, s$ntraits,
       s$Maxnphi)