Dear Statalist Users,
I'm currently working on a interviewer fixed-effects regression analysis. Specifically, I am testing an interaction of German language skills (very good / not very good) and ethnicity (German, ethnic German immigrant, mixed, Turkish and other), separately for men and women. My dependent variable is physical attractiveness on a 7-point scale. I display the predictive margins and the corresponding plots. However now I'm not quite sure how to test the statistical significance of the interaction. I checked the confidence intervals and the Wald test - but the results partly contradict each other.
I'm working with Stata 16 and this is my code:
At first glance at the confidence intervals for ethnic Germans (margins at 3 and 4) and Turks (margins at 7 and 8), it looks as if the interaction between language skills and ethnicity is not statistically significant as the confidence intervals are overlapping. However the Wald test indicates that the effect is statistically significant at the 5% level for ethnic Germans (. test _b[3._at] = _b[4._at]) and Turks (. test _b[7._at] = _b[8._at]).
Could someone give me a tip on which results I should rely on?
Is it even possible to perform the Wald test with predictive margins or is it only possible with average marginal effects?
I'm currently working on a interviewer fixed-effects regression analysis. Specifically, I am testing an interaction of German language skills (very good / not very good) and ethnicity (German, ethnic German immigrant, mixed, Turkish and other), separately for men and women. My dependent variable is physical attractiveness on a 7-point scale. I display the predictive margins and the corresponding plots. However now I'm not quite sure how to test the statistical significance of the interaction. I checked the confidence intervals and the Wald test - but the results partly contradict each other.
I'm working with Stata 16 and this is my code:
Code:
reghdfe c.att i.b1.ethni##lang_w1_di c.age i.b1.parentisced_short i.b1.isced_short c.pers_se c.pers_con c.pers_ag c.pers_ea c.sah [pweight=cdweight] if sex ==0, absorb (intid cohort) cluster (intid cohort)
(dropped 45 singleton observations)
(MWFE estimator converged in 4 iterations)
Warning: VCV matrix was non-positive semi-definite; adjustment from Cameron, Gelbach & Miller applied.
warning: missing F statistic; dropped variables due to collinearity or too few clusters
HDFE Linear regression Number of obs = 3,568
Absorbing 2 HDFE groups F( 22, 2) = .
Statistics robust to heteroskedasticity Prob > F = .
R-squared = 0.4246
Adj R-squared = 0.3612
Number of clusters (intid) = 330 Within R-sq. = 0.0569
Number of clusters (cohort) = 3 Root MSE = 1.0793
(Std. Err. adjusted for 3 clusters in intid cohort)
-------------------------------------------------------------------------------------------------------------------------------------
| Robust
att | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------------------------------------------------------------+----------------------------------------------------------------
ethni |
Aussiedler | 0.225 0.145 1.550 0.261 -0.400 0.849
Gemischter ethnischer Hintergrund | 0.120 0.084 1.428 0.290 -0.241 0.481
Türkeistämmig | 0.570 0.232 2.454 0.134 -0.430 1.570
Anderer nicht-deutscher Hintergrund | 0.154 0.144 1.066 0.398 -0.466 0.773
|
lang_w1_di |
Nicht sehr gut | -0.263 0.178 -1.477 0.278 -1.029 0.503
|
ethni#lang_w1_di |
Aussiedler#Nicht sehr gut | -0.371 0.225 -1.646 0.242 -1.340 0.599
Gemischter ethnischer Hintergrund#Nicht sehr gut | 0.227 0.260 0.870 0.476 -0.894 1.347
Türkeistämmig#Nicht sehr gut | -0.450 0.258 -1.742 0.224 -1.562 0.662
Anderer nicht-deutscher Hintergrund#Nicht sehr gut | 0.153 0.215 0.710 0.551 -0.771 1.076
|
age | 0.038 0.019 1.963 0.189 -0.045 0.122
|
parentisced_short |
Sekundarstufe 2, berufliche Bildung (3b) | 0.081 0.102 0.793 0.511 -0.357 0.518
Obere Sekundarstufe allgemein, post sek., nicht tertiär (3a,4a) | 0.114 0.088 1.295 0.325 -0.264 0.491
Tertiär | 0.118 0.097 1.211 0.349 -0.301 0.537
|
isced_short |
0. Derzeit in Ausbildung | 0.409 0.104 3.932 0.059 -0.039 0.857
2. Sekundarstufe 2, berufliche Bildung (3b) | 0.199 0.084 2.356 0.143 -0.164 0.562
3. Obere Sekundarstufe allgemein, post sek., nicht tertiär (3a,4a) | 0.455 0.074 6.132 0.026 0.136 0.774
4. Teriäre | 0.491 0.067 7.320 0.018 0.202 0.780
|
pers_se | -0.088 0.038 -2.320 0.146 -0.252 0.076
pers_con | -0.011 0.032 -0.348 0.761 -0.149 0.126
pers_ag | -0.070 0.053 -1.324 0.317 -0.298 0.158
pers_ea | -0.071 0.018 -3.992 0.057 -0.147 0.006
sah | 0.098 0.012 7.930 0.016 0.045 0.152
_cons | 3.438 0.549 6.262 0.025 1.076 5.800
-------------------------------------------------------------------------------------------------------------------------------------
Absorbed degrees of freedom:
-----------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
-------------+---------------------------------------|
intid | 330 330 0 *|
cohort | 3 3 0 *|
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation
.
