Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models



Piecewise growth mixture models 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 as follows: (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 We describe an application to mouse-tracking data for a visual recognition task.


Bayesian longitudinal data Markov chain Monte Carlo mixture model nonlinear random effects models piecewise function 



We would like to thank Sara Incera and Conor T. McLennan of Cleveland State University for graciously providing the mouse-tracking data described in Sect. 4. This work was supported in part by NIH grant ULI RR033183/KL2 RR0333182 [to EFL].

Supplementary material

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Supplementary material 1 (xlsx 69 KB)
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Supplementary material 3 (gz 28 KB)


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Copyright information

© The Psychometric Society 2017

Authors and Affiliations

  1. 1.Division of Biostatistics, School of Public HealthUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Educational Psychology, College of Education and Human DevelopmentUniversity of MinnesotaMinneapolisUSA

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