[R-sig-ME] Multivariate Growth Curve Analyses in lme4

[Ades, James]

Hi all,


I�ve been reading through Growth Curve Analysis and Visualization in R to model executive function growth over four time points. The book is a good launching pad; however, it falls short when it comes to multivariate growth curve analysis. Additionally, I haven�t been able to find much on the internet regarding multivariate growth curve analysis in R, let alone in lme4.


I�ve never really done any multivariate analysis. Growth curve analyses doesn�t seem too different from regular multilevel modeling but for the time points occurring as the first level within the second level of participant.


1) As a barebones bivariate model with DVs of a standardized math assessment score and an aggregate executive function score would something like


```

lmer(mvbind(math.score, mean.eff) ~ timepoint + (time | participant), dat�)

```

be correct? (I have time as a random slope given that the space in between when students were tested could differ by several months, so "time point" per se seemed biased). From that point, I could add in fixed effects of cohort, parent education level, etc.


2) Would it be possible to model three components from a PCA of executive function with math score in a similar model? How would one do that? Just create a new row with the four measures and run the row as the DV?


3) Lastly, I�m wondering whether AIC model comparison goes out the window if you were to model PCA (3 components)  and aggregate score (of EF)? This question applies to both univariate and multivariate models. There would be the same number of subjects, etc. but the number of observations would ostensibly triple, given that three components would be modeled vs a more parsimonious mean score. That is, even after accounting for the variability in PCA among subjects with a model like


```

lmer(mean.eff ~ pca + timepoint + (time | participant) + (time | pca:participant), dat�)

```

If these models aren�t comparable with AIC, would LOOCV be the next best option?


Thanks much!


James



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