Abstract
We often rely on the likelihood to obtain estimates of regression parameters but it is not readily available for generalized linear mixed models (GLMMs). Inferences for the regression coefficients and the covariance parameters are key in these models. We presented alternative approaches for analyzing binary data from a hierarchical structure that do not rely on any distributional assumptions: a generalized quasi-likelihood (GQL) approach and a generalized method of moments (GMM) approach. These are alternative approaches to the typical maximum-likelihood approximation approach in Statistical Analysis System (SAS) such as Laplace approximation (LAP). We examined and compared the performance of GQL and GMM approaches with multiple random effects to the LAP approach as used in PROC GLIMMIX, SAS. The GQL approach tends to produce unbiased estimates, whereas the LAP approach can lead to highly biased estimates for certain scenarios. The GQL approach produces more accurate estimates on both the regression coefficients and the covariance parameters with smaller standard errors as compared to the GMM approach. We found that both GQL and GMM approaches are less likely to result in non-convergence as opposed to the LAP approach. A simulation study was conducted and a numerical example was presented for illustrative purposes.
Original language | English (US) |
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Pages (from-to) | 409-425 |
Number of pages | 17 |
Journal | Journal of Applied Statistics |
Volume | 45 |
Issue number | 3 |
DOIs | |
State | Published - Feb 17 2018 |
Keywords
- Generalized linear mixed model
- Newton–Raphson
- R
- binary response
- correlated data
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
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Comparative GMM and GQL logistic regression models on hierarchical data
Wang, B. (Creator) & Wilson, J. (Creator), figshare Academic Research System, 2017
DOI: 10.6084/m9.figshare.4564792.v1, https://figshare.com/articles/Comparative_GMM_and_GQL_logistic_regression_models_on_hierarchical_data/4564792/1
Dataset
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Comparative GMM and GQL logistic regression models on hierarchical data
Wang, B. (Creator) & Wilson, J. (Creator), Figshare, 2017
DOI: 10.6084/m9.figshare.4564792, https://tandf.figshare.com/articles/dataset/Comparative_GMM_and_GQL_logistic_regression_models_on_hierarchical_data/4564792/1
Dataset