Mplus lets you model time-varying covariates as a function of time-invariant covariates. For example, gender and home background influence the number of math courses taken in a certain grade, in turn influencing math achievement. The substantive theory and time-ordering of events decide on the particular modeling.
Thanks for the note. I would like to go a little further on this if I might. I am working on a grant revision in which I propose a model similar to the “parallel process linear growth model as shown on page 215 of the version 2.9 user guide. The reviewer comments”
There are some serious potential problems with the analyses proposed in Aim 3, which intends to assess changes in one type of outcome (urinary and sexual) as a function of changes in other types of outcomes (psychological and general QOL). In other words, some of the outcomes will be treated as time-varying covariates for the purposes of these models. Biased estimates of both fixed and random effect will be obtained, however, unless the time-varying covariates satisfy the condition of being exogenous variables. A variable is exogenous, or external, if current and prior values of the outcome variable do not predict subsequent covariate values, conditional on current and prior covariate values.
Our aim is Aim 3: To examine how trajectories of change in sexual and urinary function are associated with trajectories of change of general QOL and psychological functioning.
I think that the reviewer has interpreted our approach as using time varying covariates rather than as two parallels models that are related.
SO my question is: With a parallel model, do we have to worry about the problems outlined above with regard to endogeneity? If not why?