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st: Testing for interaction the right way
From
Amal Khanolkar <[email protected]>
To
"[email protected]" <[email protected]>
Subject
st: Testing for interaction the right way
Date
Mon, 30 Jul 2012 12:52:41 +0000
Hi all,
I just ran a multiple linear regression where I assessed the association between birth weight (bwt) and systolic blood pressure (syst) and to see if this association differed across various ethnic groups (motherland2).
The regression looks like this:
eststo: regress syst bwt age byear i.conscript_office i.education i.motherland2 height_cons bmi if multibirth==1
Source | SS df MS Number of obs = 450426
-------------+------------------------------ F( 28,450397) = 1364.00
Model | 4314673.02 28 154095.465 Prob > F = 0.0000
Residual | 50882835.3450397 112.9733 R-squared = 0.0782
-------------+------------------------------ Adj R-squared = 0.0781
Total | 55197508.3450425 122.545392 Root MSE = 10.629
----------------------------------------------------------------------------------
syst | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
bwt | -.6055903 .0169407 -35.75 0.000 -.6387936 -.572387
age | .3577402 .0356238 10.04 0.000 .2879187 .4275617
byear | .187828 .003833 49.00 0.000 .1803154 .1953406
|
conscript_office |
2 | -3.118949 .0462395 -67.45 0.000 -3.209577 -3.028321
3 | 2.027425 .0497943 40.72 0.000 1.929829 2.12502
4 | -2.227861 .0489111 -45.55 0.000 -2.323725 -2.131996
5 | -4.333249 .0553088 -78.35 0.000 -4.441653 -4.224846
6 | 3.437194 .111964 30.70 0.000 3.217748 3.65664
7 | -4.569348 4.339404 -1.05 0.292 -13.07445 3.935751
8 | 2.297753 3.543433 0.65 0.517 -4.647265 9.242772
|
education |
2 | -.0150248 .0440086 -0.34 0.733 -.1012802 .0712306
3 | .0633803 .0559744 1.13 0.258 -.0463278 .1730884
4 | .0753617 .0541538 1.39 0.164 -.0307781 .1815014
|
motherland2 |
2 | -.5819353 .1221859 -4.76 0.000 -.821416 -.3424546
3 | .6765963 .0886953 7.63 0.000 .5027563 .8504363
4 | -.5358451 .2635669 -2.03 0.042 -1.052428 -.019262
5 | .0080501 .2306449 0.03 0.972 -.4440069 .4601071
6 | -1.598423 .1865045 -8.57 0.000 -1.963966 -1.23288
7 | -3.382436 .3841187 -8.81 0.000 -4.135297 -2.629575
12 | -4.253718 .3121056 -13.63 0.000 -4.865436 -3.642001
13 | -3.158914 .8569722 -3.69 0.000 -4.838553 -1.479275
14 | -3.447844 .5662194 -6.09 0.000 -4.557617 -2.338071
16 | -.2681013 .3770459 -0.71 0.477 -1.0071 .4708971
17 | -1.706184 .4670912 -3.65 0.000 -2.621669 -.7906999
18 | -3.592319 .5584903 -6.43 0.000 -4.686943 -2.497695
19 | -1.128695 .810724 -1.39 0.164 -2.717689 .4602997
|
height_cons | .1656332 .002582 64.15 0.000 .1605726 .1706938
bmi | .5807728 .0051275 113.27 0.000 .5707231 .5908225
_cons | -290.6302 7.611868 -38.18 0.000 -305.5492 -275.7112
----------------------------------------------------------------------------------
(est2 stored)
- There's an inverse association between bwt and systloc BP and we also see that it differs across ethnic groups.
