Abstract
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.
Highlights
Latent Markov (LM) models (Bartolucci et al 2013, 2014) permit parsimonious and flexible modeling of univariate and multivariate longitudinal data
We present a method for dimension reduction of multivariate longitudinal data, where new variables are assumed to follow a latent Markov model
Projections are obtained through different parameter initializations: random, logistic PCA (LogPCA) and logistic SVD (LogSVD)
Summary
Latent Markov (LM) models (Bartolucci et al 2013, 2014) permit parsimonious and flexible modeling of univariate and multivariate longitudinal data. Our main issue is how to classify as poor/not poor a new family, based on its nine-dimensional binary profile, and ranking families with respect to their propensity to material deprivation It is underlined in Atkinson (2003) and Dotto et al (2019) that a simple counting approach has an unsatisfactory classification performance for this task. Weighted sums can be seen as lower-dimensional projections of longitudinal measurements, which relates our method to the more general literature on dimension reduction for longitudinal data (e.g., Hall et al 2006; Jiang and Wang 2010); in relation to latent Markov models. The methodology proposed in this paper has been implemented in R functions which can be downloaded from https://github.com/afarcome/LMdim
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