  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.
