Sensitivity analysis of structural equation models

Lee, Sik‐Yum; Wang, S. J.

doi:10.1007/bf02296960

Cited by 74 publications

(97 citation statements)

References 17 publications

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“…Fungible parameter estimates provide diagnostic information about statistical results from the broader framework of sensitivity analysis (Cook, 1986;S.-Y. Lee & Wang, 1996).…”

Section: Fungible Parameter Estimatesmentioning

confidence: 99%

Section: Fungible Parameter Estimatesmentioning

confidence: 99%

“…Lee & Wang, 1996). Specifically, FPEs inform of whether their commensurate parameter estimates should be validly interpreted.…”

Section: Fungible Parameter Estimatesmentioning

confidence: 99%

“…This influence or sensitivity of parameters can be determined from a sensitivity analysis where optimal focal parameter estimatesθ f are perturbed to quantify their influence on model fit (S.-Y. Lee & Wang, 1996); parameters which strongly influence model fit are deemed sensitive whereas the converse holds for insensitive parameters.Fungible parameter estimates approach the issue of parameter sensitivity by perturbing model fit instead of optimal parameter estimates. Thus, given a slight and fixed perturbation to a specified model's fit to data, FPEs are alternative parameter estimates located within the small neigh-CONFIDENCE SETS AND FUNGIBLE ESTIMATES 7 borhood of the optimal estimate that yield the same level of perturbed model fit.…”

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confidence: 99%

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Parameter uncertainty in structural equation models: Confidence sets and fungible estimates.

Pek

2018

Psychological Methods

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Current concerns regarding the dependability of psychological findings call for methodological developments to provide additional evidence in support of scientific conclusions. This paper highlights the value and importance of two distinct kinds of parameter uncertainty which are quantified by confidence sets (CSs) and fungible parameter estimates (FPEs; T. Lee, MacCallum, & Browne, in press); both provide essential information regarding the defensibility of scientific findings. Using the structural equation model, we introduce a general perturbation framework based on the likelihood function that unifies CSs and FPEs and sheds new light on the conceptual distinctions between them. A targeted illustration is then presented to demonstrate the factors which differentially influence CSs and FPEs, further highlighting their theoretical differences. With three empirical examples on initiating a conversation with a stranger (Bagozzi & Warshaw, 1988), posttraumatic growth of caregivers in the context of pediatric palliative care (Cadell et al., 2014), and the direct and indirect effects of spirituality on thriving among youth (Dowling et al., 2004), we illustrate how CSs and FPEs provide unique information which lead to better informed scientific conclusions. Finally, we discuss the importance of considering information afforded by CSs and FPEs in strengthening the basis of interpreting statistical results in substantive research, conclude with future research directions, and provide example OpenMx code for the computation of CSs and FPEs.Keywords: confidence sets, fungible estimates, sensitivity analysis, profile likelihood, structural equation modeling CONFIDENCE SETS AND FUNGIBLE ESTIMATES 3 Parameter uncertainty in structural equation models:Confidence sets and fungible estimates Statistical practice in psychological science is undergoing reform in response to concerns over the dependability of findings (Harlow, Mulaik, & Steiger, 2016; Open Science Collaboration, 2015;Pashler & Wagenmakers, 2012;Simmons, Nelson, & Simonsohn, 2011;Sijtsma, 2015). In response to these concerns, the reporting of effect sizes or focal parameter estimates and their confidence intervals (CIs) have been recommended as best practice (Cumming, 2014; Wilkinson & the Task Force on Statistical Inference, 1999). Confidence intervals communicate precision in estimation, providing information to researchers on whether inferences about their commensurate parameters can be drawn. Note that confidence regions (CRs) are an extension of CIs from a single parameter to a set of multiple parameters, and we use the term confidence sets (CSs) to collectively refer to CIs and CRs. Additionally, recent quantitative developments show that examining parameter sensitivity (T. Lee & MacCallum, 2015) and fungible parameter estimates (FPEs; T. Lee et al., in press;MacCallum, Browne, & Lee, 2009;Waller, 2008) can add to substantive researchers' diagnostic toolkit in terms of generating more information about the validity of their statistical results. Rel...

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“…Fungible parameter estimates provide diagnostic information about statistical results from the broader framework of sensitivity analysis (Cook, 1986;S.-Y. Lee & Wang, 1996).…”

Section: Fungible Parameter Estimatesmentioning

confidence: 99%

Section: Fungible Parameter Estimatesmentioning

confidence: 99%

“…Lee & Wang, 1996). Specifically, FPEs inform of whether their commensurate parameter estimates should be validly interpreted.…”

Section: Fungible Parameter Estimatesmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Parameter uncertainty in structural equation models: Confidence sets and fungible estimates.

Pek

2018

Psychological Methods

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“…Typical examples are the applications to nonlinear mixed-effects models (Lee & Xu, 2004), growth curve models (Pan, Fang, & Liski, 1996), and principal component analysis (Shi, 1997), among others. At the same time, the local influence approach of Cook (1986) has also received a lot of attention in factor analysis or structural equation models (SEMs); see, for example, Tanaka and Odaka (1989), Lee and Wang (1996), Kwan and Fung (1998), Poon, Wang, and Lee (1999), Poon and Chan (2002), and Lee and Xu (2003a,b), and Song and Lee (2004a,b). However, as far as we know no local influence analysis for NSEMs has been developed, and it is very difficult to apply Cook's (1986) approach because the building blocks in its diagnostic measures involve intractable integrals that are induced by the nonlinearity among latent variables.…”

Section: Introductionmentioning

confidence: 99%