Generalized linear model approach for estimating and testing equality of conditional correlations
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A number of methods have been proposed to test the equality of the population correlation coefficients between two variables across a third variable of interest. Currently available tests are specific to independent or dependent correlation coefficients, and such tests include likelihood ratio tests, test statistics based on the Fisher z-transformation, and C (α) tests. Use of these testing procedures is limited, however, to the case where the third variable is categorical in nature. In the case where the third variable is numeric, standard practice is to categorize the numeric variable, and to compare correlations across these newly defined groups. For example, consider a study where the correlation coefficient of diastolic blood pressure with weight varies among people of different ages. In this study, we present a generalized linear model based approach for estimation and hypothesis testing about the correlation coefficient, where the correlation itself is modeled as a function of a numeric covariate.