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Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness

Published online by Cambridge University Press:  01 January 2025

Niansheng Tang ,
Sy-Miin Chow Open the ORCID record for Sy-Miin Chow [Opens in a new window] ,
Joseph G. Ibrahim  and
Hongtu Zhu
Niansheng Tang
Affiliation:
Yunnan University
Sy-Miin Chow*
Affiliation:
Pennsylvania State University
Joseph G. Ibrahim
Affiliation:
Unisversity of North Carolina at Chapel Hill
Hongtu Zhu
Affiliation:
Unisversity of North Carolina at Chapel Hill
*
Correspondence should be made to Sy-Miin Chow, Department of Human Development and Family Studies, Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA 16802, USA. Email: symiin@psu.edu
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Abstract

Many psychological concepts are unobserved and usually represented as latent factors apprehended through multiple observed indicators. When multiple-subject multivariate time series data are available, dynamic factor analysis models with random effects offer one way of modeling patterns of within- and between-person variations by combining factor analysis and time series analysis at the factor level. Using the Dirichlet process (DP) as a nonparametric prior for individual-specific time series parameters further allows the distributional forms of these parameters to deviate from commonly imposed (e.g., normal or other symmetric) functional forms, arising as a result of these parameters’ restricted ranges. Given the complexity of such models, a thorough sensitivity analysis is critical but computationally prohibitive. We propose a Bayesian local influence method that allows for simultaneous sensitivity analysis of multiple modeling components within a single fitting of the model of choice. Five illustrations and an empirical example are provided to demonstrate the utility of the proposed approach in facilitating the detection of outlying cases and common sources of misspecification in dynamic factor analysis models, as well as identification of modeling components that are sensitive to changes in the DP prior specification.

Keywords

Bayesian local influenceBayesian perturbation manifoldDirichlet process priornonignorable missing datanonlinear dynamic factor analysis modelsensitivity analysis
Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 4 , December 2017 , pp. 875 - 903
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-017-9587-4) contains supplementary material, which is available to authorized users.

N. Tang and S.-M. Chow: These two authors contributed equally to the work.

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