What type of analysis for multivariate regression of high-dimensional longitudinal data? I have a longitudinal dataset with few time points (N=10) and few subjects (N=10). Both independent/predictor and dependent/response variables are high-dimensional (N ~ 100 for both types of variable). Both independent and dependent variables are time series (N=10). I'm interested in determining which independent variables predict (are associated with) which dependent variables. I wonder what type of analysis I should run both at the group level and individual level (i.e. a separate analysis for each subject). Can you recommend specific statistical approaches for the 2 types of analyses along with R packages that implement them?
 A: I've thought about this issue but haven't come to a solution. I haven't been able to find much online for how to deal with it. Some economists have produced some research on it, but it's beyond me to understand the details.
here's a link to some research on it:
https://arxiv.org/abs/1411.6507
Here's a quote from it:
"A key contribution of this paper is offering a variant of the Lasso estimator that accommodates a clustered covariance structure (Cluster-Lasso). We provide formal conditions under which the estimator performs well in the sense of returning a sparse estimate and having good forecasting and rate of convergence properties."
They use a method referred to as the cluster-lasso that seems designed for panel data. It sounds like they're using fixed effects to capture the subject effects and then feeding in the time variables and using LASSO to select which time variables get selected. 
I don't see them referencing any software packages for implementation. But you could potentially do something similar by using a LASSO estimation package such as glmnet in R. You could feed in some dummies for each panel along with the time-varying potential variables and see which time variables enter first. I don't know how close that is to the approach proposed there, but it doesn't seem too far off. 
