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# Re: st: piece-wise logistic regression

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: piece-wise logistic regression Date Wed, 28 Apr 2010 07:56:58 +0000 (GMT)

```--- On Wed, 28/4/10, Jason Ferris wrote:
> I have been reading on piecewise regression in stata from
> www.ats.ucla.edu/stat/stata/faq/piecewise.htm
>
> I am interested in approaching some analysis where the
> outcome is binary and the predictor is continuous.  A lowess
> curve of the data seems to indicate a kick in my data with a
> positive slope between 1 and 10 and a negative slope from 10 to 80.
>
> Can I use the same approach mentioned in the website above
> for logistic piecewise regression?

Yes you can. Consider the example below. You would interpret the
results as: Someone works only 12 hours a week has an odds of
being a union member of .19, that is, whithin this category we
expect .19 union members for every non-union member. As long as
someone works less than 40 hours a week, this odds increases by
a ratio of 1.02 for every hour increase in working time, that is,
an increase in the odds of union-membership of 2% per hour
increase. When someone works more than 40 hours the ratio change
for a hour increase in working time is .999, that is -.1%, but
this change is not significant.

*---------- begin example ---------------
sysuse nlsw88, clear

// A 12 hour job (i.e. 1.5 day) is in my
// country the minimum duration for not
// being counted unemployed, so in that
// case it represents a natural origin
replace hours = hours - 12

// 28 + 12 = 40, i.e. full time
mkspline hours1 28 hours2=hours

// make the baseline odds visible
gen byte baseline = 1

logit union hours1 hours2 baseline, or nocons
*--------- temporary end example ------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Some people like more smooth curves, in that case
you can use the restricted cubic spline. The
interpretation of the numbers can be a bit harder.
Interpretation is than often easier with graphs,
e.g. those created by -postrcspline-, which you
-ssc install postrcspline-.

So continuing the example, We see (the left graph)
that the probability of union membership starts
at about 10% and increases to a bit less than
30%, but the rate of increase (i.e. the effect of
working hours) is clearly less for higher working
hours. In the right graph we see that this effect
starts at .5% (=100%*.005) and decreases to about
0.

*----- continuation from previous example ------
ssc install postrcspline
mkspline2 chours = hours, nknots(3) cubic
logit union chours1 chours2 baseline, or nocons
mfxrcspline, yline(0) name(dprdx, replace)
graph combine pr dprdx, ysize(3)
*---------------- end example -------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

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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```