ScaleGPCM

Master

Iteration history array, last row are current parameters

item.log

Phi.mat

PersonByItem

npersons

nitems

ncat

nless

ntraits

Matrix of fixed category scores (nitems x ncat)

starting.sv

Object that indicates which trait item loads on

item.by.trait

Scaling is internal to the function 'fit.gpcm', which fits the GPCM
version of the LMA. It imposes the required scaling identification
constraint by transforming the conditional covariance matrix 'Phi.mat' to a
conditional correlation matrix. The inverse transformation is applied to the
current estimates of the slope or 'a' parameters. Category scale values are
recomputed using the re-scale slopes (i.e., nu= a*x) and these are put back
into the Master data set so that data are ready for the next iteration of the
algorithm.

Log-multiplicative association models (LMA) are
models for cross-classifications of categorical variables
where interactions are represented by products of category
scale values and an association parameter. Maximum
likelihood estimation (MLE) fails for moderate to large
numbers of categorical variables. The 'pleLMA' package
overcomes this limitation of MLE by using pseudo-likelihood
estimation to fit the models to small or large
cross-classifications dichotomous or multi-category variables.
Originally proposed by Besag (1974,
<doi:10.1111/j.2517-6161.1974.tb00999.x>), pseudo-likelihood
estimation takes large complex models and breaks it down
into smaller ones. Rather than maximizing the likelihood
of the joint distribution of all the variables, a
pseudo-likelihood function, which is the product likelihoods
from conditional distributions, is maximized. LMA models can
be derived from a number of different frameworks including
(but not limited to) graphical models and uni-dimensional
and multi-dimensional item response theory models. More
details about the models and estimation can be found in
the vignette.

ScaleGPCM: Imposes scaling constraint to identify parameters of LMA (GPCM)

Description

Usage

Arguments

Value