Robustness of Bayesian coefficient alpha estimation under non-normal item distributions: Evidence from a Monte Carlo study using a normal posterior

Nguyen Ngoc Thach

doi:10.63065/ajafe.2026.1.005

Asian Journal of Applied Financial Econometrics (AJAFE)

Volume 1_Number 1 , Tháng 4/2026, Trang 42-54

Robustness of Bayesian coefficient alpha estimation under non-normal item distributions: Evidence from a Monte Carlo study using a normal posterior

Nguyen Ngoc Thach

DOI: 10.63065/ajafe.2026.1.005

Email: thachnn@hub.edu.vn

Đơn vị công tác: Trường Đại học Ngân hàng Tp Hồ Chí Minh

Ngày nhận bài: 09/09/2026

Ngày nhận bài sửa: 09/09/2026

Ngày duyệt đăng: 09/09/2026

Lượt xem: 6

Downloads: 0

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Tóm tắt

Purpose – This study evaluates whether a recently proposed Bayesian estimator of coefficient alpha based on a normal posterior distribution remains reliable when applied to non-normal item responses, a common feature of behavioral and social science data.

Design/methodology/approach – A Monte Carlo simulation was conducted across 1,440 conditions defined by the number of items (5, 10, 15, and 20), correlation structure (two parallel and three congeneric models), sample size (50, 100, 150, 200, 250, and 300), item response categories (2, 3, 5, and 7), and three distribution types. Using non-informative priors and 2,000 posterior draws, the study examined three 95% Bayesian credible interval methods for coefficient alpha: percentile, normal-theory, and highest probability density intervals. Performance was assessed primarily through coverage probability, with interval width also considered.

Findings – The results show that all three credible interval methods performed similarly and generally achieved acceptable coverage across most simulation conditions. However, performance deteriorated when data involved binary items, distribution type 2, and/or a parallel model with common loadings of .705, particularly when these conditions occurred jointly. The method was more dependable when items had at least three response categories and sufficient variability.

Research limitations/implications: The findings are limited to the simulation settings examined and to the normal-posterior framework used to estimate coefficient alpha. The results suggest caution when applying this approach to binary, highly skewed, or range-restricted data, and indicate the need for future comparisons with alternative Bayesian and non-Bayesian estimators, as well as sampling-based approaches such as Gibbs sampling.

Originality/value – This study extends recent Bayesian research on coefficient alpha by explicitly testing the robustness of a computationally convenient normal-posterior estimator under non-normal item distributions. It clarifies the empirical conditions under which the method performs well and identifies situations in which its use should be treated more cautiously.

Từ khóa

Bayesian approach, COVID-19 lockdown, Sectoral vulnerability, Systemic dominance, Stock return volatility

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