# The difference of Standard Error from vcov() and sigma() of poisson regression by glm in R

I got the SE of glm(y=x) by the following program. But I couldn't get the same SE as vcov() and sigma() by the following program glm(y ~ x, family=poisson(log)). I can't understand the difference of SE from vcov() and sigma(). And it has another way without covariance matrix? Please give me some advice.

glm(y~x)

x<-c(2,2,3,3,3,4,4)
y<-c(15,9,13,10,7,11,5)
model <- glm(y~x)
(result<-summary(model))
#            Estimate Std. Error z value Pr(>|z|)
#(Intercept)   16.000      5.084   3.147   0.0255 *
#x             -2.000      1.643  -1.217   0.2779
(SEvcov<-diag(sqrt(vcov(model))))#parameter SE
#(Intercept)           x
#   5.083587    1.643168
(SEsigma <-
sqrt(diag(sigma(model)^2*result$cov.unscaled)))#parameter SE #(Intercept) x # 5.083587 1.643168 glm(y~x, family=poisson) x<-c(2,2,3,3,3,4,4) y<-c(15,9,13,10,7,11,5) model<-glm(y~x,family=poisson(link=log)) (result<-summary(model)) # Estimate Std. Error z value Pr(>|z|) #(Intercept) 2.8940 0.4749 6.094 1.1e-09 *** #x -0.2010 0.1593 -1.262 0.207 (SEvcov<-diag(sqrt(vcov(model))))#parameter SE #(Intercept) x # 0.4748514 0.1592545 (SEsigma <- sqrt(diag(sigma(model)^2*result$cov.unscaled)))#parameter SE
#(Intercept)           x
#  0.5050869   0.1693948

• Why do you reference cov.unscaled? Have you noticed that the two outputs are directly proportional?
– whuber
Dec 26, 2019 at 15:03
• Thanks for your comment. hmm.., I can't get the SE values like glm(y~x)? I confuse. Dec 27, 2019 at 14:54