[R] glm(family=binomial(link=logit))

[Peter Dalgaard]

Robin Hankin <r.hankin at noc.soton.ac.uk> writes:

> Hi
> 
> I am trying to make glm() work to analyze a toy logit system.
> 
> I have a dataframe with x and y independent variables.  I have
> 
> L=1+x-y          (ie coefficients 1,1,-1)
> 
> then if I have a logit relation with L=log(p/(1-p)),
> p=1/(1+exp(L)).
> 
> If I interpret "p" as the probability of  success in a Bernouilli
> trial, and I can observe the result (0 for "no", 1 for "yes")
> how do I retrieve the coefficients c(1,1,-1)
> from the data?
> 
> n <- 300
> des <- data.frame(x=(1:n)/n,y=sample(n)/n)   # experimental design
> des <- cbind(des,L=1+des$x-des$y)            # L=1+x-y
> des <- cbind(des,p=1/(1+exp(des$L)))         # p=1/(1+e^L)
> des <- cbind(des,obs=rbinom(n,1,des$p))      # observation: prob of  
> success = p.
> 
> 
> My attempt is:
> 
> glm(obs~x+y,data=des,family=binomial(link="logit"))
> 
> But it does not retrieve the correct coefficients of c(1,1,-1) ;
> I would expect a reasonably close answer with so much data.
> 
> What is the correct glm() call to perform my logit analysis?

Apart from a sign error, the only fault seems to be that you think
that 300 is a large number... Try upping n to 30000 and you'll see.

(The sign error is of course that log(p/(1-p)) = L implies that
p = exp(L)/(1+exp(L)) = 1/(1+exp(-L))).  

-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
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