Hello,
I am conceptually stuck on the difference between random effects and mixed-effects models, when to use which one, and on the need for clustering standard errors in the mixed-effects setting. Most of the expositions of mixed-effects models I have seen frame the issue in terms of patients nested within doctors or students nested within schools. I am finding it hard to reconcile these examples with the country-level data that I am using and am hoping that the information I provide is clear enough that someone with a better understanding can help me resolve my confusion. The data and main variables that I am using are as follows:
Outside of region dummies, which identify different continents, none of the variables I am interested are time-invariant by definition. So my starting point was to run a Hausman test on the model with the time-varying independent variables only, to see if fixed effects or random effects is the consistent estimator. My understanding is that if I use the fixed effects estimator, I am controlling for the region-specific effects, the effects just aren't estimable because they are absorbed into the fixed component. I ran the Hausman test (with no region dummies) as follows:
Evidently, fixed effects is the way to go if I am not interested in knowing the coefficients on the region dummies. However, if I compare the mean of my dependent variable by region, I see that there are statistically significant differences, which may be interesting to investigate in the regression.
Moreover, a reality of my data is that most of the variation in my variables comes from that between countries as opposed to that arising from within them (see below). So even though fixed effects is the consistent estimator, my understanding is that I am ignoring what could be an interesting perspective if I don't account for the between variation.
Given this, I thought that, in addition to the fixed effects estimates, I would run an alternate specification in which I also control for the region dummy using random effects. However, I am unsure if this should be implemented as xtreg, re cluster (id) or in two-level multilevel model in which 'observations are clustered in countries'. The latter consideration came when I found a study that also uses country level data to model a very similar situation to mine. In this study, the authors used "a two-level mixed effects linear regression model".
According to the authors, country was treated as the level 2 identifier, but the explanation on why and how that they provide is very thin. I have tried to implement it to understand how it is different to the RE regression with clustered standard errors. I used the the Stata help manual on multi-level mixed effects to execute the code for the multi-level/mixed model I show below, but I am no closer to understanding if treating the country (id) as the level 2 identifier in the multilevel model is a similar thing to clustering standard errors at the country level in the random effects regression. If these approaches are not doing the same thing, I am lost on what the difference between the two approaches below is and would greatly appreciate guidance on how 'treating observations as nested in countries in my dataset' is different to clustering standard errors at the country level in the non-hierachical model (xtreg, re cluster(id)).
Thank you!
Sam
References:
