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We have longitudinal data on children(n<20) in which we measure different quantities A,B,C,D (like distance walked, time spent in school etc.). These are all continuous variables. We measure these variables daily and we have been measuring them for more than one and half years.

Now, based on these variables (A,B,C,D), I am trying to model individual growth trajectories of each child. Ideally, I want to have a single curve that explains how these variables have evolved with respect to time. For now, I am not concerned if different child have different trajectories.

I have been studying multi-level models to model growth curves. These techniques were not helpful particularly because I am not interested in modelling individual variables separately and my time series data is quite long(n>500 for each individual). I want to find a relation between all these variables and time.

I have been wandering for quite a time. I am looking for getting started papers or some ideas.

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    $\begingroup$ I am not sure what you mean by "all these variables" other than "these variables separately". The way to find a relationship between some independent variables and a dependent variable is to model them one at a time. Sometimes you can do data reduction (e.g. with principal component analysis) but that doesn't seem right here (distance walked and time spent in school don't go together in any obvious way). I don't think there's a way to get a single curve that represents all this. $\endgroup$
    – Peter Flom
    Nov 28, 2012 at 0:38
  • $\begingroup$ You also say both "I am trying to model individual growth trajectories" and "I am not concerned if different individuals have different trajectories" which is contradictory. $\endgroup$
    – Peter Flom
    Nov 28, 2012 at 0:39
  • $\begingroup$ thanks @PeterFlom for your comment.. i am looking for a technique similar to pca that supports longitudinal analysis..as i have said i want to find a common trajectory that explains how these variables are evolving with time...i can fit these variables separately but are there ways i can "aggregate" these different fitted models to find a (sort of ) single model? .... for the second comment i mean growth trajectory of each child (see edits) $\endgroup$
    – iinception
    Nov 28, 2012 at 3:52

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Functional Data Analysis probably provides the framework you are looking for. Your wording "quite long series data", "continuous variables" echoes the basic intuitions behind this approach. It actually seems you are describing a problem closely related to multivariate functional regression. Yao 's Functional Linear Regression Analysis for Longitudinal Data (preprint) describes in detail the theory behind this and Müller's et al. Inferring gene expression dynamics via functional regression analysis paper provides a nice test case (and presents some of the theory again). There is work on functional mixed effects regression also in case you are interested in "clustering" your data somehow (gender-wise, sibling associations etc.).

Assuming that your "weapon of choice" is MATLAB, the package PACE provides a lot of readily available routines for regression, smoothing, warping (time-registration) and component analysis (on a regular or irregular grid) for your data. (For the ME models you will probably need to use Functional PCA and then model the projections with R's lmer()).

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  • $\begingroup$ thanks for the comment....Functional Regression seems to be a good choice . $\endgroup$
    – iinception
    Nov 29, 2012 at 6:02

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