How do I include time-varying covariates with the RI-CLPM?

Time-varying covariates (TVC) can be included like “regular” X and Y outcomes in the RI-CLPM; hence, rather than a bivariate RI-CLPM you would specify a tri- or more-variate RI-CLPM. As such, you decompose the TVCs in within-components and a between-component (the random intercept) and model these components separately. However, if you want to control for many TVC’s, this can quickly become an unwieldly model, so researchers should think carefully about which TVC’s they want to control for.

Can I run the RI-CLPM with binary/categorical/count outcomes?

The RI-CLPM is currently only well-studied/well-developed for the continuous case. Research into RI-CLPMs with only categorical data, or with non-commensurate outcomes (i.e., outcomes measured in different scales, continuous and binary) is still ongoing. See, for example, the Mplus discussion board.

Is it possible to run an RI-CLPM with three (or more) outcomes?

Yes, it is statistically possible to run a “trivariate” RI-CLPM and empirical researchers have done so. See for example Burns, Crisp, and Burns (2019) and Van Lissa et al. (2019). We don’t provide model code here for this mode, but extension to a trivariate RI-CLPM should be relatively straight forwards.

How should I interpret the standardized cross-lagged and autoregressive parameters?

In the RI-CLPM, the standardized effects are reflective/representative of how much within-person variance in \(y_{t}\) is uniquely explained (i.e., not also explained by other predictors) by the predictor \(x_{t-1}\). Please note that this does not imply that one can make a one-on-one comparison with the percentage of explained variance. However, the standardized effects can be used to compare which effect is relatively stronger.(Schuurman, Ferrer, Boer-Sonnenschein, & Hamaker, 2016).