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• W2567742990 abstract "In the Poisson Regressions, which belong to a class of the Generalized Linear Model, all independent variables, except a scale (offset) variable, often consist of category variables. The typical cases are two-way or multi-way contingency tables, in which each count value of a cell follows the Poisson law with a mean determined by its category position in the table. This paper treats, specifically, the algorithms for obtaining the maximum likelihood estimates (MLE) of such all category Poisson Regression cases, which can be expressed generally as multilinear forms with respect to unknown parameters. For finding the MLEs of the Poisson multilinear structures, a simple and globally stable Gauss-Seidel algorithm exists. The algorithm, based on partial MLE equations, is sufficiently fast in small-sample cases. When it is preferable to accelerate the steady but not fast Gauss-Seidel algorithm, a highly efficient algorithm, which utilizes Hessian information of likelihood functions without matrix inversions, is derived and examined on some small examples. This acceleration algorithm can be interpreted as an advance version of the Successive Over-Relaxation (SOR) method. Hence, the acceleration principle developed in this paper has applicability to a wider class of problems such as optimizations or solving systems of equations, in which the Gauss-Seidel, the SOR, or the other methods are currently used. The simplicity and efficiency of the algorithms enable to introduce the Poisson multilinear models into automatic and problem-oriented applications, typically implemented in relatively slow-speed environments such as on-Web or spreadsheet platforms. I Poisson Multilinear Models Let x1, x2, ..., xn be mutually independent Poisson random variables having probabilities defined by (1) { } ( )( )( ) n k x e x x P k k k x k k k k , , 1 , 1 , 0 0 ! L L = = > = − λ λ λ , whose mean λk has a multilinear form: (2) ( )( ) p i e θ c θ θ θ c λ ki i k e p e e k k kp k k , , 1 1 or 0 , 0 , 0 2 1 2 1 L L = = > > =" @default.
• W2567742990 created "2017-01-13" @default.
• W2567742990 creator A5064891250 @default.
• W2567742990 date "2006-03-01" @default.
• W2567742990 modified "2023-09-23" @default.
• W2567742990 title "Maximum Likelihood Estimates of Poisson Multilinear Models" @default.
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