[19149] in s-news-athena
[S] Comparing poisson, quasi-log-mu, and negative binomial glm models for count data.
daemon@ATHENA.MIT.EDU (M. Epelbaum)
Wed Sep 8 14:20:51 1999
Message-Id: <19990908181517.2232.rocketmail@web219.mail.yahoo.com>
Date: Wed, 8 Sep 1999 11:15:17 -0700 (PDT)
From: "M. Epelbaum" <mepelbaum@yahoo.com>
To: s-news@wubios.wustl.edu
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Dear members of the S+ community:
For the analysis of count data, the Splus glm function offers, at
least, three useful alternatives, analyzable in three main families:
Poisson, negative binomial, and quasi (with a log-link & a
mu-variance). The negative binomial option is available in the glm.nb
function of the Venables & Ripley mass library. The glm.nb and the
quasi-log-mu are useful for overdispersed data. I present here examples
of Splus summaries of Poisson, Negative binomial, and quasi-log-mu
models for a simple data set, followed by my questions:
> summary(Pois.p)
Call: glm(formula = y ~ x, family = poisson(link = log), na.action =
na.omit, control = list(epsilon = 0.001, maxit = 50, trace = F))
Deviance Residuals:
Min 1Q Median 3Q Max
-2.581291 -0.6511567 0.004389644 0.6682641 2.398516
Coefficients:
Value Std. Error t value
(Intercept) 3.978106967 0.070943212 56.0745260
x -0.001577953 0.001769128 -0.8919385
(Dispersion Parameter for Poisson family taken to be 1 )
Null Deviance: 112.1628 on 99 degrees of freedom
Residual Deviance: 111.3664 on 98 degrees of freedom
Number of Fisher Scoring Iterations: 3
Correlation of Coefficients:
(Intercept)
x -0.9800116
> summary.negbin(NB.p)
Call: glm.nb(formula = y ~ x, init.theta = 437.586302378701, link =
log)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.457967 -0.6175625 0.004079176 0.6320885 2.256696
Coefficients:
Value Std. Error t value
(Intercept) 3.978247920 0.074911908 53.1056812
x -0.001581535 0.001867599 -0.8468279
(Dispersion Parameter for Negative Binomial family taken to be 1 )
Null Deviance: 100.6317 on 99 degrees of freedom
Residual Deviance: 99.91553 on 98 degrees of freedom
Number of Fisher Scoring Iterations: 1
Correlation of Coefficients:
(Intercept)
x -0.9800153
Theta: 438
Std. Err.: 502
Warning while fitting theta: iteration limit reached
2 x log-likelihood: 29278.190
> summary(Quasi.p)
Call: glm(formula = y ~ x, family = quasi(link = log, variance = "mu"),
na.action = na.omit, control = lis
t(
epsilon = 0.001, maxit = 50, trace = F))
Deviance Residuals:
Min 1Q Median 3Q Max
-2.581291 -0.6511567 0.004389644 0.6682641 2.398516
Coefficients:
Value Std. Error t value
(Intercept) 3.978106967 0.075487270 52.699044
x -0.001577953 0.001882444 -0.838247
(Dispersion Parameter for Quasi-likelihood family taken to be 1.132207
)
Null Deviance: 112.1628 on 99 degrees of freedom
Residual Deviance: 111.3664 on 98 degrees of freedom
Number of Fisher Scoring Iterations: 3
Correlation of Coefficients:
(Intercept)
x -0.9800116
Questions:
1. How to compare, particularly the negative binomial and quasi-log-mu
models? What criteria are most advisable to indicate that one Splus glm
model is superior to the other?
2. I saw, for example, that some authors (who use other software)
evaluate the models through a comparison of the models’
log-likelihoods. Are such comparisons appropriate?
3. If comparisons of log-likelihoods would be appropriate, the Splus
“summary” does not provide the log-likelihoods for the Poisson and the
quasi-log-mu models. Other software packages (e.g., LIMDEP) routinely
provide log-likelihoods for the Poisson models. Can log-likelihoods be
generated for the Splus Poisson and quasi-log-mu models? If so, how?
Answers to any or all of these questions would be most appreciated.
Sincerely,
Michael.
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