fit.nominal: Fits the nominal model
In pleLMA: Pseudo-Likelihood Estimation of Log-Multiplicative Association Models

Description Usage Arguments Value Examples

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'.

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
)

`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

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)

 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)