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# st: from reg to xtreg, an interaction term change also in its sign, why?

 From Luca Fumarco To "statalist@hsphsun2.harvard.edu" Subject st: from reg to xtreg, an interaction term change also in its sign, why? Date Wed, 18 Apr 2012 19:14:12 +0200

```Dear Statalister,

I have a problem with a couple of regressions I am running.

1) I run this model:
reg callback dsec m50 m50_sec
(with dsec and m50 dummy variables)
and I get

Source	SS       df       MS	Number of obs	=     272
F(  3,   268)	=    2.59
Model	1.89291395     3  .630971316	Prob > F	=  0.0529
Residual	65.1659096   268  .243156379	R-squared	=  0.0282
Total	67.0588235   271  .247449533	Root MSE	=  .49311

callback	Coef.   Std. Err.      t    P>t	[95% Conf.	Interval]

1.dsec	-.115942   .0839524    -1.38   0.168	-.2812322	.0493482
m50	-.143846   .0845766    -1.70   0.090	-.3103651	.0226731
m50_sec	.0263898   .1196094     0.22   0.826	-.2091038	.2618834
_cons	.6811594   .0593633    11.47   0.000	.5642816	.7980372

then I run the same regression but with xtreg, fe
xtreg callback dsec m50 m50_sec, fe
and I get
. xtreg callback i.dsec m50 i.dsec#i.m50 if many_appl>=0, fe
note: m50 omitted because of collinearity
note: 1.dsec#1.m50 omitted because of collinearity

Fixed-effects (within) regression               Number of obs      =       272
Group variable: sit_id                          Number of groups   =       136

R-sq:  within  = 0.1046                         Obs per group: min =         2
between = 0.0193                                        avg =       2.0
overall = 0.0145                                        max =         2

F(2,134)           =      7.83
corr(u_i, Xb)  = 0.0158                         Prob > F           =    0.0006

callback       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

1.dsec    -.115942   .0368203    -3.15   0.002    -.1887663   -.0431178
m50           0  (omitted)

dsec#m50
0 1    -.0263898    .052459    -0.50   0.616    -.1301445    .0773649
1 1            0  (omitted)

_cons     .623295   .0318091    19.59   0.000     .5603821    .6862078

sigma_u   .47076084
sigma_e   .21627055
rho   .82572684   (fraction of variance due to u_i)

F test that all u_i=0:     F(135, 134) =     9.33            Prob > F = 0.0000

why does the interaction term change sign?

2) Moreover, how can I interpret the coefficients of the interaction term in xtreg (the second model)?
0 1 is simply the coefficient of m50
1 1 is the proper coefficient of the interaction term (since the values of both terms equal 1), but it is now omitted
As far as I have understood, in this case, I do not really have an interaction term

Thank you very much in any case!
Cordially

Luca Fumarco

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```