TY - JOUR

T1 - Bayesian estimation of single-test reliability coefficients

AU - Pfadt, Julius M.

AU - Van Den Bergh, Don

AU - Sijtsma, Klaas

AU - Moshagen, Morten

AU - Wagenmakers, Eric-jan

N1 - This work was supported in part by an NWO Vici grant (016.Vici.170.083) and an Advanced ERC grant (743086 UNIFY) to EJW.

PY - 2022

Y1 - 2022

N2 - Popular measures of reliability for a single-test administration include coefficient α, coefficient λ2, the greatest lower bound (glb), and coefficient ω. First, we show how these measures can be easily estimated within a Bayesian framework. Specifically, the posterior distribution for these measures can be obtained through Gibbs sampling – for coefficients α, λ2, and the glb one can sample the covariance matrix from an inverse Wishart distribution; for coefficient ω one samples the conditional posterior distributions from a single-factor CFA-model. Simulations show that – under relatively uninformative priors – the 95% Bayesian credible intervals are highly similar to the 95% frequentist bootstrap confidence intervals. In addition, the posterior distribution can be used to address practically relevant questions, such as “what is the probability that the reliability of this test is between .70 and .90?”, or, “how likely is it that the reliability of this test is higher than .80?” In general, the use of a posterior distribution highlights the inherent uncertainty with respect to the estimation of reliability measures.

AB - Popular measures of reliability for a single-test administration include coefficient α, coefficient λ2, the greatest lower bound (glb), and coefficient ω. First, we show how these measures can be easily estimated within a Bayesian framework. Specifically, the posterior distribution for these measures can be obtained through Gibbs sampling – for coefficients α, λ2, and the glb one can sample the covariance matrix from an inverse Wishart distribution; for coefficient ω one samples the conditional posterior distributions from a single-factor CFA-model. Simulations show that – under relatively uninformative priors – the 95% Bayesian credible intervals are highly similar to the 95% frequentist bootstrap confidence intervals. In addition, the posterior distribution can be used to address practically relevant questions, such as “what is the probability that the reliability of this test is between .70 and .90?”, or, “how likely is it that the reliability of this test is higher than .80?” In general, the use of a posterior distribution highlights the inherent uncertainty with respect to the estimation of reliability measures.

KW - ALPHA

KW - Bayesian reliability estimation

KW - Cronbach’

KW - Guttman’

KW - McDonald’

KW - greatest lower bound

KW - inverse Wishart distribution

KW - s alpha

KW - s lambda-2

KW - s omega

UR - https://app-eu.readspeaker.com/cgi-bin/rsent?customerid=10118&lang=en_us&readclass=rs_readArea&url=https%3A%2F%2Fwww.tandfonline.com%2Fdoi%2Ffull%2F10.1080%2F00273171.2021.1891855&dict=math&rule=math&xslrule=math

UR - http://www.scopus.com/inward/record.url?scp=85103224585&partnerID=8YFLogxK

U2 - 10.1080/00273171.2021.1891855

DO - 10.1080/00273171.2021.1891855

M3 - Article

SN - 0027-3171

VL - 57

SP - 620

EP - 641

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

IS - 4

ER -