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List:       r-sig-mixed-models
Subject:    [R-sig-ME] GL(L)Ms, Gamma distributions, and AIC
From:       Peter R Law via R-sig-mixed-models <r-sig-mixed-models () r-project ! org>
Date:       2021-04-20 2:47:15
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Hello:

The R information from ?glm includes the following:

aic:

A version of Akaike'sAn Information Criterion, minus twice the maximized \
log-likelihood plus twice the number of parameters, computed by theaiccomponent of \
the family. For binomial and Poison families the dispersion is fixed at one and the \
number of parameters is the number of coefficients. For gaussian, Gamma and inverse \
gaussian families the dispersion is estimated from the residual deviance, and the \
number of parameters is the number of coefficients plus one. For a gaussian family \
the MLE of the dispersion is used so this is a valid value of AIC, but for Gamma and \
inverse gaussian families it is not. For families fitted by quasi-likelihood the \
value isNA.

Does the text in bold mean the AIC value contained in the summary output of a glm \
with the Gamma distribution run in R is not valid? If so, can one still use the \
output from logLik for the glm to compute AIC directly? It's not quite clear to me \
what the issue is. For a test model of the form

glm(y ~ x + y, family=Gamma)

I got
Deviance Residuals:

Min1QMedian3QMax

-0.42321-0.10661-0.020420.077280.45861

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept)3.577e-029.012e-0439.692<2e-16 ***

density-1.134e-045.469e-06 -20.730<2e-16 ***

rain2.414e-051.758e-051.3740.17

---

Signif. codes:0 ‘***' 0.001 ‘**' 0.01 ‘*' 0.05 ‘.' 0.1 ‘ ' 1

(Dispersion parameter for Gamma family taken to be 0.02430272)

Null deviance: 21.859on 499degrees of freedom

Residual deviance: 11.702on 497degrees of freedom

AIC: 3095.8

Number of Fisher Scoring iterations: 4

> logLik(M50)

'log Lik.' -1543.925 (df=4)

The logLik and AIC indicate four parameters are counted in the computation of the \
AIC, as I would have expected.

Whatever the issue is, is there a similar issue with Gamma models in glmer in lme4?

Peter Law

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