Abstract
Longitudinal designs provide a strong inferential basis for uncovering reciprocal effects or causality between variables. For this analytic purpose, a cross-lagged panel model (CLPM) has been widely used in medical research, but the use of the CLPM has recently been criticized in methodological literature because parameter estimates in the CLPM conflate between-person and within-person processes. The aim of this study is to present some alternative models of the CLPM that can be used to examine reciprocal effects, and to illustrate potential consequences of ignoring the issue. A literature search, case studies, and simulation studies are used for this purpose. We examined more than 300 medical papers published since 2009 that applied cross-lagged longitudinal models, finding that in all studies only a single model (typically the CLPM) was performed and potential alternative models were not considered to test reciprocal effects. In 49% of the studies, only two time points were used, which makes it impossible to test alternative models. Case studies and simulation studies showed that the CLPM and alternative models often produce different (or even inconsistent) parameter estimates for reciprocal effects, suggesting that research that relies only on the CLPM may draw erroneous conclusions about the presence, predominance, and sign of reciprocal effects. Simulation studies also showed that alternative models are sometimes susceptible to improper solutions, even when reseachers do not misspecify the model.
Highlights
Collecting longitudinal data has become widely popular in medical research and other disciplines due to its statistical advantages over cross-sectional data
We focus on three cross-lagged longitudinal models: the cross-lagged panel model (CLPM), the randomintercepts CLPM (RI-CLPM), and the stable trait autoregressive trait and state (STARTS) model
With regard to standard errors, interestingly, the standard errors of ^g in the RI-CLPM and the STARTS model are, on average, 1.6 and 2.7 times, respectively, the size of those with the CLPM. These results indicate that the inclusion of parameters that are specific to these models (i.e., trait factorvariances in the RI-CLPM and those and errorvariances in the STARTS model) leads to an increase in standard errors
Summary
Collecting longitudinal data has become widely popular in medical research and other disciplines due to its statistical advantages over cross-sectional data. In the RI-CLPM, individual differences are effectively controlled by the inclusion of a latent variable that represents a time-invariant (but person-variant) trait-like factor; this allows testing the reciprocal effects within individuals If this model is extended to include measurement errors, the model is equivalent to a so-called (bivariate) stable trait autoregressive trait and state (STARTS) model (Kenny & Zautra [10, 11]). Murayama, and Hamaker [12] discussed the mathematical and conceptual relations between various cross-lagged models, including these models These recent studies are insightful and informative, providing applied medical researchers a basis for thinking about how to test within-person reciprocal effects by longitudinal data. One primary reason is the fact that unlike trait factor variances (v2) and residual variances (o2t ), the contribution from measurement error variances (c2t ) is temporal: in the model-implied variance-covariance matrix, c2t appears at time point t only. Research has suggested the utility of a Bayesian approach to avoid unstable parameter estimation (Ludtke, Robitzsch, & Wagner [16])
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