I am running a multilevel model which predicts individual-level public support for the EU using Stata 14.1. My main independent variable of interest measures to what extent people have benefitted from EU integration on a scale of 0-8. I am examining if this effect is constant across EU member states or if the effect sizes vary between Eastern/Western Europe and/or countries that benefit from EU fiscal transfers. All variables (except for the country-level variables) are group-mean centered.
cbenefit = IV of interest
east = dummy for Eastern Europe
contribution = EU budgetary balance as % of GDP
eastbenefit = east*cbenefit
conbenefit = contribution*cbenefit
When adding the first interaction term, I receive the following result:
Code:
. mixed image ceducation13 cclass cfinancehh csomebill cmostbill ceuroidentity cknowledge cage cgender
> cbenefit east contribution eastbenefit, || country1: eastbenefit
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -27405.958
Iteration 1: log likelihood = -27405.958
Computing standard errors:
Mixed-effects ML regression Number of obs = 22,270
Group variable: country1 Number of groups = 28
Obs per group:
min = 363
avg = 795.4
max = 1,231
Wald chi2(13) = 3523.28
Log likelihood = -27405.958 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
image | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
ceducation13 | .0058476 .0018642 3.14 0.002 .0021938 .0095015
cclass | .0102325 .0066986 1.53 0.127 -.0028966 .0233616
cfinancehh | .1878532 .0095551 19.66 0.000 .1691255 .206581
csomebill | -.0466971 .0143436 -3.26 0.001 -.07481 -.0185842
cmostbill | -.1877039 .022934 -8.18 0.000 -.2326536 -.1427541
ceuroidentity | .4447555 .0125727 35.37 0.000 .4201135 .4693975
cknowledge | .0449204 .0066214 6.78 0.000 .0319428 .057898
cage | -.0019568 .0003392 -5.77 0.000 -.0026215 -.001292
cgender | -.054252 .0112298 -4.83 0.000 -.0762619 -.0322421
cbenefit | .0402523 .0031457 12.80 0.000 .0340868 .0464177
east | .0321025 .1468598 0.22 0.827 -.2557374 .3199423
contribution | .0313233 .0492996 0.64 0.525 -.0653022 .1279487
eastbenefit | -.0068053 .0112885 -0.60 0.547 -.0289303 .0153198
_cons | 2.20782 .0557533 39.60 0.000 2.098546 2.317095
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
country1: Independent |
var(eastbe~t) | .0011693 .0005506 .0004646 .0029426
var(_cons) | .0510652 .0140429 .0297883 .0875397
-----------------------------+------------------------------------------------
var(Residual) | .6818768 .0064678 .6693172 .6946721
------------------------------------------------------------------------------
LR test vs. linear model: chi2(2) = 1174.41 Prob > chi2 = 0.0000
The interaction term eastbenefit is not significant. When adding the second interaction term I receive this result:
Code:
. mixed image ceducation13 cclass cfinancehh csomebill cmostbill ceuroidentity cknowledge cage cgender
> cbenefit east contribution eastbenefit conbenefit, || country1: eastbenefit conbenefit
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -27380.361
Iteration 1: log likelihood = -27380.207
Iteration 2: log likelihood = -27380.158
Iteration 3: log likelihood = -27380.157
Computing standard errors:
Mixed-effects ML regression Number of obs = 22,270
Group variable: country1 Number of groups = 28
Obs per group:
min = 363
avg = 795.4
max = 1,231
Wald chi2(14) = 2943.20
Log likelihood = -27380.157 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
image | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
ceducation13 | .0055638 .0018612 2.99 0.003 .0019159 .0092117
cclass | .0106923 .0066924 1.60 0.110 -.0024246 .0238091
cfinancehh | .1867956 .0095406 19.58 0.000 .1680964 .2054949
csomebill | -.045531 .0143277 -3.18 0.001 -.0736129 -.0174492
cmostbill | -.1927679 .0229465 -8.40 0.000 -.2377422 -.1477937
ceuroidentity | .4428502 .0125575 35.27 0.000 .4182379 .4674625
cknowledge | .0452663 .0066071 6.85 0.000 .0323167 .0582158
cage | -.0018657 .000339 -5.50 0.000 -.0025301 -.0012013
cgender | -.0549059 .0112049 -4.90 0.000 -.0768671 -.0329447
cbenefit | .0289173 .0054457 5.31 0.000 .018244 .0395906
east | -.0254096 .1620855 -0.16 0.875 -.3430913 .2922721
contribution | .0562929 .0545108 1.03 0.302 -.0505463 .1631321
eastbenefit | .0945455 .0407223 2.32 0.020 .0147312 .1743597
conbenefit | -.0656482 .0175314 -3.74 0.000 -.1000091 -.0312874
_cons | 2.170424 .0625917 34.68 0.000 2.047746 2.293101
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
country1: Independent |
var(eastbe~t) | 1.52e-12 1.91e-11 3.33e-23 .0695549
var(conben~t) | .0040515 .0016208 .0018497 .0088743
var(_cons) | .0622493 .017163 .0362616 .1068619
-----------------------------+------------------------------------------------
var(Residual) | .6783882 .0064391 .6658844 .6911268
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 1226.00 Prob > chi2 = 0.0000
When adding the second interaction term, eastbenefit becomes positively (and marginally) significant. Conbenefit has a negative coefficient and is significant as well. Following my interpretation, this can be traced back to the fact that most Eastern European countries strongly benefit from EU fiscal transfers. If only eastbenefit is part of the model, the positive interaction effect of east and the negative interaction effect of contribution eliminate each other. Only if conbenefit is added, it becomes possible to isolate both interaction effects.
My questions are:
1. Is my interpretation plausible? Does the 'suppressor variable' logic also translate to moderating variables?
2. How do I exactly interpret the coefficients of two interaction effects? 'The effect of cbenefit is 0.095 points higher in Eastern Europe for countries with the mean value on contribution and keeping all individual-level variables constant.' I am insecure about how to interpret two cross-level interaction effects at the same time.
I am looking forward to your input!
Philipp
0 Response to Interpreting two cross-level interaction effects at the same time in MLM
Post a Comment