The Delta Algorithm and GLIM
Copyright policy )The Delta Algorithm and GLIM
A general maximum likelihood algorithm, called the delta algorithm, which generalizes Fisher's scoring method and several other existing algorithms, is introduced. The algorithm is derived as a modification of the Newton-Raphson algorithm, and may be interpreted as an iterative weighted least squares method. We show that for certain models, the algorithm may be implemented in GLIM, allowing a number of new models to be fitted in GLIM. The algorithm is applied to marginal and conditional maximum likelihood estimation, and the relation with the EM algorithm for incomplete data problems is discussed. Finally, the approach leads to a general definition of residuals, which we consider in some detail.
GLIM, incomplete data problems, Linear regression; mixed models, general maximum likelihood algorithm, Probabilistic methods, stochastic differential equations, modification of the Newton-Raphson algorithm, generalized linear models, delta algorithm, general definition of residuals, Linear inference, regression, marginal and conditional maximum likelihood estimation, Fisher's scoring method, EM algorithm, iterative weighted least squares method
GLIM, incomplete data problems, Linear regression; mixed models, general maximum likelihood algorithm, Probabilistic methods, stochastic differential equations, modification of the Newton-Raphson algorithm, generalized linear models, delta algorithm, general definition of residuals, Linear inference, regression, marginal and conditional maximum likelihood estimation, Fisher's scoring method, EM algorithm, iterative weighted least squares method
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