IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v79y2014i1p60-83.html
   My bibliography  Save this article

Nonlinear Random-Effects Mixture Models for Repeated Measures

Author

Listed:
  • Casey Codd
  • Robert Cudeck

Abstract

A mixture model for repeated measures based on nonlinear functions with random effects is reviewed. The model can include individual schedules of measurement, data missing at random, nonlinear functions of the random effects, of covariates and of residuals. Individual group membership probabilities and individual random effects are obtained as empirical Bayes predictions. Although this is a complicated model that combines a mixture of populations, nonlinear regression, and hierarchical models, it is straightforward to estimate by maximum likelihood using SAS PROC NLMIXED. Many different models can be studied with this procedure. The model is more general than those that can be estimated with most special purpose computer programs currently available because the response function is essentially any form of nonlinear regression. Examples and sample code are included to illustrate the method. Copyright The Psychometric Society 2014

Suggested Citation

  • Casey Codd & Robert Cudeck, 2014. "Nonlinear Random-Effects Mixture Models for Repeated Measures," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 60-83, January.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:1:p:60-83
    DOI: 10.1007/s11336-013-9358-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9358-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9358-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Anders Skrondal & Sophia Rabe‐Hesketh, 2009. "Prediction in multilevel generalized linear models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 659-687, June.
    2. Peter Lenk & Wayne DeSarbo, 2000. "Bayesian inference for finite mixtures of generalized linear models with random effects," Psychometrika, Springer;The Psychometric Society, vol. 65(1), pages 93-119, March.
    3. Geert Verbeke & Geert Molenberghs, 2003. "The Use of Score Tests for Inference on Variance Components," Biometrics, The International Biometric Society, vol. 59(2), pages 254-262, June.
    4. Bengt Muthén & Kerby Shedden, 1999. "Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm," Biometrics, The International Biometric Society, vol. 55(2), pages 463-469, June.
    5. Donna K. Pauler & Nan M. Laird, 2000. "A Mixture Model for Longitudinal Data with Application to Assessment of Noncompliance," Biometrics, The International Biometric Society, vol. 56(2), pages 464-472, June.
    6. Emmanuel Lesaffre & Bart Spiessens, 2001. "On the effect of the number of quadrature points in a logistic random effects model: an example," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(3), pages 325-335.
    7. Yiu-Fai Yung, 1997. "Finite mixtures in confirmatory factor-analysis models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 297-330, September.
    8. Kamel Jedidi & Harsharanjeet S. Jagpal & Wayne S. DeSarbo, 1997. "Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity," Marketing Science, INFORMS, vol. 16(1), pages 39-59.
    9. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
    10. William Meredith & John Tisak, 1990. "Latent curve analysis," Psychometrika, Springer;The Psychometric Society, vol. 55(1), pages 107-122, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Daniel McNeish & Jeffrey R. Harring & Denis Dumas, 2023. "A multilevel structured latent curve model for disaggregating student and school contributions to learning," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(2), pages 545-575, June.
    2. Daniel Y. Lee & Jeffrey R. Harring, 2023. "Handling Missing Data in Growth Mixture Models," Journal of Educational and Behavioral Statistics, , vol. 48(3), pages 320-348, June.
    3. Daniel McNeish & Denis Dumas & Dario Torre & Neil Rice, 2022. "Modelling time to maximum competency in medical student progress tests," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2007-2034, October.
    4. Daniel McNeish & Denis Dumas, 2021. "A seasonal dynamic measurement model for summer learning loss," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(2), pages 616-642, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anders Skrondal & Sophia Rabe‐Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745, December.
    2. Kim, Sung Hoo & Mokhtarian, Patricia L., 2023. "Finite mixture (or latent class) modeling in transportation: Trends, usage, potential, and future directions," Transportation Research Part B: Methodological, Elsevier, vol. 172(C), pages 134-173.
