Re: [R] GLM output for deviance and loglikelihood

From: peter dalgaard <pdalgd_at_gmail.com>
Date: Fri, 22 Apr 2011 00:12:40 +0200

On Apr 21, 2011, at 11:30 , Jeffrey Pollock wrote:

> So am I right in saying that Binary data isnt the only case where this is true? It would make sense to me that for a multinomial model you could have a unique factor for each data point and thus be able to create a likelihood of 1.

Yes. (I did say "pretty much"...). There are also some synthetic cases like when you enter a 2x2 table as 4 separate records:

> d <- data.frame(n=c(1,2,3,4),outcome=c(0,1,0,1),g=c(1,1,2,2))
> summary(glm(outcome~g,weights=n,binomial,data=d))

Call:
glm(formula = outcome ~ g, family = binomial, data = d, weights = n)

Deviance Residuals:

     1 2 3 4
-1.482 1.274 -2.255 2.116

Coefficients:

            Estimate Std. Error z value Pr(>|z|)
(Intercept)   1.0986     2.5658   0.428    0.669
g            -0.4055     1.4434  -0.281    0.779

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 13.460 on 3 degrees of freedom Residual deviance: 13.380 on 2 degrees of freedom AIC: 17.380 Number of Fisher Scoring iterations: 3

(The results are fine as long as you don't actually use the "residual deviance" for anything!)

-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes_at_cbs.dk  Priv: PDalgd_at_gmail.com

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