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st: Interpreting margins results of a non-significant interaction
From
Antonio Silva <[email protected]>
To
<[email protected]>
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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