Article

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

Division of Epidemiology and Biostatistics and Department of Statistics, School of Public Health, The Ohio State University, 320 West Tenth Ave., M200 Starling-Loving Hall, Columbus, OH 43210, USA
Computational Statistics & Data Analysis (Impact Factor: 1.4). 05/2007; 51(9):4450-4464. DOI: 10.1016/j.csda.2006.07.006
Source: RePEc

ABSTRACT

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.

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Available from: Kellie Archer, May 19, 2015
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    • "Due to the complex sampling designs, existing software was not yet developed or implemented for these tests based on the logistic regression. According to Archera et al.[26], available software usually takes the form of simulation studies in which results of analysis were compared with ordinary goodness-of-fit statistics. For instance, the Hosmer and Lemeshow goodness-of-fit test statistic, the Pearson residual, and the deviance residual test are not yet incorporated in the Survey Logistic procedure . "
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    • "For binary outcomes, we assessed the assumption of correct fit using Hosmer- Lemeshow tests (Hosmer & Lemeshow, 2000). We ran the tests as if the data were unstructured, since the tests are computationally unavailable for survey data (Archer, Lemeshow, & Hosmer, 2007). Overall, non-significant results were obtained; indicating no evidence to suggest that the correct fit assumption was violated. "
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    • "It is defined as an evaluation of how well model predicted outcomes agree with the observed data [2]. GOF test, on the other hand, widely referred to as lack-of-fit, because it is measuring how far the model is from the data; more than how much the model is good [3]. Omitted predictors, a misspecified form of the predictor, or an inappropriate link function can all result in poor fitting. "

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