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

• Published in: Psychometrika Vol. 82; no. 4; pp. 875 - 903
• Main Authors: Tang, Niansheng, Chow, Sy-Miin, Ibrahim, Joseph G., Zhu, Hongtu
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2017; Springer Nature B.V
• Subjects: Algorithms; Assessment; Bayes Theorem; Bayesian analysis; Behavioral Science and Psychology; Computer Simulation; Data Interpretation, Statistical; Discriminant analysis; Ecological Momentary Assessment; Economic models; Emotions; Factor Analysis; Factor Analysis, Statistical; Female; Humanities; Humans; Law; Male; Mathematical models; Missing data; Nonlinear Dynamics; Nonparametric Statistics; Psychology; Psychometrics; Sensitivity analysis; Statistical Theory and Methods; Statistics for Social Sciences; Statistics, Nonparametric; Testing and Evaluation; Time series; Young Adult; nonlinear dynamic factor analysis model; Bayesian local influence; sensitivity analysis; Bayesian perturbation manifold; Dirichlet process prior; nonignorable missing data
• ISSN: 0033-3123; 1860-0980; 1860-0980
• DOI: 10.1007/s11336-017-9587-4

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.