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, Hongtu Zhu

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)875-903
Number of pages29
JournalPsychometrika
Volume82
Issue number4
DOIs
StatePublished - Dec 1 2017

Fingerprint

Nonlinear Dynamics
Bayes Theorem
Factor analysis
Bayesian Analysis
Factor Analysis
Dynamic Analysis
Sensitivity analysis
Statistical Factor Analysis
Sensitivity Analysis
Modeling
Multiple Time Series
Time series
Dirichlet Process Prior
Local Influence
Dirichlet Process
Multivariate Time Series
Misspecification
Time Series Analysis
Multivariate Data
Time Series Data

All Science Journal Classification (ASJC) codes

  • Psychology(all)
  • Applied Mathematics

Cite this

@article{3aa28007d84644738484d7fd65dd1f49,
title = "Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness",
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.",
author = "Niansheng Tang and Sy-Miin Chow and Ibrahim, {Joseph G.} and Hongtu Zhu",
year = "2017",
month = "12",
day = "1",
doi = "10.1007/s11336-017-9587-4",
language = "English (US)",
volume = "82",
pages = "875--903",
journal = "Psychometrika",
issn = "0033-3123",
publisher = "Springer New York",
number = "4",

}

Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness. / Tang, Niansheng; Chow, Sy-Miin; Ibrahim, Joseph G.; Zhu, Hongtu.

In: Psychometrika, Vol. 82, No. 4, 01.12.2017, p. 875-903.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness

AU - Tang, Niansheng

AU - Chow, Sy-Miin

AU - Ibrahim, Joseph G.

AU - Zhu, Hongtu

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85031431399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85031431399&partnerID=8YFLogxK

U2 - 10.1007/s11336-017-9587-4

DO - 10.1007/s11336-017-9587-4

M3 - Article

C2 - 29030749

AN - SCOPUS:85031431399

VL - 82

SP - 875

EP - 903

JO - Psychometrika

JF - Psychometrika

SN - 0033-3123

IS - 4

ER -