Computations for the familial analysis of binary traits
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For familial aggregation of a binary trait, one method that has been used is the GEE2 (generalized estimating equation) method corresponding to a multivariate logit model. We solve the complex estimating equations for the GEE2 method using an automatic differentiation software which computes the derivatives of a function numerically using the chain rule of the calculus repeatedly on the elementary operations of the function. Based on this, we are able to show in a simulation study that the GEE2 estimates are quite close to the maximum likelihood estimates assuming a multivariate logit model, and that the GEE2 method is computationally faster when the dimension or family size is larger than four.
KeywordsBinary response Multivariate probit models Multivariate logit models Generalized estimating equations Familial aggregation
This research is supported from an NSERC Canada grant and US Army Medical Research grant NF990038. We are grateful to the referees for comments leading to an improved presentation.
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