Hello,
Often when I read multilevel model papers, when talking about time-varying covariates, they often only use binary time-varying variables.
If I was to do a cross product between the time variable, and a ordinal/categorical time-varying covariate with several catgeories, say 5, might this over complicate the model? As in, when I have added a time-varying covariate with multiple categories, I see that the BIC will go up, the AIC will go down, does this mean that the model is 'worse'?
Is it better to try and collapse a larger categorical time-varying covariate into just a binary category, to allow for easier interpretation? If using a timevarying variable with mutliple groups is accepted practice (Because I don't see it often), how should i determine if it is a good predictor? Is there any papers which might help? I can't see much in the literature relating to this.
Let me know your thoughts
Suggest you look at:: https://www.google.com/search?client=firefox-b-1-d&q=Time+varying+covariates+in+growth+curve+models
David Booth
Regardless of time-dependence of covariates (as long as Z is predictable) the partial likelihood method preserves the same properties as classical maximum likelihood method.
Hi the best book that I have read which i think will answer some of your questions is: Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence by Singer and Willett.
AIC and BIC are not the only indicators.
I would also look at how much residuals have been explained (level 1 and your growth parameters). If your interaction is not significant, i would not leave it in the model to keep a parsimonious model. Singer book also talked about deviance statistic. I often take all these into consideration. Having a time-varying categorical variable is acceptable. If you have cells with small n, it may be better to categorize the continuous variable for power.
Hope this helps!
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