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st: -xtreg- vs. -xtgee- (notably re vs. pa)


From   Misha Spisok <misha.spisok@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: -xtreg- vs. -xtgee- (notably re vs. pa)
Date   Fri, 30 Apr 2010 12:38:22 -0700

Hello, Statalist!

My basic question is, Why does -xtreg, re- not give the same results
as -xtreg, pa- when the [XT] manual says it should?

The [XT] manual list, on page 131, the following:

family()       link()        corr()                   Other Stata
estimation command
gaussian    identity    exchangeable    xtreg, re (see note 1)
gaussian    identity    exchangeable    xtreg, pa

Note 1. These methods produce the same results only for balanced
panels; see [XT] xt. (page 131)

I, however, have run these commands on balanced panels and obtained
similar, but not the same, results.  xtreg, pa gives the same results
as xtgee, but I expected this.  I do not understand why one would
expect xtreg, pa to match xtreg, re, except, under certain conditions
(see, e.g., Cameron and Trivedi, Microeconometrics, page 787) on the
unobserved effect parameter.  Is this related to the "scale parameter"
reported in xtreg, pa and xtgee?  If so, how is it related?  If not,
what is this "scale parameter"?  As far as I can tell (based on the
section, vce_options and playing with the scale parameter), this
"scale parameter" matters only for the calculation of (robust?)
standard errors.

For illustration of the basis question, here is output for these three
cases (-xtreg, pa-; -xtreg, re-; -xtgee-):

. xtreg y x1 x2 x3 x4 x5 x6, pa

Iteration 1: tolerance = .30364522
Iteration 2: tolerance = .20002292
Iteration 3: tolerance = .0520306
Iteration 4: tolerance = .01066464
Iteration 5: tolerance = .0020657
Iteration 6: tolerance = .00039561
Iteration 7: tolerance = .0000756
Iteration 8: tolerance = .00001444
Iteration 9: tolerance = 2.758e-06
Iteration 10: tolerance = 5.268e-07

GEE population-averaged model                   Number of obs      =	132
Group variable:                    country      Number of groups   =	11
Link:                             identity      Obs per group: min =	12
Family:                           Gaussian                     avg =	12.0
Correlation:                  exchangeable                     max =	12
Wald chi2(6)       =	163.31
Scale parameter:                  1.418231      Prob > chi2        =	0.0000

	
y	   Coef.   Std. Err.      z    P>z     [95% Conf.	Interval]
	
x1	.5915623   .2436114     2.43   0.015     .1140928	1.069032
x2	.8635387   .2506102     3.45   0.001     .3723517	1.354726
x3	.0597941   .2347826     0.25   0.799    -.4003713	.5199595
x4    	.0020669   .0345916     0.06   0.952    -.0657314	.0698652
x5	.0130697    .160236     0.08   0.935    -.3009871	.3271264
x6     -.6271902   .1482487    -4.23   0.000    -.9177524	-.336628
_cons   .4738377   1.796204     0.26   0.792    -3.046658	3.994333
	

. xtreg y x1 x2 x3 x4 x5 x6, re

Random-effects GLS regression                   Number of obs      =	132
Group variable: country                         Number of groups   =	11

R-sq:  within  = 0.5711                         Obs per group: min =	12
between = 0.2315                                        avg =	12.0
overall = 0.3957                                        max =	12

Random effects u_i ~ Gaussian                   Wald chi2(6)       =	154.12
corr(u_i, X)       = 0 (assumed)                Prob > chi2        =	0.0000

	
y	   Coef.   Std. Err.      z    P>z     [95% Conf.	Interval]
	
x1	.5912601   .2501765     2.36   0.018     .1009232	1.081597
x2  	.8622217   .2577942     3.34   0.001     .3569543	1.367489
x3	.0627535   .2415168     0.26   0.795    -.4106108	.5361177
x4    	.0014085   .0355759     0.04   0.968    -.0683191	.071136
x5    	.0071652   .1643394     0.04   0.965    -.3149341	.3292645
x6     -.6274649   .1524716    -4.12   0.000    -.9263036	-.3286261
_cons   .5036565   1.842639     0.27   0.785    -3.107849	4.115162
	
sigma_u   .91337934
sigma_e   .77411779
rho   .58196727   (fraction of variance due to u_i)


. xtgee y x1 x2 x3 x4 x5 x6, corr(exchangeable)

Iteration 1: tolerance = .30364522
Iteration 2: tolerance = .20002292
Iteration 3: tolerance = .0520306
Iteration 4: tolerance = .01066464
Iteration 5: tolerance = .0020657
Iteration 6: tolerance = .00039561
Iteration 7: tolerance = .0000756
Iteration 8: tolerance = .00001444
Iteration 9: tolerance = 2.758e-06
Iteration 10: tolerance = 5.268e-07

GEE population-averaged model                   Number of obs      =	132
Group variable:                    country      Number of groups   =	11
Link:                             identity      Obs per group: min =	12
Family:                           Gaussian                     avg =	12.0
Correlation:                  exchangeable                     max =	12
Wald chi2(6)       =	163.31
Scale parameter:                  1.418231      Prob > chi2        =	0.0000

	
y          Coef.   Std. Err.      z    P>z     [95% Conf.	Interval]
	
x1	.5915623   .2436114     2.43   0.015     .1140928	1.069032
x2  	.8635387   .2506102     3.45   0.001     .3723517	1.354726
x3    	.0597941   .2347826     0.25   0.799    -.4003713	.5199595
x4    	.0020669   .0345916     0.06   0.952    -.0657314	.0698652
x5	.0130697    .160236     0.08   0.935    -.3009871	.3271264
x6     -.6271902   .1482487    -4.23   0.000    -.9177524	-.336628
_cons   .4738377   1.796204     0.26   0.792    -3.046658	3.994333
	
Thank you for your time.

Best,

Misha
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