  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.
