It has always been my understanding that deviance for GLMs is defined
by;
D = -2(loglikelihood(model) - loglikelihood(saturated model))
and this can be calculated by (or at least usually is);
D = -2(loglikelihood(model))
As is done so in the code for 'polr' by Brian Ripley (in the package
'MASS') where the -loglikehood is minimised using optim;
res <- optim(s0, fmin, gmin, method = "BFGS", hessian = Hess, ...)
.
.
.
deviance <- 2 * res$value
If so, why is it that;
> x = rnorm(10)
> y = rpois(10,lam=exp(1 + 2*x))
> test = glm(formula = y ~ x, family = poisson)
> deviance(test)
[1] 5.483484
> -2*logLik(test)
[1] 36.86335
I'm clearly not understanding something here, can anyone shed any light?
Why is;
-2*logLik(test) =/= deviance(test) ???
I think this is something that is poorly understood all over the
internet (at least from my google searches anyway!)
Thanks,
Jeff
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