Mediation and moderated mediation models are two commonly used models for indirect effects analysis. In practice, missing data is a pervasive problem in structural equation modeling with psychological data. Multiple imputation (MI) is one method used to estimate model parameters in the presence of missing data, while accounting for uncertainty due to the missing data. Unfortunately, commonly used MI methods are not equipped to handle categorical variables or nonlinear variables such as interactions. In this study, we introduce a general MI framework that uses the Bayesian bootstrap (BB) method to generate posterior inferences for indirect effects and gradient boosted machine learning imputation models that can impute missing data in linear and logistic regression models with linear and nonlinear effects.
Two Monte Carlo simulation studies are conducted to examine the empirical performance of a BB procedure for estimation and inference of indirect effects and to examine the performance of the proposed imputation algorithm in indirect effects analysis. Results show that the BB has comparable performance to widely used frequentist methods (e.g., delta methods and nonparametric bootstrap with bias-correction) for indirect effects analysis for a variety of models and conditions. With missing data, in general, results indicate that the proposed MI framework has comparable performance to model-based estimation and other MI algorithms for indirect effects analysis in mediation models; for indirect effects analysis in moderated mediation models, results indicate that the proposed MI framework outperforms these methods in most conditions. Advantages and limitations of the BB as applied to indirect effects analysis are discussed.
","abstract_html":"<p>Mediation and moderated mediation models are two commonly used models for indirect effects analysis. In practice, missing data is a pervasive problem in structural equation modeling with psychological data. Multiple imputation (MI) is one method used to estimate model parameters in the presence of missing data, while accounting for uncertainty due to the missing data. Unfortunately, commonly used MI methods are not equipped to handle categorical variables or nonlinear variables such as interactions. In this study, we introduce a general MI framework that uses the Bayesian bootstrap (BB) method to generate posterior inferences for indirect effects and gradient boosted machine learning imputation models that can impute missing data in linear and logistic regression models with linear and nonlinear effects.</p> <p>Two Monte Carlo simulation studies are conducted to examine the empirical performance of a BB procedure for estimation and inference of indirect effects and to examine the performance of the proposed imputation algorithm in indirect effects analysis. Results show that the BB has comparable performance to widely used frequentist methods (e.g., delta methods and nonparametric bootstrap with bias-correction) for indirect effects analysis for a variety of models and conditions. With missing data, in general, results indicate that the proposed MI framework has comparable performance to model-based estimation and other MI algorithms for indirect effects analysis in mediation models; for indirect effects analysis in moderated mediation models, results indicate that the proposed MI framework outperforms these methods in most conditions. Advantages and limitations of the BB as applied to indirect effects analysis are discussed.</p>","abstract_has_math":false,"creators":["Milletich, Robert J., II"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Psychology","degree_department":null,"school":null,"contributors":["Michelle L. Kelley","James F. Paulson","Norou Diawara"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-10-01T07:00:00Z","date_published":"2016-10-01T07:00:00Z","updated_at":"2026-07-24T03:34:02Z","subjects":["Bayesian bootstrap","Machine learning","Mediation","Missing data","Moderated mediation","Structural equation modeling","Computer Sciences","Quantitative Psychology","Statistics and Probability"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["9781369564211"],"render_values":[{"text":"9781369564211","href":null,"code":true}]}]},"links":{"outbound_url":"https://digitalcommons.odu.edu/psychology_etds/44","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Michelle L. Kelley","James F. Paulson","Norou Diawara"]},{"key":"dc:creator","label":"Author","values":["Milletich, Robert J., II"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2017-02-08T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Psychology"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Bayesian bootstrap","Machine learning","Mediation","Missing data","Moderated mediation","Structural equation modeling","Computer Sciences","Quantitative Psychology","Statistics and Probability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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Two Monte Carlo simulation studies are conducted to examine the empirical performance of a BB procedure for estimation and inference of indirect effects and to examine the performance of the proposed imputation algorithm in indirect effects analysis. Results show that the BB has comparable performance to widely used frequentist methods (e.g., delta methods and nonparametric bootstrap with bias-correction) for indirect effects analysis for a variety of models and conditions. With missing data, in general, results indicate that the proposed MI framework has comparable performance to model-based estimation and other MI algorithms for indirect effects analysis in mediation models; for indirect effects analysis in moderated mediation models, results indicate that the proposed MI framework outperforms these methods in most conditions. Advantages and limitations of the BB as applied to indirect effects analysis are discussed.
"]},{"key":"dc:title","label":"Title","values":["Multiple Imputation of Missing Data in Structural Equation Models with Mediators and Moderators Using Gradient Boosted Machine Learning"]}]}],"canonical_facts":{"dc:contributor":["Michelle L. Kelley","James F. Paulson","Norou Diawara"],"dc:creator":["Milletich, Robert J., II"],"dc:date.available":["2017-02-08T08:00:00Z"],"dc:description.abstract":["Mediation and moderated mediation models are two commonly used models for indirect effects analysis. In practice, missing data is a pervasive problem in structural equation modeling with psychological data. Multiple imputation (MI) is one method used to estimate model parameters in the presence of missing data, while accounting for uncertainty due to the missing data. Unfortunately, commonly used MI methods are not equipped to handle categorical variables or nonlinear variables such as interactions. In this study, we introduce a general MI framework that uses the Bayesian bootstrap (BB) method to generate posterior inferences for indirect effects and gradient boosted machine learning imputation models that can impute missing data in linear and logistic regression models with linear and nonlinear effects.
Two Monte Carlo simulation studies are conducted to examine the empirical performance of a BB procedure for estimation and inference of indirect effects and to examine the performance of the proposed imputation algorithm in indirect effects analysis. Results show that the BB has comparable performance to widely used frequentist methods (e.g., delta methods and nonparametric bootstrap with bias-correction) for indirect effects analysis for a variety of models and conditions. With missing data, in general, results indicate that the proposed MI framework has comparable performance to model-based estimation and other MI algorithms for indirect effects analysis in mediation models; for indirect effects analysis in moderated mediation models, results indicate that the proposed MI framework outperforms these methods in most conditions. Advantages and limitations of the BB as applied to indirect effects analysis are discussed.
"],"dc:identifier":["9781369564211","https://digitalcommons.odu.edu/psychology_etds/44"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Bayesian bootstrap","Machine learning","Mediation","Missing data","Moderated mediation","Structural equation modeling","Computer Sciences","Quantitative Psychology","Statistics and Probability"],"dc:title":["Multiple Imputation of Missing Data in Structural Equation Models with Mediators and Moderators Using Gradient Boosted Machine Learning"],"thesis:degree_discipline":["Psychology"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:02Z"}