[R] A logit question?

[Achim Zeileis]

Mäkinen Jussi wrote:
> 
> 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
> binary response) with glm(y~x, family=binomial(link=logit))?
> 
> 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?

No, glm() gives you the ML estimate for the regression coefficients.
Only for the gaussian family ML and OLS are the same.
Z
 
> 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
> >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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