Hostname: page-component-5cf477f64f-rdph2 Total loading time: 0 Render date: 2025-04-03T00:59:21.477Z Has data issue: false hasContentIssue false
  • English
  • Français

Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models

Published online by Cambridge University Press:  01 January 2025

Eric F. Lock Open the ORCID record for Eric F. Lock [Opens in a new window] ,
Nidhi Kohli  and
Maitreyee Bose
Eric F. Lock*
Affiliation:
University of Minnesota
Nidhi Kohli
Affiliation:
University of Minnesota
Maitreyee Bose
Affiliation:
University of Minnesota
*
Correspondence should be made to Eric F. Lock, Division of Biostatistics, School of Public Health, University of Minnesota, A460 Mayo Building, MMC 303 420 Delaware Street, S.E., Minneapolis, MN 55455, USA. Email: [email protected]; URL: http://ericfrazerlock.com/
Get access Rights & Permissions [Opens in a new window]

Abstract

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 https://github.com/lockEF/BayesianPGMM. We describe an application to mouse-tracking data for a visual recognition task.

Keywords

Bayesianlongitudinal dataMarkov chain Monte Carlomixture modelnonlinear random effects modelspiecewise function
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 3 , September 2018 , pp. 733 - 750
Copyright
Copyright © The Psychometric Society 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-017-9594-5) contains supplementary material, which is available to authorized users.

