note19 - STAT5044: Regression and Anova Inyoung Kim 1 / 15...

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STAT5044: Regression and Anova Inyoung Kim 1 / 15
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Outline 1 Fitting GLMs 2 / 15
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Fitting GLMS We study how to find the maxlimum likelihood estimator ˆ β of GLM parameters The likelihood equaions are usually nonlinear in ˆ β We describe a general-purpose iterative method for solving nonlinear equations and apply it two ways to determine the maximum of a likelihood function 3 / 15
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Fitting GLMS Newton-Raphson method Fisher scoring method Reweighted Least Squares 4 / 15
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Newton-Raphson method The Newton-Raphson method is an iterative method for solving nonlinear equations, such as equations whose solution determines the point at which a function takes its maximum. It begins with an initial guess for the solution. It obtains a second guess by approximating the function to be maximized in a neighborhod of the initial guess by a second-degree Then we find the location of that polynomial’s maximum value. It then approximates the function in a neighborhood of the second guess by another second-order polynomial, and the third guess is the location of its maximum. In this manner, the method generates a sequences of guesses. These converge to the location of the maximum when the function is suitable and /or the initial guess is good.
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This note was uploaded on 01/02/2012 for the course STAT 5044` taught by Professor Staff during the Fall '11 term at Virginia Tech.

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note19 - STAT5044: Regression and Anova Inyoung Kim 1 / 15...

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