Re: logistic regression when saturation is not 100%

From: Marc Schwartz (MSchwartz_at_mn.rr.com)
Date: 01/11/05 

Date: Tue, 11 Jan 2005 17:31:33 GMT

Bruce Weaver wrote:
> wainer@ic.unicamp.br wrote:
>
>> Marc Schwartz <MSchwartz@mn.rr.com> writes:
>>
>> | wainer@ic.unicamp.br wrote:
>>
>>>> I am sorry if I was not clear in my previous e-mail. Let me try again.
>>>> I have 2 sets of 0/1 data. I transformed the 0/1 data into a into a
>>>> proportion variable (by determine the proportion of 1 over some
>>>> intervals of the independent variable) . The result is something of the
>>>> form
>>>
>>>
>> | Perhaps I need more coffee yet this morning, but I am unclear as to
>> | why you have performed the transformation.
>>
>> The transformation was for visualisation only. I plan to use the 0/1
>> raw data in the analysis.
>>
>> More specificaly, the 0/1 data is whether a family owns or does not a
>> particular good,
>> the independent variable is family income, and the the two data sets
>> are two racial populations.
>> There is no question that I want to answer. I am exploring the data
>> and it seems to me that the two racial groups behave differently - one
>> group seems to be more willing to aquire the good than the other which
>> would indicate some cultural/social factor beyond family income is
>> relevant (there is a complication that both groups do not have the
>> same distribution of family income..)
>>
>> I applied logistic regression on the raw data and the results were
>> suprising. If the logistic regression is log(P/1-P) = A+Bx
>> then B is one measure of willingness to aquire the good - the larger
>> the B the more willing the group is. The B for the "+" group was
>> smaller than for the "o" group, which can be
>> explained because standard logistic regression assumes that the S
>> curve saturates on 100% which in not the case for this data
>>
>> jacques
>
>
> That sounds like two logistic regressions, one for each group. A more
> conventional approach would be to one analysis with "B", Group, and
> their interaction as terms in the model. The null hypothesis for the
> interaction term states that the effect of "B" does not depend on Group.
> Based on what you've said, I would expect a significant interaction.
>
> Also, your table of regression coefficients may have a column headed
> "EXP(B)", or something like that. These are the odds ratios, which
> folks in biomedical research, at least, prefer to the raw coefficients
> for descriptive purposes.

With the clarification, I agree with Bruce's recommendation regarding
the use of a single model with an interaction term.

Simplistically, the R code would look something like the following:

glm(FamilyOwns ~ FamilyIncome * Race, family = binomial)

The use of "*" provides for the crossed interaction of the two IV's and
would be equivalent to using "FamilyIncome + Race + FamilyIncome:Race".

This will give you a tabular output that includes the main effects plus
the interaction term.

As you are now going to be getting into R specific issues, you might
want to subscribe to the r-help list and post further queries there.
More information is available at:

http://www.r-project.org/mail.html

HTH,

Marc Schwartz

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