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Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach

The present article proposes and evaluates marginal maximum likelihood (ML) estimation methods for hierarchical multinomial processing tree (MPT) models with random and fixed effects. We assume that an identifiable MPT model with S parameters holds for each participant. Of these S parameters, R para...

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Detalles Bibliográficos
Autores principales: Nestler, Steffen, Erdfelder, Edgar
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10444666/
https://www.ncbi.nlm.nih.gov/pubmed/37247167
http://dx.doi.org/10.1007/s11336-023-09921-w
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author Nestler, Steffen
Erdfelder, Edgar
author_facet Nestler, Steffen
Erdfelder, Edgar
author_sort Nestler, Steffen
collection PubMed
description The present article proposes and evaluates marginal maximum likelihood (ML) estimation methods for hierarchical multinomial processing tree (MPT) models with random and fixed effects. We assume that an identifiable MPT model with S parameters holds for each participant. Of these S parameters, R parameters are assumed to vary randomly between participants, and the remaining [Formula: see text] parameters are assumed to be fixed. We also propose an extended version of the model that includes effects of covariates on MPT model parameters. Because the likelihood functions of both versions of the model are too complex to be tractable, we propose three numerical methods to approximate the integrals that occur in the likelihood function, namely, the Laplace approximation (LA), adaptive Gauss–Hermite quadrature (AGHQ), and Quasi Monte Carlo (QMC) integration. We compare these three methods in a simulation study and show that AGHQ performs well in terms of both bias and coverage rate. QMC also performs well but the number of responses per participant must be sufficiently large. In contrast, LA fails quite often due to undefined standard errors. We also suggest ML-based methods to test the goodness of fit and to compare models taking model complexity into account. The article closes with an illustrative empirical application and an outlook on possible extensions and future applications of the proposed ML approach.
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spelling pubmed-104446662023-08-24 Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach Nestler, Steffen Erdfelder, Edgar Psychometrika Theory and Methods The present article proposes and evaluates marginal maximum likelihood (ML) estimation methods for hierarchical multinomial processing tree (MPT) models with random and fixed effects. We assume that an identifiable MPT model with S parameters holds for each participant. Of these S parameters, R parameters are assumed to vary randomly between participants, and the remaining [Formula: see text] parameters are assumed to be fixed. We also propose an extended version of the model that includes effects of covariates on MPT model parameters. Because the likelihood functions of both versions of the model are too complex to be tractable, we propose three numerical methods to approximate the integrals that occur in the likelihood function, namely, the Laplace approximation (LA), adaptive Gauss–Hermite quadrature (AGHQ), and Quasi Monte Carlo (QMC) integration. We compare these three methods in a simulation study and show that AGHQ performs well in terms of both bias and coverage rate. QMC also performs well but the number of responses per participant must be sufficiently large. In contrast, LA fails quite often due to undefined standard errors. We also suggest ML-based methods to test the goodness of fit and to compare models taking model complexity into account. The article closes with an illustrative empirical application and an outlook on possible extensions and future applications of the proposed ML approach. Springer US 2023-05-29 2023 /pmc/articles/PMC10444666/ /pubmed/37247167 http://dx.doi.org/10.1007/s11336-023-09921-w Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Theory and Methods
Nestler, Steffen
Erdfelder, Edgar
Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach
title Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach
title_full Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach
title_fullStr Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach
title_full_unstemmed Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach
title_short Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach
title_sort random effects multinomial processing tree models: a maximum likelihood approach
topic Theory and Methods
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10444666/
https://www.ncbi.nlm.nih.gov/pubmed/37247167
http://dx.doi.org/10.1007/s11336-023-09921-w
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