Growth Curve Episode 6: Time-Invariant Covariates

Once an optimal model of linear or nonlinear change has been established, it is often of interest to then incorporate one or more time-invariant covariates (TICs) as predictors of the growth factors. TICs are predictors that do not change as a function of time...

Examples of TICs include biological sex, country of origin, birth order, or any person-level characteristic assessed only at the initial time point. TICs are used as predictors of the latent growth factors in the SEM or entered as Level 2 predictors in the MLM; in both approaches, tests are obtained regarding the extent to which information on the TIC in part contributes to the growth process under study. Although the interpretation of predictors of the intercept factor are straightforward, predictors of the slope factor are more complex given the interaction between the predictor and time. These slope effects must be probed further to more fully understand the nature of the effect. Patrick discusses these issues in greater details and makes recommendations for using these in practice.

Bauer, D.J., & Curran, P.J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40, 373-400.

Curran, P. J., Bauer, D. J., & Willoughby, M. T. (2004). Testing main effects and interactions in latent curve analysis. Psychological Methods, 9, 220-237.

Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interactions in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31, 437-448.

[leod]

great video. why don't intercept and slope covary directly anymore? and, how can I identify the variance of slope and intercept after adjusting for covariates in SEM?
before integrating timeinvariant covariate, the double headed arrows back and to the slope/intercept were the variances. now these are just residual variances now if I understand correctly. Or do I still have to create separate latents for the residual variances, like you did?