# [R] a question about glm( )

Peter Dalgaard p.dalgaard at biostat.ku.dk
Thu Jul 6 23:53:09 CEST 2006

```qli at math.wustl.edu writes:

> Hi,
>
> I am working on an example about generalized linear model in a paper using
> glm( ). The code is quite simple and straightforward, but the result is
> rediculous. The true parameter is c(4, -6), but the result is c(2.264774,
> -3.457114) Can anybody tell me the reason for this? Thanks a lot!!!

What's ridiculous about that? With a sample size of 100, the
estimation variation is going to be substantial. I get

> beta.old
(Intercept)      x[, 2]
3.096393   -4.845186
> confint(glm (y~x[,2],family=binomial()))
Waiting for profiling to be done...
2.5 %    97.5 %
(Intercept)  1.251333  5.574944
x[, 2]      -8.093080 -2.370165

and c(4, -6) is well within the confidence limits.

> Here is the code:
>
>
> g=function(t){exp(t)/(1+exp(t))}	#the given link function
>
>
> n = 100	 # sample size
> beta.true = c(4,-6)	#the true parameter
>
> #----------------------------------------- the given x
> x = rep(0,n)
>
> for(i in 1:n)
>
> 	{if (i<=80)
>
> 		x[i]=0.90-0.0025*i
>
> 	 else
>
> 		x[i]=0.70-0.035*(i-80)
>
> 	}
>
> x = cbind(1,x)
>
> #----------------------------------------- to generate y
>
> meany = g(x%*%beta.true)
>
>
> y = rep(0,100)
> for(i in 1:n)
>
> 	{ # simulate the data from a binomial distribution
>
> 		y[i] = rbinom(1,1,meany[i])
> 	}
>
>
> #------------------------------------------ to do the Quasi-likelihood
> beta.old = glm (y~x[,2],family=binomial())\$coef
>
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