Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models

TL;DR

This paper introduces a Bayesian approach for detecting multiple random changepoints in piecewise growth mixture models, allowing for individual differences in transition times, with a new R package and empirical validation.

Contribution

It develops a Bayesian PGMM that estimates multiple random changepoints and provides a method to empirically determine their number within each class.

Findings

The method accurately estimates multiple random changepoints in simulated data.

The BayesianPGMM package facilitates practical application of the methodology.

Application to mouse-tracking data demonstrates real-world utility.

Abstract

Piecewise growth mixture models (PGMM) are a flexible and useful class of methods for analyzing segmented trends in individual growth trajectory over time, where the individuals come from a mixture of two or more latent classes. These models allow each segment of the overall developmental process within each class to have a different functional form; examples include two linear phases of growth, or a quadratic phase followed by a linear phase. The changepoint (knot) is the time of transition from one developmental phase (segment) to another. Inferring the location of the changepoint(s) is often of practical interest, along with inference for other model parameters. A random changepoint allows for individual differences in the transition time within each class. The primary objectives of our study are: (1) to develop a PGMM using a Bayesian inference approach that allows the estimation of multiple random changepoints within each class; (2) to develop a procedure to empirically detect the number of random changepoints within each class; and (3) to empirically investigate the bias and precision of the estimation of the model parameters, including the random changepoints, via a simulation study. We have developed the user-friendly package BayesianPGMM for R to facilitate the adoption of this methodology in practice, which is available at https://github.com/lockEF/BayesianPGMM . We describe an application to mouse-tracking data for a visual recognition task.