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Title: Marginal additive models: Simultaneous marginal and conditional non-linear regression for cluster-correlated data Authors:  Alex Stringer - University of Waterloo (Canada) [presenting]
Glen McGee - University of Waterloo (Canada)
Abstract: Regression models for cluster-correlated data model either the population-averaged or the cluster-conditional mean response. We introduce a Marginal Additive Model (MAM), which produces simultaneous estimates of cluster-conditional and population-averaged effects in regression models with non-linear covariate effects, including longitudinal and spatial models. The method is applied to a longitudinal study of beaver foraging habits, in which population-averaged inferences are desired, but only cluster-conditional inferences had previously been made; and a well-known spatial analysis of loa loa parasite infection rates, in which we argue that the usual assumption of independence of responses at the same spatial location presumably made due to the lack of methods for fitting marginal models to spatial data with additional within cluster-correlation is inappropriate, a challenge to which the MAM offers a solution. On the technical side, standard errors are obtained using efficient numerical linear algebra that avoids storing square matrices whose dimension depends on the sample size, a situation that occurs when attempting to apply the delta method in this context.