I then decided to run the above regression, using and interaction term to test the association between bwt & syst. BP across th ethnic groups as follows:
eststo: xi: regress syst i.motherland2*bwtgestage_sd age byear i.conscript_office bmi height_cons i.education if multibirth==1
i.motherland2 _Imotherlan_1-19 (naturally coded; _Imotherlan_1 omitted)
i.moth~2*bwtg~d _ImotXbwtg_# (coded as above)
i.conscript_o~e _Iconscript_1-8 (naturally coded; _Iconscript_1 omitted)
i.education _Ieducation_1-4 (naturally coded; _Ieducation_1 omitted)
Source | SS df MS Number of obs = 450426
-------------+------------------------------ F( 41,450384) = 932.27
Model | 4318031.46 41 105317.84 Prob > F = 0.0000
Residual | 50879476.9450384 112.969104 R-squared = 0.0782
-------------+------------------------------ Adj R-squared = 0.0781
Total | 55197508.3450425 122.545392 Root MSE = 10.629
--------------------------------------------------------------------------------
syst | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------+----------------------------------------------------------------
_Imotherlan_2 | -.5874048 .1227888 -4.78 0.000 -.8280669 -.3467426
_Imotherlan_3 | .683286 .0887272 7.70 0.000 .5093833 .8571886
_Imotherlan_4 | -.5563245 .2640057 -2.11 0.035 -1.073768 -.0388815
_Imotherlan_5 | .0597168 .23162 0.26 0.797 -.3942513 .5136848
_Imotherlan_6 | -1.597917 .1865016 -8.57 0.000 -1.963454 -1.23238
_Imotherlan_7 | -3.310564 .3865541 -8.56 0.000 -4.068198 -2.55293
_Imotherlan_12 | -4.130756 .3193387 -12.94 0.000 -4.75665 -3.504862
_Imotherlan_13 | -3.244462 .8992277 -3.61 0.000 -5.006921 -1.482003
_Imotherlan_14 | -3.318599 .6340628 -5.23 0.000 -4.561342 -2.075855
_Imotherlan_16 | -.2317969 .3840539 -0.60 0.546 -.9845308 .520937
_Imotherlan_17 | -1.561494 .473224 -3.30 0.001 -2.488999 -.6339895
_Imotherlan_18 | -3.662905 .5608097 -6.53 0.000 -4.762075 -2.563736
_Imotherlan_19 | -.7276308 .8554279 -0.85 0.395 -2.404243 .9489816
bwtgestage_sd | -.6190095 .0175477 -35.28 0.000 -.6534024 -.5846166
_ImotXbwtg_2 | -.0460479 .123675 -0.37 0.710 -.2884471 .1963512
_ImotXbwtg_3 | .237833 .0881634 2.70 0.007 .0650356 .4106305
_ImotXbwtg_4 | -.3626542 .276502 -1.31 0.190 -.9045897 .1792813
_ImotXbwtg_5 | .5851381 .2379974 2.46 0.014 .1186706 1.051606
_ImotXbwtg_6 | .1122759 .1890387 0.59 0.553 -.2582343 .482786
_ImotXbwtg_7 | .65864 .3941392 1.67 0.095 -.1138606 1.431141
_ImotXbwtg_12 | .5947493 .3221191 1.85 0.065 -.0365944 1.226093
_ImotXbwtg_13 | -.2570831 .8595135 -0.30 0.765 -1.941703 1.427537
_ImotXbwtg_14 | .2705031 .5700428 0.47 0.635 -.8467633 1.38777
_ImotXbwtg_16 | .1923672 .3666169 0.52 0.600 -.5261908 .9109251
_ImotXbwtg_17 | 1.01004 .5251355 1.92 0.054 -.0192099 2.039289
_ImotXbwtg_18 | -.8186397 .5970026 -1.37 0.170 -1.988746 .351467
_ImotXbwtg_19 | 1.217611 .8207839 1.48 0.138 -.3911001 2.826322
age | .3586605 .0356241 10.07 0.000 .2888383 .4284827
byear | .1878326 .003833 49.00 0.000 .1803199 .1953452
_Iconscript_2 | -3.118173 .0462396 -67.44 0.000 -3.208802 -3.027545
_Iconscript_3 | 2.026937 .0497946 40.71 0.000 1.929341 2.124533
_Iconscript_4 | -2.227908 .0489106 -45.55 0.000 -2.323772 -2.132045
_Iconscript_5 | -4.333038 .0553081 -78.34 0.000 -4.44144 -4.224636
_Iconscript_6 | 3.435944 .1119626 30.69 0.000 3.216501 3.655387
_Iconscript_7 | -4.573244 4.339324 -1.05 0.292 -13.07819 3.931697
_Iconscript_8 | 2.301005 3.543369 0.65 0.516 -4.64389 9.245899
bmi | .5806188 .0051276 113.23 0.000 .5705689 .5906687
height_cons | .1656371 .002582 64.15 0.000 .1605765 .1706978
_Ieducation_2 | -.014658 .0440085 -0.33 0.739 -.1009133 .0715973
_Ieducation_3 | .0644483 .0559753 1.15 0.250 -.0452616 .1741582
_Ieducation_4 | .0764128 .0541545 1.41 0.158 -.0297283 .1825539
_cons | -290.6543 7.611886 -38.18 0.000 -305.5734 -275.7353
--------------------------------------------------------------------------------
1. I would like to know if I have included the interaction term (i.motherland2*bwtgestage_sd) in the right way?
2. I would have expected more of the interaction tests to be significant (given the results by ethnic group in the first regression model above).
3. I also ran the bwt-syst. BP regression 'stratified' by ethnic group. But then I assume it's not sensible to text for interaction after each stratified analysis separately as it does not make sense, since the bwt-syst. BP association is now a comparison only between one ethnic gropu and the reference group?
for eg:
regress syst bwtgestage_sd age byear i.conscript_office bmi height_cons i.education if multibirth==1 & motherland2==1
regress syst bwtgestage_sd age byear i.conscript_office bmi height_cons i.education if multibirth==1 & motherland2==2
....and so on and so forth.
Thanks & regards,
/Amal.
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