[R] A logit question?

[Mäkinen Jussi]

Hello dear r-gurus!

I have a question about the logit-model. I think I have misunderstood
something and I'm trying to find a bug from my code or even better from my
head. Any help is appreciated.

The question is shortly: why I'm not having same coefficients from the
logit-regression when using a link-function and an explicite transformation
of the dependent. Below some details.

I'm not very familiar with the concept. As far as I have understood it's all
about transformation of the dependent variable if one have frequency data
(grouped data, instead of raw binaries):

ln(^p(i)/(1-^p(i)) = c + b_1(X_1) +...+ b_k(X_k) + e(i).

where ^p(i) is (estimated) frequency of incident (happened/all = n(i)/N), i
is index of observation, c and b_. are coefficients (objects of the
estimation), X_. are the explanatory variables and e is residual. So a
linear regression. 

And some testing:


> y <- runif(100)
> X <- rnorm(100)
> glm(y~ X, family=binomial(link=logit))

Call:  glm(formula = y ~ X, family = binomial(link = logit)) 

Coefficients:
(Intercept)            X  
   -0.00956      0.10760  

Degrees of Freedom: 99 Total (i.e. Null);  98 Residual
Null Deviance:      43.83 
Residual Deviance: 43.49        AIC: 142.3 
Warning message: 
non-integer #successes in a binomial glm! in: eval(expr, envir, enclos) 



### OR
> glm(cbind(y, 1-y)~ X, family=binomial(link=logit))	### ?glm

Call:  glm(formula = cbind(y, 1 - y) ~ X, family = binomial(link = logit)) 

Coefficients:
(Intercept)            X  
   -0.00956      0.10760  

Degrees of Freedom: 99 Total (i.e. Null);  98 Residual
Null Deviance:      43.83 
Residual Deviance: 43.49        AIC: 142.3 
Warning message: 
non-integer counts in a binomial glm! in: eval(expr, envir, enclos) 



### BUT
> glm(y.logit.transformation(y)~ X)

Call:  glm(formula = y.logit.transformation(y) ~ X) 

Coefficients:
(Intercept)            X  
     0.1233       0.1023  

Degrees of Freedom: 99 Total (i.e. Null);  98 Residual
Null Deviance:      465.6 
Residual Deviance: 464.4        AIC: 443.3 


### OR
> lm(y.logit.transformation(y)~ X)

Call:
lm(formula = y.logit.transformation(y) ~ X)

Coefficients:
(Intercept)            X  
     0.1233       0.1023  


It's close (AIC and residual deviance is different due transformation) but I
think that relationship should be exact? Or is it just calculation
inaccurance? Or is there some hidden reason (to me..)? Is it legimitate to
use frequency regression when using R for the logit-model (alternatives?).

I would like to know what does exactly mean the warning message: 
non-integer counts in a binomial glm! in: eval(expr, envir, enclos)

For the dependent transformation:

"y.logit.transformation" <- function(y)
{
	y.trans <- log(y/(1-y))
	y.trans
}

version

platform i386-pc-mingw32
arch     i386           
os       mingw32        
system   i386, mingw32  
status                  
major    1              
minor    5.0            
year     2002           
month    04             
day      29             
language R 

OS is Windows2000.

Thank you for any help.

deadlocked,

Jussi Mäkinen
Analyst
State Treasury, Finland
phone:  +358-9-7725 616
mobile: +358-50-5958 710
www.statetreasury.fi
mailto:jussi.makinen at valtiokonttori.fi



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