Autoregressive mediation models using composite scores and latent variables: Comparisons and recommendations.

We studied three models for longitudinal mediation analysis: the autoregressive mediation model (AMM) using composite scores (uncorrected composite model, UCM), AMM using composite scores with correction for measurement error (corrected composite model, CCM), and AMM using latent variables with multiple indicators (latent variable model, LVM). Under the condition of unidimensional measurement model, we showed analytically that UCM yielded asymptotically biased direct and indirect effect estimates when composite reliabilities of observed variables were less than 1, and had unbiased estimates only under stringent and unlikely conditions. Further, CCM yielded asymptotically unbiased effect estimates when the sums of loadings for items measuring a latent variable were invariant over time. We verified conclusions from the analytical study regarding parameter estimation accuracy via a simulation study. Specifically, under different levels of measurement invariance, sample sizes, numbers of time points, and reliabilities, CCM and LVM had reasonably accurate direct and indirect effect estimates and good coverage rates in general. On the other hand, UCM was not recommended given inaccurate effect estimates and/or low coverage of true parameters across our considered conditions. In addition, CCM was much simpler in model structure and less sensitive to sample sizes in comparison with LVM in terms of model chi-square test and fit indexes. An empirical study was conducted for illustration. Mplus code for fitting the three models is provided. (PsycInfo Database Record (c) 2020 APA, all rights reserved).