Foundations of Linear and Generalized Linear Models by Alan Agresti

Author:Alan Agresti
Language: eng
Format: epub
ISBN: 9781118730058
Publisher: Wiley
Published: 2015-01-12T00:00:00+00:00

in terms of a model matrix and model parameters. For ηi = log μi, ∂μi/∂ηi = μi, so the likelihood equations are

(7.1)

as we found in Section 4.2.2.

For a Poisson loglinear model, the mean satisfies the exponential relation

A 1-unit increase in xij has a multiplicative impact of : the mean at xij + 1 equals the mean at xij multiplied by , adjusting for the other explanatory variables.

7.1.4 Model Fitting and Goodness of Fit

Except for simple models such as for the one-way layout or balanced two-way layout, the likelihood equations have no closed-form solution. However, the log-likelihood function is concave, and the Newton–Raphson method (which is equivalent to Fisher scoring for the canonical log link) yields fitted values and estimates of corresponding model parameters. From Section 4.2.4, the estimated covariance matrix (4.14) of is

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