I'm investigating associations between socioeconomic factors and dichotomous outcome. I use generalised linear models (GLM) with log link for Bernoulli family, i.e., modelling the prevalence ratio. At the epidemiology course of K.J. Rothman & E.Hatch we were told, that goodness of fit tests are designed to prediction models and in causal inference it is not important with model fit. I can not find any reference on that. Can anybody comment on this and suggest a reference? Thank you in advance!
This is correct. In the epidemiology or social science, we would like to find the causal association between, say exposure and outcome. Then the most important thing is to identify the confounding factors, which need to be adjusted in your multivarate model settings. This does not necessarily mean to fit a model well, but only for adjustment purpose which makes ur estimate of interest unbaised due to other factors associated with outcome as well. For example, if we want to study the assocaiton between lung cancer and heavy drinking, then smoking status has to be adjusted as a confounding variable. Because smoking has been recognized as a risk factor of lung cancer. Therefore the heavy drinking status is confounded to the smoking, probably because heavy drinkers usually a smoker too. This is usually the utmost important consideration behind medical research.
If your purpose is for prediction, then you dont need to think confounding at first place, and you can include interaction terms, 2 ways, three ways interactions as a model budiling procedure, testing goodness-of-fit, and etc. And algorithms such as forward/backward selection are valid to provide a good model.
If you purpose is to provide a valid measure of an effect, then those selections are not quite appropriate. Because even a variable is not significant in a model, it still might be kept in the model such as age and gender, which are always adjusted in those epidemilogy study. Also the interaction effect might or might not be of interest in the epidemiology study.
Chapter 6 in the book of "Logistic Regression A Self-learning Text" provides a detailed explanation of model building strategy for what you asked about.
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