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A logistic model can be used to evaluate the effect of a (binary) factor combined with other variables on the observed consequences. Consider the example

A logistic model can be used to evaluate the effect of a (binary) factor combined with other variables on the observed consequences.

Consider the example as follows.

In a five-year follow-up study on N disease-free human subjects, researchers aim to assess the effect of the environmental exposure to a heavy metal (E=1, exposed or 0 not exposed) on the development (or not) of a certain disease. The continuous variables of interests are age (AGE) and obesity status (OBS), the environmental factor E of each subject was determined at the start of the study. Devise the logistic form of a logistic regression model that assesses the interaction effects of AGE with E and OBS with E, and explain how the model can be learned from the data (where each data point represents a human subject with the known disease status (0/1), AGE, OBS, and E). (Hint: the interaction effects of AGE and E can be modeled by a created variable AGEE = AGE *E; similar for OBSE =OBE*E. You also need to consider the effects of the independent variables AGE, OBS and E, respectively).

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