Changes in size and interpretation of parameter estimates in within-person models in the presence of time-invariant and time-varying covariates

For several decades, cross-lagged panel models (CLPM) have been the dominant statistical model in relationship research for investigating reciprocal associations between two (or more) constructs over time. However, recent methodological research has questioned the frequent usage of the CLPM because, amongst other things, the model commingles within-person associations with between-person associations, while most developmental research questions pertain to within-person processes. Furthermore, the model presumes that there are no third variables that confound the relationships between the longitudinally assessed variables. Therefore, the usage of alternative models such as the Random-Intercept Cross-Lagged Panel Model (RI-CLPM) or the Latent Curve Model with Structured Residuals (LCM-SR) has been suggested. These models separate between-person from within-person variation and they also control for time constant covariates. However, there might also be third variables that are not stable but rather change across time and that can confound the relationships between the variables studied in these models. In the present article, we explain the differences between the two types of confounders and investigate how they affect the parameter estimates of within-person models such as the RI-CLPM and the LCM-SR.