A generalized linear model approach to estimating and testing the equality of conditional correlations

Methods of testing the equality of conditional correlation of bivariate data across a third variable of interest (covariate) have been studied [9, 10, 11, 12, 13, 14, 15, 16]. Most of these methods, such as the test based on Fisher z-transformation [15], the likelihood ratio tests, and the C(α) statistics [9], are limited to the case where a categorical covariate is considered. When the covariate is numeric, existing methods typically categorize data into groups based on percentiles of the covariate before estimating and comparing sub-group correlations. As an example, consider a study where the Pearson correlation coefficient of diastolic blood pressure with weight is tested among people of different ages. Using current methods, an analyst would first define meaningful age groups before performing the equality test. In this study, we propose a generalized linear model approach for estimation and hypothesis testing about the Pearson correlation coefficient, where the correlation itself can be modeled as a function of numeric covariates. This approach allows for flexible and robust inference and prediction of the