Regime Switching Modeling of Substance Use: Time-Varying and Second-Order Markov Models and Individual Probability Plots

Abstract

A linear latent growth curve mixture model with regime switching is extended in 2 ways. Previously, the matrix of first-order Markov switching probabilities was specified to be time-invariant, regardless of the pair of occasions being considered. The first extension, time-varying transitions, specifies different Markov transition matrices between each pair of occasions. The second extension is second-order time-invariant Markov transition probabilities, such that the probability of switching depends on the states at the 2 previous occasions. The models are implemented using the R package OpenMx, which facilitates data handling, parallel computation, and further model development. It also enables the extraction and display of relative likelihoods for every individual in the sample. The models are illustrated with previously published data on alcohol use observed on 4 occasions as part of the National Longitudinal Survey of Youth, and demonstrate improved fit to the data.

Keywords:

• finite mixture
• latent growth curve
• Markov model
• OpenMx
• R
• regime switching

Notes

¹ The symbol is used for Big notation of the order of magnitude, rather than the exact numeric formula. Thus, is read “on the order of R²”.