Scale

Master

Iteration history of LogLike, lambda, and item parameters

item.log

Phi.mat

PersonByItem

npersons

nitems

ncat

nless

ntraits

Indicates the trait an item load on.

item.by.trait

Scaling is internal to the function 'fit.nominal', which corresponds
the the nominal item response theory model. It imposes the required
scaling identification constraint by transforming the conditional
covariance matrix 'Phi.mat' to a conditional correlation matrix (i.e.,
set phi_mm=1 for all m). The inverse transformation is applied to
the current category scale value estimates and these are put back
into the Master data frame 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.

Carolyn Anderson

pleLMA

Pseudo-Likelihood Estimation of Log-Multiplicative Association
Models

Scale function

Imposes scaling constraint to identify parameters of the LMA (nominal) model — Scale

Imposes scaling constraint to identify parameters of the LMA (nominal) model

Scale: Imposes scaling constraint to identify parameters of the LMA (nominal) model

Description

Usage

Arguments

Value