StataCorp. 2023. Stata 18 Multilevel Mixed-Effects Reference Manual. College Station, TX: Stata Press.
I am conceptually stuck on the difference between random effects and mixed-effects models, when to use which one, and on the need for clustering standard errors in the mixed-effects setting. Most of the expositions of mixed-effects models I have seen frame the issue in terms of patients nested within doctors or students nested within schools. I am finding it hard to reconcile these examples with the country-level data that I am using and am hoping that the information I provide is clear enough that someone with a better understanding can help me resolve my confusion. The data and main variables that I am using are as follows:
Code:
* Example generated by -dataex-. For more info, type help dataex clear input str56 country float id double price_dispersion_use float TS_ce2 byte E double(coc unem) float lnGDPPC str3 region float region_id int year "Afghanistan" 1 15 . 4 -1.36474287509918 7.91 8.014661 "EMR" 3 2014 "Afghanistan" 1 . . 5 -1.54035270214081 10.092 7.994392 "EMR" 3 2016 "Afghanistan" 1 13.333333333333334 . 5 -1.50288057327271 11.131 7.974823 "EMR" 3 2018 "Afghanistan" 1 11.76470588235294 . 5 -1.49369978904724 11.71 7.928968 "EMR" 3 2020 "Afghanistan" 1 . . 5 -1.18377649784088 14.1 . "EMR" 3 2022 "Albania" 2 44.44444444444444 1 5 -.586141347885132 18.05 9.465752 "EUR" 4 2014 "Albania" 2 56.666666666666664 1 5 -.471469223499298 15.42 9.524819 "EUR" 4 2016 "Albania" 2 62.5 1 5 -.545840263366699 12.3 9.604934 "EUR" 4 2018 "Albania" 2 60.60606060606061 1 5 -.572924494743347 12.833 9.60202 "EUR" 4 2020 "Albania" 2 60 1 5 -.407875537872314 11.629 9.756207 "EUR" 4 2022 "Algeria" 3 33.33333333333333 6 4 -.61265641450882 10.21 9.511575 "AFR" 1 2014 "Algeria" 3 35.714285714285715 . 4 -.67341673374176 10.2 9.539472 "AFR" 1 2016 "Algeria" 3 15 . 5 -.658660113811493 12.145 9.525714 "AFR" 1 2018 "Algeria" 3 50 . 5 -.66646021604538 14.036 9.447598 "AFR" 1 2020 "Algeria" 3 48.57142857142857 5 5 -.637929856777191 12.491 9.4796715 "AFR" 1 2022 "Andorra" 4 72.85714285714285 6 2 1.22070860862732 3.4574213637138524 11.030043 "EUR" 4 2014 "Andorra" 4 72.85714285714285 6 2 1.15955591201782 3.4620623503549632 11.067958 "EUR" 4 2016 "Andorra" 4 77.77777777777777 1 2 1.17916560173035 3.4856245150448624 11.053652 "EUR" 4 2018 "Andorra" 4 68.44993141289439 1 2 1.26600527763367 3.5770777680298496 10.91981 "EUR" 4 2020 "Andorra" 4 69.86301369863014 1 2 1.27020359039307 3.890483345078273 11.056888 "EUR" 4 2022 "Angola" 5 75 . 2 -1.45779824256897 16.317 9.236285 "AFR" 1 2014 "Angola" 5 . . 2 -1.48333728313446 16.577 9.147498 "AFR" 1 2016 "Angola" 5 . . 4 -1.19925093650818 16.626 9.06262 "AFR" 1 2018 "Angola" 5 25 2 4 -.938672542572021 16.698 8.9309025 "AFR" 1 2020 "Angola" 5 25 . 4 -.601941287517548 14.478 8.910195 "AFR" 1 2022 "Antigua and Barbuda" 6 75 . 2 .634897768497467 3.4574213637138524 10.143725 "AMR" 2 2014 "Antigua and Barbuda" 6 50 . 2 .645558714866638 3.4620623503549632 10.18348 "AMR" 2 2016 "Antigua and Barbuda" 6 66.875 . 5 .236239701509476 3.4856245150448624 10.263378 "AMR" 2 2018 "Antigua and Barbuda" 6 62.05673758865249 . 5 .238533273339272 3.5770777680298496 10.073401 "AMR" 2 2020 "Antigua and Barbuda" 6 63.829787234042556 . 