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Title page for ETD etd-11052015-135440

Type of Document Master's Thesis
Author Rights, Jason Douglas
Author's Email Address jason.d.rights@vanderbilt.edu
URN etd-11052015-135440
Title The relationship between multilevel models and nonparametric multilevel mixture models
Degree Master of Science
Department Psychology
Advisory Committee
Advisor Name Title
Kristopher Preacher Committee Member
Sonya Sterba Committee Member
Sun-Joo Cho Committee Member
  • nonparametric multilevel mixture models
  • multilevel models
Date of Defense 2015-09-14
Availability unrestricted
Multilevel data structures are common in the social sciences. Often, such nested data are analyzed with multilevel models (MLMs) wherein heterogeneity between clusters is modeled by continuously-distributed random intercepts and/or slopes. Alternatively, nonparametric multilevel regression mixture modeling (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this thesis is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of NPMM as a nonparametric approximation of MLM. I define how seven standard and nonstandard MLM specifications are indirectly approximated by particular NPMM specifications. I provide formulas showing how NPMM can serve as an approximation of MLM in terms of intraclass correlation, random effect variances, and heteroscedasticity of residuals at level-1 and level-2. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. I demonstrate how the indirect relationships can be utilized in inferential testing of implied MLM parameters and provide Mplus code to implement these tests. I also provide and describe an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed.
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
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