References

Akaike, H. (1974). A new look at the statistical model identification..IEEE Transactions on Automatic Control, ,19(6),716–723..CrossRefGoogle Scholar
Bradway, K. P., & Thompson, C. W. (1962). Intelligence at adulthood: A twenty-five year follow-up..Journal of Educational Psychology, ,53(1),1.CrossRefGoogle Scholar
Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations..Journal of Computational and Graphical Statistics, ,7(4)434–455..CrossRefGoogle Scholar
Carlin, B. P.,Gelfand, A. E., & Smith, A. F. (1992). Hierarchical Bayesian analysis of changepoint problems..Applied Statistics, ,41(2)389–405..CrossRefGoogle Scholar
Casella, G., & George, E. I. (1992). Explaining the Gibbs sampler..The American Statistician, ,46(3)167–174..CrossRefGoogle Scholar
Chib, S. (1998). Estimation and comparison of multiple change-point models..Journal of Econometrics, ,86(2)221–241..CrossRefGoogle Scholar
Cudeck, R., & Klebe, K. J. (2002). Multiphase mixed-effects models for repeated measures data..Psychological Methods, ,7(1)41.CrossRefGoogle ScholarPubMed
Daniels, M. J., & Kass, R. E. (1999). Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models..Journal of the American Statistical Association, ,94(448)1254–1263..CrossRefGoogle Scholar
Delattre, M.,Lavielle, M.,Poursat, M. -A.,et.al (2014). A note on BIC in mixed-effects models..Electronic Journal of Statistics, ,8(1)456–475..CrossRefGoogle Scholar
Dominicus, A.,Ripatti, S.,Pedersen, N. L., & Palmgren, J. (2008). A random change point model for assessing variability in repeated measures of cognitive function..Statistics in Medicine, ,27(27)5786–5798..CrossRefGoogle ScholarPubMed
Fearnhead, P. (2006). Exact and efficient Bayesian inference for multiple changepoint problems..Statistics and Computing, ,16(2)203–213..CrossRefGoogle Scholar
Fearnhead, P., & Liu, Z. (2011). Efficient Bayesian analysis of multiple changepoint models with dependence across segments..Statistics and Computing, ,21(2)217–229..CrossRefGoogle Scholar
Gallistel, C. R.,Fairhurst, S., & Balsam, P. (2004). The learning curve: Implications of a quantitative analysis..Proceedings of the National Academy of Sciences of the United States of America, ,101(36)13124–13131..CrossRefGoogle ScholarPubMed
Gelman, A.,et.al (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)..Bayesian Analysis, ,1(3)515–534..CrossRefGoogle Scholar
Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences..Statistical Science, ,7(4)457–472..CrossRefGoogle Scholar
Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images..IEEE Transactions on Pattern Analysis and Machine Intelligence, ,6 721–741..CrossRefGoogle ScholarPubMed
Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination..Biometrika, ,82(4)711–732..CrossRefGoogle Scholar
Hall, C. B.,Lipton, R. B.,Sliwinski, M., & Stewart, W. F. (2000). A change point model for estimating the onset of cognitive decline in preclinical Alzheimer’s disease..Statistics in Medicine, ,19(11–12)1555–1566..3.0.CO;2-3>CrossRefGoogle ScholarPubMed
Hall, C. B.,Ying, J.,Kuo, L.,Sliwinski, M.,Buschke, H.,Katz, M.,et.al (2001). Estimation of bivariate measurements having different change points, with application to cognitive ageing..Statistics in Medicine, ,20(24)3695–3714..CrossRefGoogle ScholarPubMed
Incera, S., & McLennan, C. T. (2016). Mouse tracking reveals that bilinguals behave like experts..Bilingualism: Language and Cognition, ,19(03)610–620..CrossRefGoogle Scholar
Karlberg, J. (1987). On the modelling of human growth..Statistics in Medicine, ,6(2)185–192..CrossRefGoogle ScholarPubMed
Karlberg, J.,Jalil, F.,Lam, B.,Low, L., & Yeung, C. (1994). Linear growth retardation in relation to the three phases of growth..European Journal of Clinical Nutrition, ,48 S25–43..Google Scholar
Kieffer, M. J. (2012). Before and after third grade: Longitudinal evidence for the shifting role of socioeconomic status in reading growth..Reading and Writing, ,25(7)1725–1746..CrossRefGoogle Scholar
Kohli, N.,Harring, J. R., & Hancock, G. R. (2013). Piecewise linear-linear latent growth mixture models with unknown knots..Educational and Psychological Measurement, ,73(6)935–955..CrossRefGoogle Scholar
Kohli, N.,Harring, J., & Zopluoglu, C. (2016). A finite mixture of nonlinear random coefficient models for continuous repeated measures data..Psychometrika, ,81(3)851–880..CrossRefGoogle ScholarPubMed
Kohli, N.,Hughes, J.,Wang, C.,Zopluoglu, C., & Davison, M.Fitting a linear-linear piecewise growth mixture model with unknown knots: A comparison of two common approaches to inference..Psychological Methods, ,(2015a). 20(2)259–275..CrossRefGoogle Scholar
Kohli, N.,Sullivan, A. L.,Sadeh, S., & Zopluoglu, C.Longitudinal mathematics development of students with learning disabilities and students without disabilities: A comparison of linear, quadratic, and piecewise linear mixed effects models..Journal of School Psychology, ,(2015b). 53(2)105–120..CrossRefGoogle ScholarPubMed
Kreisman, M. B. (2003). Evaluating academic outcomes of head start: An application of general growth mixture modeling..Early Childhood Research Quarterly, ,18(2)238–254..CrossRefGoogle Scholar
Lai, Y., & Albert, P. S. (2014). Identifying multiple change points in a linear mixed effects model..Statistics in Medicine, ,33(6)1015–1028..CrossRefGoogle Scholar
Morrell, C. H.,Pearson, J. D.,Carter, H. B., & Brant, L. J. (1995). Estimating unknown transition times using a piecewise nonlinear mixed-effects model in men with prostate cancer..Journal of the American Statistical Association, ,90(429)45–53..CrossRefGoogle Scholar
Muniz Terrera, G.,Van den Hout, A., & Matthews, F. (2011). Random change point models: investigating cognitive decline in the presence of missing data..Journal of Applied Statistics, ,38(4)705–716..CrossRefGoogle Scholar
Myung, I. J. (2000). The importance of complexity in model selection..Journal of Mathematical Psychology, ,44(1)190–204..CrossRefGoogle ScholarPubMed
Naumova, E. N.,Must, A., & Laird, N. M. (2001). Tutorial in biostatistics: Evaluating the impact of critical periods in longitudinal studies of growth using piecewise mixed effects models..International Journal of Epidemiology, ,30(6)1332–1341..CrossRefGoogle ScholarPubMed
Papastamoulis, P. (2014). Handling the label switching problem in latent class models via the ECR algorithm..Communications in Statistics-Simulation and Computation, ,43(4)913–927..CrossRefGoogle Scholar
Papastamoulis, P. (2015). label. switching: An R package for dealing with the label switching problem in MCMC outputs.. arXiv preprint, , arXiv:1503.02271.Google Scholar
Plummer, M. (2016). rjags: Bayesian Graphical Models using MCMC..R package version 4-6, .Google Scholar
Schwarz, G.et.al (1978). Estimating the dimension of a model..The annals of statistics, ,6(2)461–464..CrossRefGoogle Scholar
Sinharay, S. (2004). Experiences with Markov chain Monte Carlo convergence assessment in two psychometric examples..Journal of Educational and Behavioral Statistics, ,29(4)461–488..CrossRefGoogle Scholar
Spiegelhalter, D.,Thomas, A.,Best, N., & Gilks, W. (1996). BUGS 0.5: Bayesian inference using Gibbs sampling manual.1–59..CambridgeMRC Biostatistics Unit, Institute of Public HealthGoogle Scholar
Spiegelhalter, D. J.,Best, N. G.,Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit..Journal of the Royal Statistical Society: Series B (Statistical Methodology), ,64(4)583–639..CrossRefGoogle Scholar
Sullivan, A. L.,Kohli, N.,Farnsworth, E. M.,Sadeh, S., & Jones, L. (2017). Longitudinal models of reading achievement of students with learning disabilities and without disabilities..School Psychology Quarterly, ,32(3),336–349..CrossRefGoogle Scholar
Vaida, F., & Blanchard, S. (2005). Conditional Akaike information for mixed-effects models..Biometrika, ,92(2)351–370..CrossRefGoogle Scholar
Vehtari, A.,Gelman, A.,& Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC..Statistics and Computing, ,27(5)1413–1432..CrossRefGoogle Scholar
Wang, L., & McArdle, J. J. (2008). A simulation study comparison of Bayesian estimation with conventional methods for estimating unknown change points..Structural Equation Modeling, ,15(1)52–74..CrossRefGoogle Scholar
Wang, Y.,& Fang, Y. (2009). Least square and empirical Bayes approaches for estimating random change points..Journal of Data Science, ,7(1)111–127..CrossRefGoogle Scholar
Zhao, L., & Banerjee, M. (2012). Bayesian piecewise mixture model for racial disparity in prostate cancer progression..Computational Statistics & Data Analysis, ,56(2)362–369..CrossRefGoogle ScholarPubMed
Supplementary material: File

Lock et al. supplementary material

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-017-9594-5) contains supplementary material, which is available to authorized users.
Download Lock et al. supplementary material(File)
File 70.9 KB
Supplementary material: File

Lock et al. supplementary material

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-017-9594-5) contains supplementary material, which is available to authorized users.
Download Lock et al. supplementary material(File)
File 622.9 KB
Supplementary material: File

Lock et al. supplementary material

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-017-9594-5) contains supplementary material, which is available to authorized users.
Download Lock et al. supplementary material(File)
File 28.9 KB