Goodness-of-fit for GEE: an example with mental health service utilization

Abstract

Suppose we use generalized estimating equations to estimate a marginal regression model for repeated binary observations. There are no established summary statistics available for assessing the adequacy of the fitted model. In this paper we propose a goodness-of-fit test statistic which has an approximate chi-squared distribution when we have specified the model correctly. The proposed statistic can be viewed as an extension of the Hosmer and Lemeshow goodness-of-fit statistic for ordinary logistic regression to marginal regression models for repeated binary responses. We illustrate the methods using data from a study of mental health service utilization by children. The repeated responses are a set of binary measures of service use. We fit a marginal logistic regression model to the data using generalized estimating equations, and we apply the proposed goodness-of-fit statistic to assess the adequacy of the fitted model.

Prevalence and predictors of osteoporosis treatment in nursing home residents with known osteoporosis or recent fracture

“…To check the goodness of fit of our reduced GEE model, Horton's method was used and the model was a good fit with p=0.08. [17] …”

“…Goodness of fit was assessed using an extension of the Hosmer and Lemeshow statistic for ordinary logistic regression to marginal regression models for repeated binary observations. [17] This test has been proposed to assess the adequacy of fitted GEE models, with p values >0.05 indicating "good" fit.…”

A Longitudinal Study of Risk Factors for Incident Albuminuria in Diabetic American Indians: The Strong Heart Study

“…The variable with the largest non-significant P value was removed and the model was refitted at each step to remove the least significant variable until all remaining variables had individual P values <0.05. An extension of the Hosmer-Lemeshow goodness-of-fit test for ordinary logistic regression to marginal regression models for repeated binary responses 26 was used to assess the fit of the repeated binary response model. Statistical significance was defined as 2-tailed P<0.05 for all tests.…”

Between-litter variation in developmental studies of hormones and behavior: Inflated false positives and diminished power

“…In contrast to MLMs, GEEs are less documented in R (Bates et al, 2015;Halekoh et al, 2006;Pinheiro and Bates, 2000), present difficulties for evaluating model fit (Horton et al, 1999), and there are few examples of their use in the hormones and behavior literature (Muth et al, 2016). When sample sizes are small, GEEs require bias corrections to ensure nominal type I error rates (Gunsolley et al, 1995;Li and Redden, 2015).…”