Multiple Regression With Data Collected From Relatives: Testing Assumptions of the Model

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Abstract
Multiple regression is a causal model of the relationship between sets of independent (X) and dependent (Y) variables. This model is extended to cover data collected from relatives, where the observations are not independent. If correct, the model permits appropriate statistical tests of regression coefficients in data collected from relatives. Across relative covariances, particularly across the independent and dependent variables may reject the basic regression model. Further extensions of the model are developed that permit tests of several assumptions implicit in multiple regression: (a) the assignment of variables as dependent or independent; (b) the relationship between X and Y variables is not due to some latent variable which causes variation in both; and (c) there is no reciprocal interaction between the X and the Y variables. Discrimination between these alternatives is especially strong if data are collected from more than one class of relative, which differ in their X and Y variable covariance...