Longitudinal multi-trait-state-method model using ordinal data

Multi-trait multi-method (MTMM) models were designed as a way to assess convergent and discriminant validity using multiple traits measured by multiple methods. In recent years, longitudinal extensions of multi-trait multi-method models have been proposed in the structural equation modeling framework to evaluate whether and how the trait as well as method factors change over time. This thesis is intended to propose a longitudinal second-order multi-trait-state-method (M-TSM) model that combines a measurement model for ordinal data, a vector autoregressive moving average (VARMA) model at the latent level to examine changes in the state as well as method factors over time, and a second-order factor analytic model to capture shared trait variances among the state affect factors. A set of affect items from the Affective Dynamics and Individual Differences (Emotions and Dynamic Systems Laboratory, 2010) study was used to illustrate the proposed longitudinal M-TSM model. This study features affect items asked in both a lab and a diary setting. Results of the final model showed that the method factors, lab and diary, had perfect stability across time. Furthermore, factor loadings within the lab factor showed a systemic pattern of positive and negative loadings illustrating the complexity of individuals' affective responses to stimuli in the lab setting. Contrary to conventional theories on emotions, the covariances between positive and negative affect factors at the state level were not significantly different from zero; however, evaluation of higher-order shared covariance between the affect factors across method settings indicates a negative association between the two at the "trait" level. Comparisons of the auto- and cross-regression regression parameters associated with the state affect factors indicated some key differences in how people regulated negative emotions in a lab versus in a diary setting. Methodological issues associated with fitting the M-TSM model are discussed.