(1) Indian Institute of Management, Post Box No. 16757, Calcutta, 700 027, India;(2) Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, Canada, A1C 5S7
Abstract:
Binary and Poisson generalized linear mixed models are used to analyse over/under-dispersed proportion and count data, respectively. As the positive definiteness of the information matrix is a required property for valid inference about the fixed regression vector and the variance components of the random effects, this paper derives the relevant necessary and sufficient conditions under both these models. It is found that the conditions for the positive definiteness are not identical for these two nonlinear mixed models and that a mere analogy with the usual linear mixed model does not dictate these conditions.