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st: Interpreting margins results of a non-significant interaction


From   Antonio Silva <antonio.silva.09@ucl.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Interpreting margins results of a non-significant interaction
Date   Fri, 13 Jul 2012 13:15:38 +0100

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

-- 
Human Evolutionary Ecology Group
Department of Anthropology
University College London
14 Taviton Street
London WC1H OBW

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