arXiv subjects

Jolynn Pek

Publications and source records attributed to Jolynn Pek.

3 recordsLinked to original sources

arXiv2024

On a General Theoretical Framework of Reliability

Reliability is an essential measure of how closely observed scores represent latent scores (reflecting constructs), assuming some latent variable measurement model. We present a general theoretical framework of reliability, placing emphasis on measuring the association between latent and observed scores. This framework was inspired by McDonald's (2011) regression framework, which highlighted the coefficient of determination as a measure of reliability. We extend McDonald's (2011) framework beyond coefficients of determination and introduce four desiderata for reliability measures (estimability, normalization, symmetry, and invariance). We also present theoretical examples to illustrate distinct measures of reliability and report on a numerical study that demonstrates the behavior of different reliability measures. We conclude with a discussion on the use of reliability coefficients and outline future avenues of research.

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arXiv2024

Understanding Measurement Precision from a Regression Perspective

We adopt and expand McDonald's (2011) regression framework for measurement precision, integrating two key perspectives: (a) reliability of observed scores and (b) optimal prediction of latent scores. Reliability arises from a measurement decomposition of an observed score into its true score and measurement error. In contrast, proportional reduction in mean squared error (PRMSE) arises from a prediction decomposition of a latent score into its optimal predictor (the observed expected a posteriori [EAP] score) and prediction error. Reliability is the coefficient of determination obtained by two isomorphic regressions: regressing the observed score on its true score or on all the latent variables. Similarly, PRMSE is the coefficient of determination obtained from two isomorphic regressions: regressing the latent score on its observed EAP score or all the manifest variables. A key implication of this regression framework is that both reliability and PRMSE can be estimated using a Monte Carlo (MC) method, which is particularly useful when no analytic formula is available or when the analytic calculation is involved. We illustrate these concepts with a factor analysis model and a two parameter logistic model, in which we compute reliability coefficients for different observed scores and PRMSE for different latent scores. Additionally, we provide a numerical example demonstrating how the MC method can be used to estimate reliability and PRMSE within a two-dimensional item response tree model.

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arXiv2017

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

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); 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, posttraumatic growth of caregivers in the context of pediatric palliative care, and the direct and indirect effects of spirituality on thriving among youth, 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.

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