Modeling Coefficient Alpha for Measurement of Individualized Test Score Internal Consistency

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.