# [R] Where is the SD in output of glm with Gaussian distribution

Marc Girondot m@rc_grt @end|ng |rom y@hoo@|r
Mon Dec 9 17:25:40 CET 2019

```Le 09/12/2019 à 16:45, Bert Gunter a écrit :
> In addition, as John's included output shows, only 1 parameter, the
> intercept, is fit. As he also said, the sd is estimated from the
> residual deviance -- it is not a model parameter.
>
> Suggest you spend some time with a glm tutorial/text.

I tried ! But I miss this point. I understand now this point. Thanks a
lot... big progress for me.

But still I don't understand why AIC calculation uses 2 parameters if
the SD is estimated from the residual deviance.

> y=rnorm(100)
> gnul <- glm(y ~ 1)
> logLik(gnul)
'log Lik.' -136.4343 (df=2)
> AIC(gnul)
[1] 276.8687
> -2*logLik(gnul)+2*2
'log Lik.' 276.8687 (df=2)

This is not intuitive when to count SD as a parameter (in AIC) or not in
df.resuidual !

>
> Bert
>
> On Mon, Dec 9, 2019 at 7:17 AM Marc Girondot via R-help
> <r-help using r-project.org <mailto:r-help using r-project.org>> wrote:
>
>     Let do a simple glm:
>
>      > y=rnorm(100)
>      > gnul <- glm(y ~ 1)
>      > gnul\$coefficients
>     (Intercept)
>        0.1399966
>
>     The logLik shows the fit of two parameters (DF=2) (intercept) and sd
>
>      > logLik(gnul)
>     'log Lik.' -138.7902 (df=2)
>
>     But where is the sd term in the glm object?
>
>     If I do the same with optim, I can have its value
>
>      > dnormx <- function(x, data) {1E9*-sum(dnorm(data, mean=x["mean"],
>     sd=x["sd"], log = TRUE))}
>      > parg <- c(mean=0, sd=1)
>      > o0 <- optim(par = parg, fn=dnormx, data=y, method="BFGS")
>      > o0\$value/1E9
>     [1] 138.7902
>      > o0\$par
>           mean        sd
>
>     0.1399966 0.9694405
>
>     But I would like have the value in the glm.
>
>     (and in the meantime, I don't understand why gnul\$df.residual
>     returned
>     99... for me it should be 98=100 - number of observations) -1 (for
>     mean)
>     - 1 (for sd); but it is statistical question... I have asked it in
>     crossvalidated [no answer still] !)
>
>     Thanks
>
>     Marc
>
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