function logit() vs logistic regression

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function logit() vs logistic regression

swertie
Hello!
When I am analyzing proportion data, I usually apply logistic regression using a glm model with binomial family. For example:  
m <- glm( cbind("not realized", "realized") ~ v1 + v2 , family="binomial")

However, sometimes I don't have the number of cases (realized, not realized), but only the proportion and thus cannot compute the binomial model. I just found out that the package car contains a function "logit" which allows for logit transformation. Would it be possible to transform the proportion data with this function and analyze the transformed data with a glm with family="gaussian"?

Thank you very much
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Re: function logit() vs logistic regression

David Winsemius

On Oct 17, 2012, at 11:58 AM, swertie wrote:

> Hello!
> When I am analyzing proportion data, I usually apply logistic  
> regression
> using a glm model with binomial family. For example:
> m <- glm( cbind("not realized", "realized") ~ v1 + v2 ,  
> family="binomial")
>
> However, sometimes I don't have the number of cases (realized, not
> realized), but only the proportion and thus cannot compute the  
> binomial
> model. I just found out that the package car contains a function  
> "logit"
> which allows for logit transformation. Would it be possible to  
> transform the
> proportion data with this function and analyze the transformed data  
> with a
> glm with family="gaussian"?

If you had the total number and the row proportions, shouldn't you be  
able to calculate the original numbers? If you think not then you need  
to be more clear about exactly what data you do and do not have.

--

David Winsemius, MD
Alameda, CA, USA

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Re: function logit() vs logistic regression

Rolf Turner-3
In reply to this post by swertie
On 18/10/12 07:58, swertie wrote:

> Hello!
> When I am analyzing proportion data, I usually apply logistic regression
> using a glm model with binomial family. For example:
> m <- glm( cbind("not realized", "realized") ~ v1 + v2 , family="binomial")
>
> However, sometimes I don't have the number of cases (realized, not
> realized), but only the proportion and thus cannot compute the binomial
> model. I just found out that the package car contains a function "logit"
> which allows for logit transformation. Would it be possible to transform the
> proportion data with this function and analyze the transformed data with a
> glm with family="gaussian"?
>
> Thank you very much.

Of course it's possible, but I doubt me an it maketh a great deal of sense.

(1) You don't need the car package to get a logit() function.  You can roll
your own in a couple of lines.

(2) I believe that the conventional wisdom is that the arcsin(sqrt(x))
function
should be used to transform proportion data to something which vaguely
resembles Gaussian data.  This transformation has the effect of "stabilizing
the variance".  (Others on the list may correct me on this point.)

(3) Whatever you try is not going to work very well if you have proportion
values that are close to 0 or to 1.

(4) Whatever you try is going to be a pretty shaganappi approximation.
The fact is that the variance of proportions does vary with the number of
cases.  A variance stabilizing transformation mitigates this effect but does
not eliminate it.  See fortune(111).

     cheers,

         Rolf Turner

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Re: function logit() vs logistic regression

Achim Zeileis-4
In reply to this post by swertie
On Wed, 17 Oct 2012, swertie wrote:

> Hello!
> When I am analyzing proportion data, I usually apply logistic regression
> using a glm model with binomial family. For example:
> m <- glm( cbind("not realized", "realized") ~ v1 + v2 , family="binomial")
>
> However, sometimes I don't have the number of cases (realized, not
> realized), but only the proportion and thus cannot compute the binomial
> model. I just found out that the package car contains a function "logit"
> which allows for logit transformation. Would it be possible to transform
> the proportion data with this function and analyze the transformed data
> with a glm with family="gaussian"?

In situations like this, beta regression can be useful. It models the mean
and optionally also the precision (related to the variance) of a
beta-distributed response on the open (0, 1) interval. See
http://www.jstatsoft.org/v34/i02/ for an introduction to the betareg
package in R and http://www.jstatsoft.org/v48/i11/ for various extended
features.

Best,
Z

> Thank you very much
>
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/function-logit-vs-logistic-regression-tp4646498.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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Re: function logit() vs logistic regression

swertie
Thank you very much for replies and the nice explanation about variance stabilization. I heard about the arcsin transformation, but some recent papers were very critical about it (i.e., Warton & Hui, 2011), so that I would better try another way. I will have a look at beta regression.
Best,
V.