[R] A logit question?

[Kenneth Cabrera]

Mäkinen Jussi wrote:

>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)
>>
Should you use a binomial (0,1) response variable?

best regards!

>>
>>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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