Analysis of multitrait-multioccasion data:: Additive versus multiplicative models

The aim of this article is to address the question of whether empirical multitrait-multioccasion data conform more closely to multiplicative models than to additive models. Four additive models and two versions of the multiplicative Direct Product (DP) model (Browne, 1984) are tested. A set of 21 multitrait-multioccasion matrices is analyzed by means of LISREL 8 (Joreskog & Sorbom, 1993). The results obtained across different models are evaluated according to plausibility of solutions and goodness-of-fit. The different good-fitting models are compared in terms of goodness-of-fit and in terms of the conclusions about construct validity derived from the models. Results show that both additive and multiplicative models (specifically the additive Correlated Trait-Correlated Uniqueness model and the multiplicative Composite Direct Product model) usually fit the same MTMO data. Moreover both kinds of models are frequently equivalent in terms of goodness-of-fit. Finally, although general conclusions about construct validity are similar across models, the results obtained suggest that the conclusions about the relevance of each trait and occasion derived from additive and multiplicative models can differ substantially depending on the number of traits and occasions.