Log - multiplicative Association Models as Multidimensional Item Response Models for Polytomous Items ∗

Log-multiplicative association models (LMA), which are special cases of log-linear models, have been derived as models for manifest probabilities based on multidimensional latent variables models for multi-category response data. Since discussion of between multiple derivations is lacking, we draw connections between multiple derivations with an emphasis on those pertaining to item response modeling. In particular, we extend Anderson and Yu (2007) who studied LMA models as uni-dimensional IRT models for dichotomous items to the case of multi-dimensional latent variables for polytomous items. This research also extends Hessen’s (2012) conditional multinomial partial credit models to more general IRT models. The empirical studies presented here demonstrate that LMA models perform extremely well compared to standard MIRT models in terms of model fit to data, parameter recovery, and estimation of values on the latent variables. Some example applications using data from a study on bullying (Espelage, Holt & Henkel, 2004) are presented.