. margins, at (ethni=(1(1)5) lang_w1_di=(0(1)1))
Predictive margins Number of obs = 3,568
Model VCE : Robust
Expression : Linear prediction, predict()
1._at : ethni = 1
lang_w1_di = 0
2._at : ethni = 1
lang_w1_di = 1
3._at : ethni = 2
lang_w1_di = 0
4._at : ethni = 2
lang_w1_di = 1
5._at : ethni = 3
lang_w1_di = 0
6._at : ethni = 3
lang_w1_di = 1
7._at : ethni = 4
lang_w1_di = 0
8._at : ethni = 4
lang_w1_di = 1
9._at : ethni = 5
lang_w1_di = 0
10._at : ethni = 5
lang_w1_di = 1
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at |
1 | 5.240 0.010 543.499 0.000 5.222 5.259
2 | 4.977 0.179 27.770 0.000 4.626 5.329
3 | 5.465 0.152 35.872 0.000 5.167 5.764
4 | 4.832 0.209 23.081 0.000 4.421 5.242
5 | 5.360 0.081 66.006 0.000 5.201 5.519
6 | 5.324 0.307 17.332 0.000 4.722 5.926
7 | 5.811 0.231 25.144 0.000 5.358 6.263
8 | 5.097 0.145 35.158 0.000 4.813 5.382
9 | 5.394 0.138 39.023 0.000 5.123 5.665
10 | 5.284 0.172 30.806 0.000 4.947 5.620
------------------------------------------------------------------------------
.
. margins, at (ethni=(1(1)5) lang_w1_di=(0(1)1)) coeflegend post
Predictive margins Number of obs = 3,568
Model VCE : Robust
Expression : Linear prediction, predict()
1._at : ethni = 1
lang_w1_di = 0
2._at : ethni = 1
lang_w1_di = 1
3._at : ethni = 2
lang_w1_di = 0
4._at : ethni = 2
lang_w1_di = 1
5._at : ethni = 3
lang_w1_di = 0
6._at : ethni = 3
lang_w1_di = 1
7._at : ethni = 4
lang_w1_di = 0
8._at : ethni = 4
lang_w1_di = 1
9._at : ethni = 5
lang_w1_di = 0
10._at : ethni = 5
lang_w1_di = 1
------------------------------------------------------------------------------
| Margin Legend
-------------+----------------------------------------------------------------
_at |
1 | 5.240 _b[1bn._at]
2 | 4.977 _b[2._at]
3 | 5.465 _b[3._at]
4 | 4.832 _b[4._at]
5 | 5.360 _b[5._at]
6 | 5.324 _b[6._at]
7 | 5.811 _b[7._at]
8 | 5.097 _b[8._at]
9 | 5.394 _b[9._at]
10 | 5.284 _b[10._at]
------------------------------------------------------------------------------
.
. test _b[1._at] = _b[2._at]
( 1) 1bn._at - 2._at = 0
chi2( 1) = 2.18
Prob > chi2 = 0.1396
.
. test _b[3._at] = _b[4._at]
( 1) 3._at - 4._at = 0
chi2( 1) = 8.61
Prob > chi2 = 0.0033
.
. test _b[5._at] = _b[6._at]
( 1) 5._at - 6._at = 0
chi2( 1) = 0.01
Prob > chi2 = 0.9050
.
. test _b[7._at] = _b[8._at]
( 1) 7._at - 8._at = 0
chi2( 1) = 7.68
Prob > chi2 = 0.0056
.
. test _b[9._at] = _b[10._at]
( 1) 9._at - 10._at = 0
chi2( 1) = 0.97
Prob > chi2 = 0.3240
At first glance at the confidence intervals for ethnic Germans (margins at 3 and 4) and Turks (margins at 7 and 8), it looks as if the interaction between language skills and ethnicity is not statistically significant as the confidence intervals are overlapping. However the Wald test indicates that the effect is statistically significant at the 5% level for ethnic Germans (. test _b[3._at] = _b[4._at]) and Turks (. test _b[7._at] = _b[8._at]).
Could someone give me a tip on which results I should rely on?
Is it even possible to perform the Wald test with predictive margins or is it only possible with average marginal effects?
Comment