Longitudinal Multi-Trait-State-Method Model Using Ordinal Data

Abstract

Multi-trait multi-method (MTMM) models provide a way to assess convergent and discriminant validity when multiple traits are measured by multiple methods. In recent years, longitudinal extensions of MTMM 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. We propose a novel longitudinal ordinal MTMM model that can be used to effectively distinguish volatile “state” processes from “trait” processes that tend to remain stable and invariant over time. The proposed model, termed a longitudinal multi-trait-state-method (LM-TSM) model, combines 3 key modeling components: (a) a measurement model for ordinal data, (b) a vector autoregressive moving average model at the latent level to examine changes in the state as well as the method factors over time, and (c) a second-order factor-analytic model to capture time-invariant traits as shared variances among the state factors across all measurement occasions. Data from the Affective Dynamics and Individual Differences (ADID; Emotions and Dynamic Systems Laboratory, 2010) study was used to illustrate the proposed longitudinal LM-TSM model. Methodological issues associated with fitting the LM-TSM model are discussed.

Notes

Note that such growth curve-based longitudinal MTMM models include the latent difference score models proposed by McArdle and Hamagami (2001), which can be structured as constrained versions of the latent growth curve models.

In traditional item response theory terminology, this is referred to as the latent ability level.

Mplus code for this model can be obtained at http://quantdev.ssri.psu.edu/?page_id=115

That is, the eigenvalues of the transition matrix have moduli less than one or alternatively, all the roots of the characteristic polynomial are outside the unit circle (Du Toit & Browne, 2007; Hamilton, 1994).