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Non-addictive effects in logistic regression Kazi, Azad Mahbubur Rashid

Abstract

Logistic regression is commonly used in epidemiology to model the relationship between risk factors and presence/absence of a disease. Usually it is difficult to look for interaction structure (many possible pairwise interactions, for instance) to include in the model. So a model which is additive on the logit scale is fitted. If the number of risk factors is relatively large such an additive relationship may not make good sense. A new logistic regression model is proposed to incorporate non-additive interaction effects. In some scenarios this model might better reflect the relationship between the response variable and the risk factors. The Bayesian approach is followed to fit the model and a Markov chain Monte Carlo (MCMC) algorithm, known as the hybrid algorithm is used to simulate the parameters. We apply the new model to three examples and interpret the parameter estimates. We compare the predictive performance of the new model with that of the step-wise and the ordinary logistic regression models.

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