Modeling Coefficient Alpha for Measurement of Individualized Test Score Internal Consistency

TL;DR

This paper introduces a novel regression-based method using generalized estimating equations to measure individualized internal consistency of tests, accommodating heterogeneity and missing data, with proven asymptotic properties and validated through simulations and real health literacy data.

Contribution

It develops a new GEE-based approach to estimate individualized coefficient alpha, extending traditional methods to handle heterogeneity and missing data.

Findings

Method accurately estimates individualized reliability.

Simulation studies confirm robustness and validity.

Application to health literacy data demonstrates practical utility.

Abstract

A method for measuring individualized reliability of several tests on subjects with heterogenecity is proposed. A regression model is developed based on three sets of generalized estimating equations (GEE). The first set of GEE models the expectation of the responses, the second set of GEE models the response's variance, and the third set is proposed to estimate the individualized coefficient alpha, defined and used to measure individualized internal consistency of the responses. We also extend our method to handle missing data in the covariates. Asymptotic property of the estimators is discussed, based on which interval estimation of the coefficient alpha and significance detection are derived. Performance of our method is evaluated through simulation study and real data analysis. The real data application is from a health literacy study in Hunan province of China.