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

Psychometrika
Niansheng TangHongtu Zhu

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 id...Continue Reading

References

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Apr 22, 2011·The British Journal of Mathematical and Statistical Psychology·Sy-Miin ChowHongtu Zhu
Sep 12, 2012·Psychological Methods·Bengt Muthén, Tihomir Asparouhov
Jan 1, 2012·Journal of the American Statistical Association·David B Dunson, Chuanhua Xing
Jun 1, 2011·Biometrika·Hongtu ZhuNiansheng Tang
Sep 16, 2014·Structural Equation Modeling : a Multidisciplinary Journal·Shelley A BlozisDavid Reiss
Jun 18, 2016·Multivariate Behavioral Research·Zhao-Hua LuEric Loken

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Citations

Jul 3, 2019·Multivariate Behavioral Research·Dongjun YouSy-Miin Chow
Jan 1, 2020·European Journal of Psychological Assessment : Official Organ of the European Association of Psychological Assessment·Jonathan J ParkPeter C M Molenaar

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