Quasi-likelihood estimation for GLM with random scales |
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| Institution: | 1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0205, USA;2. Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA;1. Istituto Dalle Molle di Studi sull''Intelligenza Artificiale (IDSIA), Galleria 2, 6928 Manno (Lugano), Switzerland;2. Queen''s University Belfast, School of Electronics, Electrical Engineering and Computer Science, Computer Science at Elmwood, ECS1, Elmwood Avenue, BT9 6AZ, Belfast, United Kingdom;1. Department of Statistics, Purdue University, 250 North University Street, West Lafayette, IN 47907-2066, USA;2. Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, IN, 47907, USA;3. Department of Agronomy, Purdue University, West Lafayette, IN, 47907, USA;1. Department of Urology, University of Wisconsin School of Medicine and Public Health, Madison, WI;2. Department of Medicine, University of Wisconsin School of Medicine and Public Health, Madison, WI;1. Ophthalmology Clinic, Seconda Università degli Studi di Napoli (SUN), Naples, Italy;2. Ophthalmology Department, Università Cattolica del Sacro Cuore, Rome, Italy;3. Ophthalmic Surgery Clinic, Azienda Ospedaliero-Universitaria Pisana, Pisa, Italy;4. Ophthalmology Clinic, Università Politecnica delle Marche, Ancona, Italy |
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| Abstract: | This paper uses random scales similar to random effects used in the generalized linear mixed models to describe “inter-location” population variation in variance components for modeling complicated data obtained from applications such as antenna manufacturing. Our distribution studies lead to a complicated integrated extended quasi-likelihood (IEQL) for parameter estimations and large sample inference derivations. Laplace's expansion and several approximation methods are employed to simplify the IEQL estimation procedures. Asymptotic properties of the approximate IEQL estimates are derived for general structures of the covariance matrix of random scales. Focusing on a few special covariance structures in simpler forms, the authors further simplify IEQL estimates such that typically used software tools such as weighted regression can compute the estimates easily. Moreover, these special cases allow us to derive interesting asymptotic results in much more compact expressions. Finally, numerical simulation results show that IEQL estimates perform very well in several special cases studied. |
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