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Bayesian Semi- and Non-Parametric Models for Longitudinal Data with Multiple Membership Effects in R

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  • Savitsky, Terrance
  • Paddock, Susan

Abstract

We introduce growcurves for R that performs analysis of repeated measures multiple membership (MM) data. This data structure arises in studies under which an intervention is delivered to each subject through the subject’s participation in a set of multiple elements that characterize the intervention. In our motivating study design under which subjects receive a group cognitive behavioral therapy (CBT) treatment, an element is a group CBT session and each subject attends multiple sessions that, together, comprise the treatment. The sets of elements, or group CBT sessions, attended by subjects will partly overlap with some of those from other subjects to induce a dependence in their responses. The growcurves package offers two alternative sets of hierarchical models: 1. Separate terms are specified for multivariate subject and MM element random effects, where the subject effects are modeled under a Dirichlet process prior to produce a semi-parametric construction; 2. A single term is employed to model joint subject-by-MM effects. A fully non-parametric dependent Dirichlet process formulation allows exploration of differences in subject responses across different MM elements. This model allows for borrowing information among subjects who express similar longitudinal trajectories for flexible estimation. growcurves deploys “estimation” functions to perform posterior sampling under a suite of prior options. An accompanying set of “plot” functions allows the user to readily extract by-subject growth curves. The design approach intends to anticipate inferential goals with tools that fully extract information from repeated measures data. Computational efficiency is achieved by performing the sampling for estimation functions using compiled C++ code.

Suggested Citation

  • Savitsky, Terrance & Paddock, Susan, 2014. "Bayesian Semi- and Non-Parametric Models for Longitudinal Data with Multiple Membership Effects in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i03).
  • Handle: RePEc:jss:jstsof:v:057:i03
    DOI: http://hdl.handle.net/10.18637/jss.v057.i03
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    References listed on IDEAS

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    1. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    2. Louis T. Mariano & Daniel F. McCaffrey & J. R. Lockwood, 2010. "A Model for Teacher Effects From Longitudinal Data Without Assuming Vertical Scaling," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 253-279, June.
    3. Jara, Alejandro & Hanson, Timothy & Quintana, Fernando A. & Müller, Peter & Rosner, Gary L., 2011. "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i05).
    4. Zeileis, Achim & Croissant, Yves, 2010. "Extended Model Formulas in R: Multiple Parts and Multiple Responses," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i01).
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    1. Pereira, Luz Adriana & Gutiérrez, Luis & Taylor-Rodríguez, Daniel & Mena, Ramsés H., 2023. "Bayesian nonparametric hypothesis testing for longitudinal data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

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