xtmixed vs. xtreg - results are not identical

Carlos Marena

Join Date: Dec 2016

Posts: 2
#16

10 Apr 2017, 16:53

Hi everyone.

I have the same problem. When I use the xtmixed command, Why obtain a sd(_cons) from the random intercept (or second level) which differs greatly from the sigma_u of the xtreg command? I´m sure that my syntaxis is not wrong because first I had run a null model (without covariates) and as a coesequence both commands gives me the same coefficients, std, sigma_u, sigma_e, sd(_cons) and sd(residual). However, in a second model (model with covariates), I ran the same data but it reports me a simga_u = 0 (and also rho = 0) and the xtmixed command reports an sd(_cons) from the second level different from. Why it is happening? Thanks in advance for your help.
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Clyde Schechter

Join Date: Apr 2014

Posts: 28624
#17

10 Apr 2017, 17:07

Without posting the exact code and the exact output you got, it is unlikely anyone can give you an answer. The little details are often crucial, and you don't provide anything but a broad description of the problem. Please read the FAQ for good advice on how to post questions in ways that enhance your likelihood of getting a timely and helpful response. Also focus on FAQ #12 to learn about code delimiters so that you can post code and output readably.
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Carlos Marena

Join Date: Dec 2016

Posts: 2
#18

10 Apr 2017, 18:42

The following text contains the code and the output previously mentioned.

PHP Code:

