Dimension reduction for longitudinal multivariate data by optimizing class separation of projected latent Markov models

We present a method for dimension reduction of multivariate longitudinal data, where new variables are assumed to follow a latent Markov model. New variables are obtained as linear combinations of the multivariate outcome as usual. Weights of each linear combination maximize a measure of separation of the latent intercepts, subject to orthogonality constraints. We evaluate our proposal in a simulation study and illustrate it using an EU-level data set on income and living conditions, where dimension reduction leads to an optimal scoring system for material deprivation. An R implementation of our approach can be downloaded from https://github.com/afarcome/LMdim.