Choice of generalized linear mixed models using predictive crossvalidation |
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| Affiliation: | 1. Department of Cardiology, University Heart Center, University Hospital Zurich, Zurich, Switzerland;2. Department of Biostatistics, Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Zurich, Switzerland;3. Faculty Mechanical and Medical Engineering, Furtwangen University, Furtwangen, Germany;4. Department of Cardiology, University Hospital Basel, Basel, Switzerland;1. Department of Diagnostic Radiology, City of Hope National Medical Center, Duarte, CA, United States;2. Center for Cancer and Aging, City of Hope National Medical Center, Duarte, CA, United States;3. Magnetic Resonance Innovations, Inc., Detroit, MI, United States;4. Department of Population Science, City of Hope National Medical Center, Duarte, CA, United States;5. Division of Mathematical Oncology, City of Hope National Medical Center, Duarte, CA, United States;6. Department of Biomedical Engineering, Wayne State University, Detroit, MI, United States;7. Neurocognitive Research Lab, Memorial Sloan Kettering Cancer Center, New York, NY, United States;8. Center for Neuroimaging, Indiana University School of Medicine, Indianapolis, IN, United States;9. Department of Radiology, Memorial Sloan-Kettering Cancer Center, New York, NY, United States;10. Division of Neurology, City of Hope National Medical Center, Duarte, CA, United States;11. Department of Medical Oncology, City of Hope National Medical Center, Duarte, CA, United States |
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| Abstract: | The choice of generalized linear mixed models is difficult, because it involves the selection of both fixed and random effects. Classical criteria like Akaike’s information criterion (AIC) are often not suitable for the latter task, and others which are useful in linear mixed models are difficult to extend to the generalized case, especially for overdispersed data. A predictive leave-one-out crossvalidation approach is suggested that can be applied for choosing both fixed and random effects, even in models with overdispersion, and is based on proper scoring rules. An attractive feature of this approach is the fact that the model has to be fitted just once to the data set, which makes computations fast and convenient. As the calculation of the leave-one-out predictive distribution is not possible analytically, it is shown how an iteratively weighted least squares algorithm combined with some analytic approximations can be used for this task. A simulation study and two applications of the methodology to binary and count data are provided, as well as comparisons with two other methods. |
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| Keywords: | Predictive model choice Proper scoring rules Poisson regression Logistic regression Conditional AIC Overdispersion |
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