# -xtreg- vs. -xtgee- (notably re vs. pa)

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## -xtreg- vs. -xtgee- (notably re vs. pa)

 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 * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/