# [R] A logit question?

Mäkinen Jussi Jussi.Makinen at valtiokonttori.fi
Mon May 6 11:01:58 CEST 2002

```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

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)

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.

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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```