pleLMA

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.