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

Niansheng Tang, Sy-Miin Chow (), Joseph G. Ibrahim and Hongtu Zhu
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Niansheng Tang: Yunnan University
Sy-Miin Chow: Pennsylvania State University
Joseph G. Ibrahim: Unisversity of North Carolina at Chapel Hill
Hongtu Zhu: Unisversity of North Carolina at Chapel Hill

Psychometrika, 2017, vol. 82, issue 4, No 1, 875-903

Abstract: 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 influence; Bayesian perturbation manifold; Dirichlet process prior; nonignorable missing data; nonlinear dynamic factor analysis model; sensitivity analysis (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11336-017-9587-4

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