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# Re: st: Logistic regression interpretation

 From "Dr. Bill Westman" To statalist@hsphsun2.harvard.edu Subject Re: st: Logistic regression interpretation Date Wed, 22 Sep 2010 11:22:45 -0700

```This is incredibly helpful!

after the margins command, we have the four outcomes.  The last line

1 1  |   .4279095  _b[1.married#1.collgrad] in my example  17.87322.
How do you interpret the 17.87 margin?

Also - those two di statements at show the exact same odds - was this
intentional?

1.6475143
.
1.6475143

Lastly, I read the manual on margins and I am wondering whether I need
to use the test command.

Thanks for this very excellent email.

On Wed, Sep 22, 2010 at 2:06 AM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> --- On Tue, Sep 21, Dr. Bill Westman  wrote:
>> > A simple logistic regression was run - outcome - Survived/Non Survived
>> > (1/0), with Group(Treatmeant/Control -- 1/0) & Risk(High/Low -- 1/0)
>> >
>> > The results
>> >
>> > ---------+-------------
>> > Survived | Odds Ratio
>> > ---------+-------------
>> >     Risk |   4.790295
>> >    group |   2.111181
>> > ---------+-------------
>> >
>> > Can I assume that odds of treatment survival were 2.1 times higher in
>> > the treatment Group for LOW risk patients?
>> > And for High Risk patients in the treatment group is the adds 4. 8 +
>> > 2.1 (or 7 times higher)?
>
> There are no interactions so the odds increases with a factor 2.1 when
> one receives the treatment regardless of whether one is in the high or
> low risk group (the baseline odds differs between the high and low risk
> group, but does not change our result).
>
> You can see this in the example below. The -margins- command is used in
> this example to get the odds (exp(linear predictor)) for each of the
> four groups. The -coefl- option is added to show how -margins stores
> each of these odds. The -di- commands use those odds to calculate the
> odds ratios again. Lets assume that group in your example is collgrad
> in mine, and that risk in your example is married in mine. You can see
> that without adding the interaction terms the odds ratio is the same
> for both married and unmarried people.
>
> *-------------------- begin example ---------------------
> sysuse nlsw88, clear
> gen byte baseline = 1
> logit union i.married i.collgrad baseline, or nocons
>
> margins, exp(exp(xb())) over(married collgrad) post coefl
> *-------------------- end example ------------------------
> (For more on examples I sent to the Statalist see:
> http://www.maartenbuis.nl/example_faq )
>
>> - Also - Is the command
>>
>> listcoef, help percent
>>
>> indicating that the odds of survival are 111% higher for
>> Treatment group?
>
> Yes, and you could have seen that directly from the output of
> your -logit- command. If something changes by a factor 2 it
> increases 100%, and if something changes by a factor .7 then it
> decreases 30%. The general rule to move from a ratio to a percentage
> is (ratio - 1) * 100%. You found an odds ratio of 2.11, so the
> odds changes (2.11 - 1)*100% = 111%
>
>> and if so - is that 111% at both High/Low risk Levels?
>
> Yes, as I explained above.
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://www.maartenbuis.nl
> --------------------------
>
>
>
>
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```