Generalized Reliability Coefficients for Complex Surveys with Unit Nonresponse

Regarding the reliability that explains a construct formed by a weighted sum of multiple variables, this study employs a nonmodel-based approach independent of factor models. Specifically, we generalize the conventional Cronbach’s alpha and define an estimation method that applies design weights and nonresponse adjustment weights to the reliability coefficient when using sample data from a complex sample design, and then investigate the asymptotic unbiasedness of the estimator. To support the theory, in the simulation study, we generate multivariate data to perform sampling and calculate the expectations and MSEs of the reliability coefficient estimators computed by various methods according to the combinations of weights among variables and response probabilities. Ultimately, we empirically demonstrate the population-level utility of the reliability coefficient based on variable-specific weights, as well as the unbiasedness and efficiency of its estimator using sample survey weights. In addition, two empirical examples are demonstrated to investigate the application of the reliability coefficients discussed in this paper.