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Re: st: Interpreting margins results of a non-significant interaction


From   Christoph Engel <engel@coll.mpg.de>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpreting margins results of a non-significant interaction
Date   Sat, 14 Jul 2012 17:31:49 +0200

Antonio,

You are asking for the marginal effect of a one unit increase in the percentage of catholics at the means of the remaining covariates, and at the specified levels of the income score. So you essentially replicate your (significant) main effect of the percentage of catholics at several levels of income score. Except if the income score is 10 or higher, you have a significant main effect.

For exploring the interaction effect in your non-linear model, you might want to use the inteff command (to be downloaded with findit). Or you could simply run a linear probability model, and could then directly read off the interaction effect from the coefficient of the multiplicative term (i.e. c.perc##c.income).

Hope this helps

Christoph Engel

Am 7/13/2012 2:15 PM, schrieb Antonio Silva:
I'm using the margins command to understand the effect of an
interaction between two continous variables (perc_catholics and
income_score) on the binary response using logistic regression. When
running the logistic regression with other co-variates, both the
interaction term and one of the variables of this term (income_score)
are not significant, however when running the margins command I obtain
a significant relationship for the majority of values of income_score.
I'm trying to understand how if the overal interaction is not
significant, there is nevertheless a significant interaction when
looking at most of the values of income_score. I would appreciate if
someone has ideas how this may happen. Output for the the regression
and the margins is below

//logistic regression with interaction term and co-variates
logit return c.perc_catholics##c.income_score perc_catholics_3km
crime_disorder_score wall_path_distance  postboxes if catholic==1

------------------------------------------------------------------------------
       return |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
perc_catho~s |   .0239559   .0097542     2.46   0.014     .0048381    .0430738
income_score |  -.1066493   1.490582    -0.07   0.943    -3.028137    2.814838
              |
           c. |
perc_catho~s#|
           c. |
income_score |  -.0131006   .0176606    -0.74   0.458    -.0477146    .0215135
              |
perc_cat~3km |  -.0130098   .0076235    -1.71   0.088    -.0279516    .0019321
crime_diso~e |  -.0188915   .0114732    -1.65   0.100    -.0413786    .0035957
wall_path~ce |   .5054887   .2408849     2.10   0.036      .033363    .9776144
    postboxes |   .3747876   .1275695     2.94   0.003     .1247561    .6248192
        _cons |  -.9355062    .749677    -1.25   0.212    -2.404846    .5338338
------------------------------------------------------------------------------

//margins command allowing income_score to vary and keeping
co-variates at their means.
margins, dydx(perc_catholics) at (income_score=(0(0.1)1)
perc_catholics_3km=(42.57777)  crime_disorder_score=(33.82767)
wall_path_distance=(1.041
307)  postboxes=(2.966667 )) vsquish post
Expression   : Pr(return), predict()
dy/dx w.r.t. : perc_catholics
1._at        : income_score    =           0
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
2._at        : income_score    =          .1
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
3._at        : income_score    =          .2
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
4._at        : income_score    =          .3
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
5._at        : income_score    =          .4
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
6._at        : income_score    =          .5
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
7._at        : income_score    =          .6
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
8._at        : income_score    =          .7
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
9._at        : income_score    =          .8
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
10._at       : income_score    =          .9
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667
11._at       : income_score    =           1
                perc_cat~3km    =    42.57777
                crime_diso~e    =    33.82767
                wall_path~ce    =    1.041307
                postboxes       =    2.966667


------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
perc_catho~s |
          _at |
           1  |   .0046361   .0014882     3.12   0.002     .0017192    .0075529
           2  |   .0045107   .0012751     3.54   0.000     .0020115    .0070098
           3  |   .0043706   .0010694     4.09   0.000     .0022746    .0064666
           4  |   .0042144   .0008866     4.75   0.000     .0024767    .0059521
           5  |   .0040407   .0007597     5.32   0.000     .0025516    .0055297
           6  |   .0038483   .0007406     5.20   0.000     .0023968    .0052999
           7  |   .0036367   .0008592     4.23   0.000     .0019526    .0053207
           8  |   .0034054   .0010909     3.12   0.002     .0012672    .0055436
           9  |   .0031548   .0013964     2.26   0.024     .0004179    .0058917
          10  |   .0028859   .0017492     1.65   0.099    -.0005425    .0063142
          11  |   .0026002   .0021333     1.22   0.223    -.0015811    .0067815
------------------------------------------------------------------------------


Antonio Silva



--
_________________________________________________________________
Prof. Dr. Christoph Engel
Max-Planck-Institut zur
Erforschung von Gemeinschaftsgütern
Max Planck Institute for Research on Collective Goods
Kurt-Schumacher-Strasse 10
D 53113 Bonn
Tel. +49/228/91416-10
Fax +49/228/91416-11
e-mail:engel@coll.mpg.de
http://www.coll.mpg.de
http://www.coll.mpg.de/engel.html
http://ideas.repec.org/e/pen22.html
http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=251559
_________________________________________________________________

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