[R] Where is the SD in output of glm with Gaussian distribution
Fox, John
j|ox @end|ng |rom mcm@@ter@c@
Mon Dec 9 16:32:29 CET 2019
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.
More information about the R-help
mailing list