Hierarchical multinomial models 1 Running head: HIERARCHICAL MULTINOMIAL MODELS Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach

Hierarchical multinomial models 2 Multinomial processing tree models are widely used in many areas of psychology. Their application relies on the assumption of parameter homogeneity, that is, on the assumption that participants do not differ in their parameter values. Tests for parameter homogeneity are proposed that can be routinely used as part of multinomial model analyses to defend the assumption. If parameter homogeneity is found to be violated, a new family of models, termed latent-class multinomial processing tree models, can be applied that accomodates parameter heterogeneity and correlated parameters, yet preserves most of the advantages of the traditional multinomial method. Estimation, goodness-of-fit tests and tests of other hypotheses of interest are considered for the new family of models. Hierarchical multinomial models 3 In the last two decades, multinomial processing tree models, henceforth referred to as multinomial models, have been extensively used in many areas o