# [R] A logit question?

Mäkinen Jussi Jussi.Makinen at valtiokonttori.fi
Mon May 6 13:56:51 CEST 2002

```I have got few answers which has pointed out that usually logit-model is for
a binary response (dependent) variable. And this was a part of my (obviously
badly written) question: is it possible to regress frequency data (e.g. not

glm-help says:

<snip>...For `binomial' models the response can also be specified as a
`factor' (when the first level denotes failure and all others success) or as
a two-column matrix with the columns giving the numbers of successes and
failures....<snip>

which led me think that it can handle frequency data (grouped data) as well.

But that should give the same result as transforming response and running
regular OLS?

Jussi

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
>
>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)
>>

>>
>
>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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