Evaluation of Structural Relationships in Autoregressive Cross-Lagged Models Under Longitudinal Approximate Invariance:A Bayesian Analysis

Abstract

To infer longitudinal relationships among latent factors, traditional analyses assume that the measurement model is invariant across measurement occasions. Alternative to placing cross-occasion equality constraints on parameters, approximate measurement invariance (MI) can be analyzed by specifying informative priors on parameter differences between occasions. This study evaluated the estimation of structural coefficients in multiple-indicator autoregressive cross-lagged models under various conditions of approximate MI using Bayesian structural equation modeling. Design factors included factor structures, conditions of non-invariance, sizes of structural coefficients, and sample sizes. Models were analyzed using two sets of small-variance priors on select model parameters. Results showed that autoregressive coefficient estimates were more accurate for the mixed pattern than the decreasing pattern of non-invariance. When a model included cross-loadings, an interaction was found between the cross-lagged estimates and the non-invariance conditions. Implications of findings and future research directions are discussed.

Keywords:

• approximate measurement invariance
• Bayesian structural equation modeling
• autoregressive cross-lagged model

Notes

¹ In the current study, q_x = 1 and q_y = 1. The total number of latent factors q = 2.

² In this study, for reducing the number of analysis models, the same informative prior was used for approximate MI, cross-loadings and correlated errors. However, different priors can be assigned to different parameters in practice, depending on the availability of prior knowledge.

³ We chose to use the deviance instead of relative bias because population values for cross-lagged coefficients were small (i.e., .055 or .133). Calculating relative bias using a small population value as the denominator in the computing fraction would lead to unreasonably large relative bias. The general rule for negligible relative bias (< 10%; Hoogland & Boomsma, 1998) would make little sense in our situation.