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# Re: st: test for trend of an ordinal predictor

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: test for trend of an ordinal predictor Date Mon, 26 Apr 2010 06:10:51 -0700 (PDT)

```--- On Mon, 26/4/10, Georgia wrote:
> I am fitting a regression model with a normally distributed
> outcome (y) and an ordinal variable in 3 levels (x) as
> predictor. Obviously, when I use the command
>
> xi: regress y i.x
>
> I get separate coefficients for the second and the third
> level of the predictor while the first level is treated as
> reference. However, I would be very interested in testing
> the trend of the ordinal variable. In such a case, do I
> simply treat my ordinal var as a continuous one by typing
>
> regress y x
>
> or is there  a better way to test the trend of x?

The latter model assumes that the "distance" between the
first and second category is the same as the "distance"
between the second and the third. To test this null-
hypothesis you can use either -test- after your model
with dummy variables, or estimate both models and
compare them using -ftest- (downloadable from SSC). As
you can see in the example below, the results are
exactly the same.

*---------- begin example ------------
sysuse auto, clear
recode rep78 1/2=3
reg mpg i.rep78, coeflegend
test 2*_b[4.rep78] = _b[5.rep78]
est store a
ssc install ftest
reg mpg rep78
ftest a .
*----------- end example --------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

However, the hypothesis that the distances between
categories are the same in a categorical variable
is usualy not a sensible hypothesis. In those cases
you can better estimate the distances between the
categories together with the effect of the underlying
continuous variable. A straightforward way of doing
is to use so-called sheaf coefficients (Heise 1972)
This approach is implemented in the -sheafcoef-
package (also downloadable from SSC), which is
discussed here:
<http://www.maartenbuis.nl/wp/prop.html>

*------------ begin example ----------
sysuse auto, clear
recode rep78 1/2=3
tab rep78, gen(rep)
reg mpg rep2 rep3
ssc install sheafcoef
sheafcoef, latent(rep: rep2 rep3)
*------------- end example ------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

Heise, David R. (1972). Employing nominal variables,
induced variables, and block variables in path
analysis.  Sociological Methods & Research, 1(2):
147--173.

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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```

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