Goodness-of-fit tests for logistic regression models when data are collected using a complex sampling design

Logistic regression models are frequently used in epidemiological studies for estimating associations that demographic, behavioral, and risk factor variables have on a dichotomous outcome, such as disease being present versus absent. After the coefficients in a logistic regression model have been estimated, goodness-of-fit of the resulting model should be examined, particularly if the purpose of the model is to estimate probabilities of event occurrences. While various goodness-of-fit tests have been proposed, the properties of these tests have been studied under the assumption that observations selected were independent and identically distributed. Increasingly, epidemiologists are using large-scale sample survey data when fitting logistic regression models, such as the National Health Interview Survey or the National Health and Nutrition Examination Survey. Unfortunately, for such situations no goodness-of-fit testing procedures have been developed or implemented in available software. To address this problem, goodness-of-fit tests for logistic regression models when data are collected using complex sampling designs are proposed. Properties of the proposed tests were examined using extensive simulation studies and results were compared to traditional goodness-of-fit tests. A Stata ado function svylogitgof for estimating the F-adjusted mean residual test after svylogit fit is available at the author's website http://www.people.vcu.edu/~kjarcher/Research/Data.htm.