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

[Fox, John]

Dear Marc,

For your simple model, the standard deviation of y is the square-root of the estimated dispersion parameter:

> set.seed(123)
> y <- rnorm(100)
> gnul <- glm(y ~ 1)
> summary(gnul)

Call:
glm(formula = y ~ 1)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.39957  -0.58426  -0.02865   0.60141   2.09693  

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.09041    0.09128    0.99    0.324

(Dispersion parameter for gaussian family taken to be 0.8332328)

    Null deviance: 82.49  on 99  degrees of freedom
Residual deviance: 82.49  on 99  degrees of freedom
AIC: 268.54

Number of Fisher Scoring iterations: 2

> sqrt(0.8332328)
[1] 0.9128159
> mean(y)
[1] 0.09040591
> sd(y)
[1] 0.9128159

I hope this helps,
 John

  -----------------------------
  John Fox, Professor Emeritus
  McMaster University
  Hamilton, Ontario, Canada
  Web: http::/socserv.mcmaster.ca/jfox

> On Dec 9, 2019, at 10:16 AM, Marc Girondot via R-help <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
> 
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.