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Average effects for regression models with misspecifications and diffuse interaction models Liu, Juxin

Abstract

In epidemiological studies, how best to assess and interpret interaction of risk factors of interest has been the subject of a lively debate. In statistical regression models, the interaction between two putative risk factors is described by the regression coefficient of the product of the risk factors. What happens if a linear regression model without pairwise interaction terms is used to fit the data actually generated from a linear regression model with all possible pairwise interactions? We apply the idea of average effect to evaluate the consequence of misspecified models and find out that the average effect estimates are still consistent if the joint distribution of risk factors satisfy some certain conditions. It is known that pairwise interaction models encounter intractable problems especially when the number of risk factor under consideration is quite large. The number of pairwise interaction terms is p (p -1)/2, if the number of risk factors is p. As an alternative strategy, we introduce diffuse interaction model with only one parameter to reflect the interactions among all the risk factors, without specifying which of the risk factors do indeed interact. We compare the two kinds of interaction models in terms of ability to detect interactions. Another issue investigated in the thesis is to devise MCMC algorithms to estimate diffuse interaction models. This is done not only for the diffuse interaction model assuming all risk factors interact in the same direction, either synergistically or antagonistically, but also for extended diffuse interaction models which relaxing this strong assumption.

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