Lecture 22—Monday, February 20, 2006

What was covered?

Terminology Defined

Further details on probability distributions used in GLIMs

Probability Distribution
Canonical Link g(μ) Other links supported in R Variance function Historic name for these models
Poisson
log:
identity, sqrt
Poisson regression, loglinear model
Normal (Gaussian)
identity:
log, inverse
1
ordinary linear regression
Binomial
logit:
probit, cloglog, log
logistic regression, probit analysis
Gamma
inverse:
identity, log
gamma regression
Inverse Gaussian
identity, inverse, log
"Negative Binomial"
log, sqrt, identity
negative binomial regression

The deviance as a goodness of fit test

Recall that LR has an asymptotic chi-squared distribution with degrees of freedom equal to the difference in the number of parameters estimated by the two models. Alternatively, the degrees of freedom is the number of parameters that are fixed to have a specific value in one model but are freely estimated in the other model.

Thus the deviance statistic can be used in a goodness of fit test. But just like the Pearson chi-squared test, the G2 test, and the likelihood ratio test on which it is based, there are sample size and cell size issues that may make the asymptotic chi-squared distribution suspect in specific applications.

Analysis of deviance

Written this way L1 is the larger of the two models (more estimated parameters) and L0 is the simpler model in which some of those parameters have been assigned specific values (such as zero).

where D1 and D2 are the deviances of models 1 and 2, respectively.

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Jack Weiss
Phone: (919) 962-5930
E-Mail: jack_weiss@unc.edu
Address: Curriculum in Ecology, Box 3275, University of North Carolina, Chapel Hill, 27516
Copyright © 2006
Last Revised--Feb 26, 2006
URL: http://www.unc.edu/courses/2006spring/ecol/145/001/docs/lectures/lecture22.htm