use "appenddata2010.dta", clear . . xtset division panel variable: division (unbalanced) . . glob controls began_unregistered years_unregistered firmage export_orientation foreign_ownership manager_experience temporary_workers permanent_workers female_involved_ > ownership access_to_finance transport electricity quality_certification external_auditor website e_mail i.economic_sector . . *null model . xtreg gemployment if firm_size_b==3 , mle Iteration 0: log likelihood = -5426.7507 Iteration 1: log likelihood = -5426.4992 Iteration 2: log likelihood = -5426.4953 Iteration 3: log likelihood = -5426.4953 Random-effects ML regression Number of obs = 1,413 Group variable: division Number of groups = 31 Random effects u_i ~ Gaussian Obs per group: min = 1 avg = 45.6 max = 216 Wald chi2(0) = 0.00 Log likelihood = -5426.4953 Prob > chi2 = . ------------------------------------------------------------------------------ gemployment | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _cons | 2.281579 .4752067 4.80 0.000 1.350191 3.212967 -------------+---------------------------------------------------------------- /sigma_u | 1.498766 .458781 .8225765 2.730811 /sigma_e | 11.20319 .212167 10.79498 11.62685 rho | .0175825 .0106306 .0048458 .0519464 ------------------------------------------------------------------------------ LR test of sigma_u=0: chibar2(01) = 9.63 Prob >= chibar2 = 0.001 . xtmixed gemployment if firm_size_b==3 ||division:, mle Performing EM optimization: Performing gradient-based optimization: Iteration 0: log likelihood = -5426.4959 Iteration 1: log likelihood = -5426.4953 Iteration 2: log likelihood = -5426.4953 Computing standard errors: Mixed-effects ML regression Number of obs = 1,413 Group variable: division Number of groups = 31 Obs per group: min = 1 avg = 45.6 max = 216 Wald chi2(0) = . Log likelihood = -5426.4953 Prob > chi2 = . ------------------------------------------------------------------------------ gemployment | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _cons | 2.281578 .4726836 4.83 0.000 1.355135 3.208021 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ division: Identity | sd(_cons) | 1.498773 .458782 .8225808 2.730819 -----------------------------+------------------------------------------------ sd(Residual) | 11.20319 .2121669 10.79498 11.62685 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 9.63 Prob >= chibar2 = 0.0010 . . *model with covariates . xtreg gemployment $controls if firm_size_b==3 , mle Fitting constant-only model: Iteration 0: log likelihood = -4965.8246 Iteration 1: log likelihood = -4965.642 Iteration 2: log likelihood = -4965.6419 Fitting full model: Iteration 0: log likelihood = -4939.2437 Iteration 1: log likelihood = -4939.1502 Iteration 2: log likelihood = -4939.1502 Random-effects ML regression Number of obs = 1,308 Group variable: division Number of groups = 31 Random effects u_i ~ Gaussian Obs per group: min = 1 avg = 42.2 max = 203 LR chi2(21) = 52.98 Log likelihood = -4939.1502 Prob > chi2 = 0.0001 -------------------------------------------------------------------------------------------------------- gemployment | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------------------------------------+---------------------------------------------------------------- began_unregistered | -.7790503 1.381053 -0.56 0.573 -3.485865 1.927765 years_unregistered | .0857678 .065635 1.31 0.191 -.0428745 .21441 firmage | -.048905 .0140202 -3.49 0.000 -.076384 -.021426 export_orientation | -1.505309 .6666039 -2.26 0.024 -2.811828 -.1987892 foreign_ownership | -.7543359 .8783151 -0.86 0.390 -2.475802 .96713 manager_experience | -.0235406 .0254821 -0.92 0.356 -.0734846 .0264034 temporary_workers | .0001227 .0006893 0.18 0.859 -.0012284 .0014738 permanent_workers | .0002445 .0002621 0.93 0.351 -.0002693 .0007583 female_involved_ownership | .2723627 .712606 0.38 0.702 -1.124319 1.669045 access_to_finance | 2.239303 .7097259 3.16 0.002 .8482655 3.63034 transport | .3602209 .7125367 0.51 0.613 -1.036325 1.756767 electricity | -.1818435 .6727118 -0.27 0.787 -1.500334 1.136647 quality_certification | .6279148 .6427971 0.98 0.329 -.6319444 1.887774 external_auditor | -.3331411 .7624314 -0.44 0.662 -1.827479 1.161197 website | .2814078 .9655758 0.29 0.771 -1.611086 2.173902 e_mail | -.5884869 2.684828 -0.22 0.827 -5.850653 4.673679 | economic_sector | Hotels & Rest | -1.704953 4.232523 -0.40 0.687 -10.00055 6.590639 Manufacturing | .6477709 2.360216 0.27 0.784 -3.978168 5.273709 Real estate, renting and business act | 6.572925 2.833487 2.32 0.020 1.019393 12.12646 Transport, storage and communications | 1.553171 2.853824 0.54 0.586 -4.040222 7.146563 Wholesale & Retail trade | 1.349625 2.456442 0.55 0.583 -3.464913 6.164163 | _cons | 2.774814 3.768193 0.74 0.462 -4.610709 10.16034 ---------------------------------------+---------------------------------------------------------------- /sigma_u | 0 (omitted) /sigma_e | 10.56102 .2064843 10.16398 10.97358 rho | 0 (omitted) -------------------------------------------------------------------------------------------------------- LR test of sigma_u=0: chibar2(01) = 0.00 Prob >= chibar2 = 1.000 . xtmixed gemployment $controls if firm_size_b==3 ||division: , mle Performing EM optimization: Performing gradient-based optimization: Iteration 0: log likelihood = -4936.9417 Iteration 1: log likelihood = -4936.935 Iteration 2: log likelihood = -4936.935 Computing standard errors: Mixed-effects ML regression Number of obs = 1,308 Group variable: division Number of groups = 31 Obs per group: min = 1 avg = 42.2 max = 203 Wald chi2(21) = 51.88 Log likelihood = -4936.935 Prob > chi2 = 0.0002 -------------------------------------------------------------------------------------------------------- gemployment | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------------------------------------+---------------------------------------------------------------- began_unregistered | -.7666805 1.378154 -0.56 0.578 -3.467813 1.934452 years_unregistered | .0831349 .065523 1.27 0.205 -.0452878 .2115575 firmage | -.0540928 .0141128 -3.83 0.000 -.0817534 -.0264323 export_orientation | -1.314988 .6700306 -1.96 0.050 -2.628224 -.0017525 foreign_ownership | -.893929 .8777134 -1.02 0.308 -2.614216 .8263576 manager_experience | -.0190642 .0254847 -0.75 0.454 -.0690132 .0308848 temporary_workers | .0000481 .0006873 0.07 0.944 -.001299 .0013953 permanent_workers | .000242 .0002623 0.92 0.356 -.000272 .0007561 female_involved_ownership | .342937 .7103798 0.48 0.629 -1.049382 1.735256 access_to_finance | 2.305546 .7085896 3.25 0.001 .9167362 3.694356 transport | .3111839 .7102677 0.44 0.661 -1.080915 1.703283 electricity | -.1955359 .6714072 -0.29 0.771 -1.51147 1.120398 quality_certification | .3900236 .648665 0.60 0.548 -.8813364 1.661384 external_auditor | -.4112777 .7600924 -0.54 0.588 -1.901031 1.078476 website | .364885 .9667361 0.38 0.706 -1.529883 2.259653 e_mail | -.6192891 2.676627 -0.23 0.817 -5.865382 4.626804 | economic_sector | Hotels & Rest | -1.611018 4.419231 -0.36 0.715 -10.27255 7.050517 Manufacturing | .3646481 2.550047 0.14 0.886 -4.633352 5.362648 Real estate, renting and business act | 6.569056 3.119996 2.11 0.035 .4539764 12.68414 Transport, storage and communications | 1.533619 3.05554 0.50 0.616 -4.45513 7.522367 Wholesale & Retail trade | 1.354568 2.690641 0.50 0.615 -3.918992 6.628128 | _cons | 2.875613 3.873086 0.74 0.458 -4.715497 10.46672 -------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ division: Identity | sd(_cons) | .9432973 .3500096 .4558386 1.952028 -----------------------------+------------------------------------------------ sd(Residual) | 10.5115 .2063431 10.11475 10.9238 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 4.43 Prob >= chibar2 = 0.0177 . . . end of do-file
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Joseph Coveney

Join Date: Apr 2014

Posts: 4139
#19

10 Apr 2017, 19:16

The maximization algorithms are different: see the iteration logs. xtreg , mle found a local maximum where the second level variance collapsed to zero.

Parameterizations of the variance components seem to be different, too, inasmuch as mixed will allow them to go to an infinitesimal value but not completely to zero as xtreg does.

Use the final coefficient vector from mixed as the starting values for xtreg , mle and see whether it will converge to the same maximum likelihood value.

Code:

mixed gemployment $controls if firm_size_b==3 || division: , mle matrix define B = e(b) xtreg gemployment $controls if firm_size_b==3, i(division) mle from(B)

Last edited by Joseph Coveney; 10 Apr 2017, 19:19.
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