Matrix Decomposition-Based Approach to Estimate the STARTS Model

TL;DR

This paper introduces a new two-stage matrix decomposition method for estimating the STARTS model, reducing improper solutions and bias, and improving estimation reliability in structural equation modeling.

Contribution

It presents a novel matrix decomposition-based estimation approach for the STARTS model, combining factor analysis with SEM principles, and demonstrates its advantages over existing methods.

Findings

Lower risk of improper solutions compared to ML and other estimators.

Similar solutions to ML but without requiring prior distributions.

Effective bias mitigation when the number of time points is small.

Abstract

We propose a new estimation method for the Stable Trait, Auto Regressive Trait, and State (STARTS) model, which is well known for its frequent occurrence of improper solutions. The proposed approach is implemented through a two-stage estimation procedure that combines matrix decomposition factor analysis (MDFA) based on eigenvalue decomposition with conventional SEM estimation principles. By reformulating the STARTS model within a factor-analytic framework, this study presents a novel way of applying MDFA in the context of structural equation modeling (SEM). Through a simulation study and an empirical application to ToKyo Teen Cohort data, the proposed method was shown to entail a substantially lower risk of improper solutions than commonly used maximum likelihood, conditional ML, and (unweighted) least squares estimators, while tending to yield solutions similar to those obtained by ML. Compared with Bayesian estimation, the proposed method does not require the specification of appropriate (weakly informative) prior distributions and may effectively mitigate bias issues that arise when the number of time points is small. Applying the proposed method, as well as conducting sensitivity analyses informed by it, will enable researchers to more effectively delineate the range of plausible conclusions from data in estimating the STARTS model and other SEMs.