pleLMA: Pseudo-Likelihood Estimation of Log-Multiplicative Association
Models
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.
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