GLM output for deviance and loglikelihood

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