Hello,
I have some doubts about choosing appropriate _at values for the modifying variable when using margins for plotting interactions after a Fixed Effect regression (xtreg, fe).
Do i chose the original scale of the variable or the scale of the demeaned variable that will actually be used in a fixed effect regression? The interaction is between two continuous variables.
My opinion is that one need to inspect the scale of the demeaned variables to chose appropriate values for the moderator variable. Is this correct?
The difference became apparent when I calculated the same fixed effects model with xtreg, fe and reg for which I calculated the demeaned variables directly. Using reg with the demeaned variables I would naturally inspect the demeaned variable and not the original one.
What follows is an example that illustrates the differences:
I have some doubts about choosing appropriate _at values for the modifying variable when using margins for plotting interactions after a Fixed Effect regression (xtreg, fe).
Do i chose the original scale of the variable or the scale of the demeaned variable that will actually be used in a fixed effect regression? The interaction is between two continuous variables.
My opinion is that one need to inspect the scale of the demeaned variables to chose appropriate values for the moderator variable. Is this correct?
The difference became apparent when I calculated the same fixed effects model with xtreg, fe and reg for which I calculated the demeaned variables directly. Using reg with the demeaned variables I would naturally inspect the demeaned variable and not the original one.
What follows is an example that illustrates the differences:
HTML Code:
. *** Continous*Continous Interaction in a Fixed Effects model
. xtreg DV c.var1##c.var2, fe
Fixed-effects (within) regression Number of obs = 820
Group variable: ccode Number of groups = 59
R-sq: within = 0.1696 Obs per group: min = 4
between = 0.4895 avg = 13.9
overall = 0.4106 max = 23
F(3,758) = 51.60
corr(u_i, Xb) = 0.3716 Prob > F = 0.0000
-------------------------------------------------------------------------------
DV | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
var1 | -.6884199 .3839652 -1.79 0.073 -1.442181 .0653416
var2 | -.2343191 .194814 -1.20 0.229 -.6167581 .1481199
|
c.var1#c.var2 | .0133886 .0039325 3.40 0.001 .0056686 .0211085
|
_cons | 44.74163 19.18391 2.33 0.020 7.081734 82.40153
--------------+----------------------------------------------------------------
sigma_u | 14.244203
sigma_e | 9.0203402
rho | .71376406 (fraction of variance due to u_i)
-------------------------------------------------------------------------------
F test that all u_i=0: F(58, 758) = 22.62 Prob > F = 0.0000
.
. ***Inspect descriptives of var2, so I can see the minimal and maximum values (range) of the scale and chosee approriate _at values for margins
. sum var2
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
var2 | 934 85.85625 11.44415 -10.91209 111.5349
.
. ***Plot the marginal effect of var1 conditional on var2
. margins, dydx(var1) at(var2=(-10 (20) 110))
Average marginal effects Number of obs = 820
Model VCE : Conventional
Expression : Linear prediction, predict()
dy/dx w.r.t. : var1
1._at : var2 = -10
2._at : var2 = 10
3._at : var2 = 30
4._at : var2 = 50
5._at : var2 = 70
6._at : var2 = 90
7._at : var2 = 110
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
var1 |
_at |
1 | -.8223054 .418488 -1.96 0.049 -1.642527 -.002084
2 | -.5545343 .3504558 -1.58 0.114 -1.241415 .1323464
3 | -.2867632 .2878854 -1.00 0.319 -.8510082 .2774819
4 | -.018992 .2351777 -0.08 0.936 -.4799319 .4419478
5 | .2487791 .2002769 1.24 0.214 -.1437564 .6413146
6 | .5165502 .1930929 2.68 0.007 .1380951 .8950053
7 | .7843214 .2164039 3.62 0.000 .3601775 1.208465
------------------------------------------------------------------------------
. marginsplot, recast(line) recastci(rarea) yline(0)
HTML Code:
. ***Create the demeaned values of var2
. egen var2_groupmean = mean(var2), by(country)
. gen var2_demeaned = var2 - var2_groupmean
.
. ***Inspect descriptives of var2_demeaned: Now i see that the scale ranges from -86 to 30, so I chose these values for the _at in margins
. sum var2_demeaned
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
var2_demea~d | 934 5.55e-07 8.802017 -86.65811 30.35748
.
. ***Plotting the marginal effect now shows a very different picture
. margins, dydx(var1) at(var2=(-90 (30) 30))
Average marginal effects Number of obs = 820
Model VCE : Conventional
Expression : Linear prediction, predict()
dy/dx w.r.t. : var1
1._at : var2 = -90
2._at : var2 = -60
3._at : var2 = -30
4._at : var2 = 0
5._at : var2 = 30
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
var1 |
_at |
1 | -1.89339 .7128124 -2.66 0.008 -3.290477 -.4963033
2 | -1.491733 .6000342 -2.49 0.013 -2.667779 -.3156879
3 | -1.090077 .4897111 -2.23 0.026 -2.049893 -.1302605
4 | -.6884199 .3839652 -1.79 0.073 -1.440978 .064138
5 | -.2867632 .2878854 -1.00 0.319 -.8510082 .2774819
------------------------------------------------------------------------------
. marginsplot, recast(line) recastci(rarea) yline(0)
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