    3. Heungsun Hwang & Wayne Desarbo & Yoshio Takane, 2007. "Fuzzy Clusterwise Generalized Structured Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 181-198, June.
    4. Yu Ding & Wayne S. DeSarbo & Dominique M. Hanssens & Kamel Jedidi & John G. Lynch & Donald R. Lehmann, 2020. "The past, present, and future of measurement and methods in marketing analysis," Marketing Letters, Springer, vol. 31(2), pages 175-186, September.
    5. Heungsun Hwang & Marc Tomiuk, 2010. "Fuzzy clusterwise quasi-likelihood generalized linear models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 4(4), pages 255-270, December.
    6. Pietro Lovaglio & Mario Mezzanzanica, 2013. "Classification of longitudinal career paths," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(2), pages 989-1008, February.
    7. Leila Amiri & Mojtaba Khazaei & Mojtaba Ganjali, 2018. "A mixture latent variable model for modeling mixed data in heterogeneous populations and its applications," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(1), pages 95-115, January.
    8. Lu, Xiaosun & Huang, Yangxin & Zhu, Yiliang, 2016. "Finite mixture of nonlinear mixed-effects joint models in the presence of missing and mismeasured covariate, with application to AIDS studies," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 119-130.
    9. Yangxin Huang & Xiaosun Lu & Jiaqing Chen & Juan Liang & Miriam Zangmeister, 2018. "Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 699-718, October.
    10. Ralf van der Lans & Joseph A. Cote & Catherine A. Cole & Siew Meng Leong & Ale Smidts & Pamela W. Henderson & Christian Bluemelhuber & Paul A. Bottomley & John R. Doyle & Alexander Fedorikhin & Janaki, 2009. "Cross-National Logo Evaluation Analysis: An Individual-Level Approach," Marketing Science, INFORMS, vol. 28(5), pages 968-985, 09-10.
      • van der Lans, R.J.A. & Cote, J.A. & Cole, C.A. & Leong, S.M. & Smidts, A. & Henderson, P.W. & Bluemelhuber, C. & Bottomley, P.A. & Doyle, J.R. & Fedorikhin, A.S. & Janakiraman, M. & Ramaseshan, B. & S, 2008. "Cross-National Logo Evaluation Analysis: An Individual Level Approach," ERIM Report Series Research in Management ERS-2008-055-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    11. De la Cruz-Mesia, Rolando & Quintana, Fernando A. & Marshall, Guillermo, 2008. "Model-based clustering for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1441-1457, January.
    12. Asim Ansari & Kamel Jedidi & Sharan Jagpal, 2000. "A Hierarchical Bayesian Methodology for Treating Heterogeneity in Structural Equation Models," Marketing Science, INFORMS, vol. 19(4), pages 328-347, August.
    13. Silvia Cagnone & Cinzia Viroli, 2014. "A factor mixture model for analyzing heterogeneity and cognitive structure of dementia," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(1), pages 1-20, January.
    14. Jan-Michael Becker & Christian Ringle & Marko Sarstedt & Franziska Völckner, 2015. "How collinearity affects mixture regression results," Marketing Letters, Springer, vol. 26(4), pages 643-659, December.
    15. Hong-Tu Zhu & Sik-Yum Lee, 2001. "A Bayesian analysis of finite mixtures in the LISREL model," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 133-152, March.
    16. Williams, John & Temme, Dirk & Hildebrandt, Lutz, 2002. "A Monte Carlo study of structural equation models for finite mixtures," SFB 373 Discussion Papers 2002,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    17. Fokoué, Ernest, 2005. "Mixtures of factor analyzers: an extension with covariates," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 370-384, August.
    18. Pennoni, Fulvia & Romeo, Isabella, 2016. "Latent Markov and growth mixture models for ordinal individual responses with covariates: a comparison," MPRA Paper 72939, University Library of Munich, Germany.
    19. Jianan Wu & Wayne DeSarbo & Pu-Ju Chen & Yao-Yi Fu, 2006. "A latent structure factor analytic approach for customer satisfaction measurement," Marketing Letters, Springer, vol. 17(3), pages 221-238, July.
    20. Anindita Chakravarty & Rajdeep Grewal & V. Sambamurthy, 2013. "Information Technology Competencies, Organizational Agility, and Firm Performance: Enabling and Facilitating Roles," Information Systems Research, INFORMS, vol. 24(4), pages 976-997, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:79:y:2014:i:1:p:60-83. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.