convergenceGPCM {pleLMA}

Computes statistics to assess convergence for generalized partial credit models

Description

For the generalized partial credit model, convergence statistics are computed for each item, as well as the algorithm as a whole. The convergence statistics are the differences between current values of the log likelihoods and item parameter estimates and those from the previous iteration. The maximum over items' differences of the log likelihood values is used to determine convergence of the pseudo-likelihood algorithm. This function is used internally, but it can also be used after fitting a model to examine how many iterations are required for parameter estimates to get close to the final values and whether any item parameters are still changing.

Usage

convergenceGPCM(item.log, nitems, ncat, nless, LambdaName)

Arguments

item.log

Iteration history of items' log likelihoods and parameter estimates

nitems

Number of items

ncat

Number of categories

nless

Number of unique lambdas

LambdaName

Names of lambdas in formula used to fit item regressions (internal to fit_gpcm)

Value

diff.last Differences between item's log likelihoods and parameters for each item

criterion.loglike Maximum overs item of the absolute value of differences between item LogLike values

criterions.items Sum of item differences of their parameters

Examples

# 9 items from dass data for 250 cases
 data(dass)
 inData <- dass[1:250,c("d1", "d2", "d3", "a1","a2","a3","s1","s2","s3")]

 #---   input for uni-dimensional
 inTraitAdj  <- matrix(1, nrow=1, ncol=1)
 inItemTraitAdj <- matrix(1, nrow=9, ncol=1)
 

 #--- fit Unidiemsional gpcm Model
 g1<- ple.lma(inData, model.type="gpcm",inItemTraitAdj,inTraitAdj, tol= 1e-03)

 # Since convergenceGPCM is internal to fit.gpcm, need to get 'Lambdaname'
 s <- set.up(inData, model.type='gpcm', inTraitAdj, inItemTraitAdj)

 convergenceGPCM(g1$item.log, g1$nitems, g1$ncat, g1$nless, s$LambdaName)

#--- Multidimensional models
#--- re-define inTraitAdj and inItemTraitAdj for 3 dimensional models
 inData <- dass[1:250,c("d1", "d2", "d3", "a1","a2","a3","s1","s2","s3")]
 inTraitAdj  <- matrix(1, nrow=3, ncol=3)
 dpress <- matrix(c(1,0,0), nrow=3, ncol=3, byrow=TRUE)
 anxiety <- matrix(c(0,1,0), nrow=3, ncol=3, byrow=TRUE)
 stress <- matrix(c(0,0,1), nrow=3, ncol=3, byrow=TRUE)
 das <- list(dpress, anxiety, stress)
 inItemTraitAdj <- rbind(das[[1]], das[[2]], das[[3]])

#--- 3 dimensional gpcm
 g3 <- ple.lma(inData, model.type="gpcm", inItemTraitAdj, inTraitAdj, tol=1e-03)
 s <- set.up(inData, model.type='gpcm', inTraitAdj, inItemTraitAdj)
 convergenceGPCM(g1$item.log, g1$nitems, g1$ncat, g1$nless, s$LambdaName)