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Goodness‐of‐fit Tests for GEE with Correlated Binary Data

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  • WEI PAN

Abstract

The marginal logistic regression, in combination with GEE, is an increasingly important method in dealing with correlated binary data. As for independent binary data, when the number of possible combinations of the covariate values in a logistic regression model is much larger than the sample size, such as when the logistic model contains at least one continuous covariate, many existing chi‐square goodness‐of‐fit tests either are not applicable or have some serious drawbacks. In this paper two residual based normal goodness‐of‐fit test statistics are proposed: the Pearson chi‐square and an unweighted sum of residual squares. Easy‐to‐calculate approximations to the mean and variance of either statistic are also given. Their performance, in terms of both size and power, was satisfactory in our simulation studies. For illustration we apply them to a real data set.

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  • Wei Pan, 2002. "Goodness‐of‐fit Tests for GEE with Correlated Binary Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 101-110, March.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:1:p:101-110
    DOI: 10.1111/1467-9469.00091
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    Cited by:

    1. Chung-Wei Shen & Yi-Hau Chen, 2012. "Model Selection for Generalized Estimating Equations Accommodating Dropout Missingness," Biometrics, The International Biometric Society, vol. 68(4), pages 1046-1054, December.
    2. Shinpei Imori, 2015. "Model Selection Criterion Based on the Multivariate Quasi-Likelihood for Generalized Estimating Equations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1214-1224, December.
    3. M. C. Pardo & R. Alonso, 2012. "A generalized Q--Q plot for longitudinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2349-2362, July.
    4. Lin, Kuo-Chin, 2010. "Goodness-of-fit tests for modeling longitudinal ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1872-1880, July.
    5. Lan Wang & Annie Qu, 2009. "Consistent model selection and data‐driven smooth tests for longitudinal data in the estimating equations approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 177-190, January.
    6. Kuo-Chin Lin & Yi-Ju Chen, 2016. "Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2053-2064, August.
    7. Lin, Hui-Yi & Myers, Leann, 2006. "Power and Type I error rates of goodness-of-fit statistics for binomial generalized estimating equations (GEE) models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3432-3448, August.
    8. Andreas Blöchlinger & Markus Leippold, 2011. "A New Goodness-of-Fit Test for Event Forecasting and Its Application to Credit Defaults," Management Science, INFORMS, vol. 57(3), pages 487-505, March.

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