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Modeling and Multivariate Methods - SAS

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Chapter 6<br />

Fitting Generalized Linear Models<br />

Using the Fit Model Platform<br />

Generalized Linear Models provide a unified way to fit responses that do not fit the usual requirements of<br />

least-squares fits. In particular, frequency counts, which are characterized as having a Poisson distribution<br />

indexed by a model, are easily fit by a Generalized Linear Model.<br />

The technique, pioneered by Nelder <strong>and</strong> Wedderburn (1972), involves a set of iteratively reweighted<br />

least-squares fits of a transformed response.<br />

Additional features of JMP’s Generalized Linear Model personality include the following:<br />

• likelihood ratio statistics for user-defined contrasts, that is, linear functions of the parameters, <strong>and</strong><br />

p-values based on their asymptotic chi-square distributions<br />

• estimated values, st<strong>and</strong>ard errors, <strong>and</strong> confidence limits for user-defined contrasts <strong>and</strong> least-squares<br />

means<br />

• graphical profilers for examining the model<br />

• confidence intervals for model parameters based on the profile likelihood function<br />

• optional bias-corrected maximum likelihood estimator discussed by Firth (1993)

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