Using Bayesian Statistics to Model Uncertainty in Mixture Models: A Sensitivity Analysis of Priors

Depaoli, Sarah; Yu-lin, Yang; Felt, John M.

doi:10.1080/10705511.2016.1250640

Cited by 24 publications

(18 citation statements)

References 60 publications

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“…There are many research scenarios within the Bayesian context where informative (or user-specified) priors have an impact on final model estimates. Some examples include research with models such as the latent growth mixture model ( Depaoli et al, 2017b ; van de Schoot et al, 2018 ), the confirmatory factor analytic model ( Golay et al, 2013 ), and logistic regression ( Heitjan et al, 2008 ).…”

Section: What Do We Know About the Impact Of Priors?mentioning

confidence: 99%

The Importance of Prior Sensitivity Analysis in Bayesian Statistics: Demonstrations Using an Interactive Shiny App

2020

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The current paper highlights a new, interactive Shiny App that can be used to aid in understanding and teaching the important task of conducting a prior sensitivity analysis when implementing Bayesian estimation methods. In this paper, we discuss the importance of examining prior distributions through a sensitivity analysis. We argue that conducting a prior sensitivity analysis is equally important when so-called diffuse priors are implemented as it is with subjective priors. As a proof of concept, we conducted a small simulation study, which illustrates the impact of priors on final model estimates. The findings from the simulation study highlight the importance of conducting a sensitivity analysis of priors. This concept is further extended through an interactive Shiny App that we developed. The Shiny App allows users to explore the impact of various forms of priors using empirical data. We introduce this Shiny App and thoroughly detail an example using a simple multiple regression model that users at all levels can understand. In this paper, we highlight how to determine the different settings for a prior sensitivity analysis, how to visually and statistically compare results obtained in the sensitivity analysis, and how to display findings and write up disparate results obtained across the sensitivity analysis. The goal is that novice users can follow the process outlined here and work within the interactive Shiny App to gain a deeper understanding of the role of prior distributions and the importance of a sensitivity analysis when implementing Bayesian methods. The intended audience is broad (e.g., undergraduate or graduate students, faculty, and other researchers) and can include those with limited exposure to Bayesian methods or the specific model presented here.

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Section: What Do We Know About the Impact Of Priors?mentioning

confidence: 99%

The Importance of Prior Sensitivity Analysis in Bayesian Statistics: Demonstrations Using an Interactive Shiny App

2020

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“…The large sample size to some extent does cover one of the potential weaknesses of BSEM in that it can be highly sensitive to prior specifications (Depaoli, Yang, & Felt, ; van Erp, Mulder, & Oberski, ). Informative priors for one parameter have the property of inducing implicit priors for other covariant parameters in a fashion that is difficult to predict and manage (MacCallum, Edwards, & Cai, ).…”

Section: Discussionmentioning

confidence: 99%

An application of Bayesian measurement invariance to modelling cognition over time in the English Longitudinal Study of Ageing

Williams

Chandola

Pendleton

2018

Int J Methods Psych Res

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Objectives Recommended cut‐off criteria for testing measurement invariance (MI) using the comparative fit index (CFI) vary between −0.002 and −0.01. We compared CFI results with those obtained using Bayesian approximate MI for cognitive function. Methods We used cognitive function data from Waves 1–5 of the English Longitudinal Study of Ageing (ELSA; Wave 1 n = 11,951), a nationally representative sample of English adults aged ≥50. We tested for longitudinal invariance using CFI and approximate MI (prior for a difference between intercepts/loadings ~N(0,0.01)) in an attention factor (orientation to date, day, week, and month) and a memory factor (immediate and delayed recall, verbal fluency, and a prospective memory task). Results Conventional CFI criteria found strong invariance for the attention factor (CFI + 0.002) but either weak or strong invariance for the memory factor (CFI −0.004). The approximate MI results also supported strong MI for attention but found 9/20 intercepts or thresholds were noninvariant for the memory factor. This supports weak rather than strong invariance. Conclusions Within ELSA, the attention factor is suitable for longitudinal analysis but not the memory factor. More generally, in situations where the appropriate CFI criteria for invariance are unclear, Bayesian approximate MI could alternatively be used.

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“…However, they tend to converge with frequentist estimation with weakly informative priors like those used here and provide an efficient means of estimation for complex mixture models. (Depaoli et al, 2017;Helm et al, 2017) A substantial limitation of the current analysis is the unavailability of a measure of brain status. (Stern et al, 2018) As explained in the 2018 whitepaper from the Reserve, Resilience and Protective Factors PIA Empirical Definitions and Conceptual Frameworks Workgroup, studies of the cognitive reserve should ideally have a sociobehavioural proxy for reserve (education in our case), cognitive performance outcomes and a measure brain status.…”

Section: Strengths and Limitationsmentioning

confidence: 99%

Does the association between cognition and education differ between older adults with gradual or rapid trajectories of cognitive decline?

Williams

Pendleton

Chandola

2021

Aging, Neuropsychology, and Cognition

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Using Bayesian Statistics to Model Uncertainty in Mixture Models: A Sensitivity Analysis of Priors

Cited by 24 publications

References 60 publications

The Importance of Prior Sensitivity Analysis in Bayesian Statistics: Demonstrations Using an Interactive Shiny App

The Importance of Prior Sensitivity Analysis in Bayesian Statistics: Demonstrations Using an Interactive Shiny App

An application of Bayesian measurement invariance to modelling cognition over time in the English Longitudinal Study of Ageing

Does the association between cognition and education differ between older adults with gradual or rapid trajectories of cognitive decline?

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