5 .310604453086853 3.890483345078273 10.23125 "AMR" 2 2022 "Argentina" 7 41.935483870967744 2 4 -.549443066120148 7.27 10.25563 "AMR" 2 2014 "Argentina" 7 37.75 3 4 -.298964887857437 8.085 10.240202 "AMR" 2 2016 "Argentina" 7 45.34920634920635 3 4 -.098668172955513 9.22 10.220944 "AMR" 2 2018 "Argentina" 7 18.726114649681527 3 4 -.16378065943718 11.46 10.076843 "AMR" 2 2020 "Argentina" 7 13.384615384615383 3 4 -.447030484676361 6.805 10.2083 "AMR" 2 2022 "Armenia" 8 30 6 2 -.565155386924744 11.989 9.488754 "EUR" 4 2014 "Armenia" 8 26.666666666666668 6 2 -.659123718738556 12.625 9.530623 "EUR" 4 2016 "Armenia" 8 42.857142857142854 3 2 -.408891350030899 13.21 9.663906 "EUR" 4 2018 "Armenia" 8 47.5 1 5 -.00343869999051094 12.18 9.673404 "EUR" 4 2020 "Armenia" 8 48.23529411764706 1 5 .0280352365225554 8.588 9.857456 "EUR" 4 2022 "Australia" 9 78.93318965517241 1 4 1.84946465492249 6.08 10.90798 "WPR" 6 2014 "Australia" 9 73.84341637010677 1 4 1.77200365066528 5.71 10.92716 "WPR" 6 2016 "Australia" 9 82.34126984126985 1 4 1.76737761497498 5.3 10.947303 "WPR" 6 2018 "Australia" 9 71.02189781021899 6 4 1.63295590877533 6.46 10.938417 "WPR" 6 2020 "Australia" 9 68.45524542829644 6 4 1.76448953151703 3.7 10.987324 "WPR" 6 2022 "Austria" 10 80.61224489795919 4 4 1.46674907207489 5.67 11.040983 "EUR" 4 2014 "Austria" 10 80 4 4 1.49696803092957 6.06 11.048753 "EUR" 4 2016 "Austria" 10 80 4 4 1.56836605072021 4.93 11.083235 "EUR" 4 2018 "Austria" 10 82.45614035087719 4 4 1.47778916358948 5.2 11.020405 "EUR" 4 2020 "Austria" 10 68.35820895522387 4 4 1.25861942768097 4.99 11.094935 "EUR" 4 2022 "Azerbaijan" 11 24 6 4 -1.02249026298523 4.91 9.938668 "EUR" 4 2014 "Azerbaijan" 11 56.25 1 4 -.852654457092285 5 9.894967 "EUR" 4 2016 "Azerbaijan" 11 23.076923076923077 6 5 -.852769494056702 4.9 9.893378 "EUR" 4 2018 "Azerbaijan" 11 47.05882352941177 6 5 -1.07708406448364 7.24 9.858809 "EUR" 4 2020 "Azerbaijan" 11 55.55555555555556 6 5 -1.04057228565216 5.65 9.953777 "EUR" 4 2022 "Bahamas" 12 48.658536585365916 1 2 1.30873775482178 . 10.381657 "AMR" 2 2014 "Bahamas" 12 40.22346368715088 1 2 1.06738793849945 12.7 10.366473 "AMR" 2 2016 "Bahamas" 12 . . 2 1.09553563594818 10 10.405302 "AMR" 2 2018 "Bahamas" 12 61.08949416342412 1 2 1.10620594024658 12.563 10.118558 "AMR" 2 2020 "Bahamas" 12 . 1 2 1.25618994235992 10.089 10.401076 "AMR" 2 2022 "Bahrain" 13 50 . 5 .273521840572357 1.147 10.890368 "EMR" 3 2014 "Bahrain" 13 33.33333333333333 . 5 -.0476647540926933 1.193 10.877423 "EMR" 3 2016 "Bahrain" 13 40 2 5 -.176231503486633 1.198 10.88669 "EMR" 3 2018 "Bahrain" 13 34.78260869565218 3 5 -.0935939401388168 1.786 10.867227 "EMR" 3 2020 "Bahrain" 13 58.333333333333336 3 5 .139385640621185 1.339 10.944588 "EMR" 3 2022 "Bangladesh" 14 15.789473684210526 . 4 -.892129957675934 4.405 8.543592 "SEA" 5 2014 "Bangladesh" 14 22.727272727272727 . 4 -.88687801361084 4.35 8.651562 "SEA" 5 2016 "Bangladesh" 14 33.33333333333333 . 4 -.926946818828583 4.373 8.761912 "SEA" 5 2018 "Bangladesh" 14 32.142857142857146 . 4 -1.00367724895477 5.316 8.849105 "SEA" 5 2020 "Bangladesh" 14 25 . 4 -1.0755273103714 4.271 8.96254 "SEA" 5 2022 "Barbados" 15 79.32850559578671 1 2 1.13345634937286 12.17 9.704554 "AMR" 2 2014 "Barbados" 15 81.25 1 2 1.2135511636734 8.25 9.7494 "AMR" 2 2016 "Barbados" 15 45.23433385992628 1 2 1.37191247940063 8.32 9.741538 "AMR" 2 2018 "Barbados" 15 . . 2 1.19406688213348 9.743 9.604329 "AMR" 2 2020 "Barbados" 15 78.84615384615384 1 2 1.28457343578339 8.501 9.700481 "AMR" 2 2022 "Belarus" 16 35.625 6 4 -.23470650613308 5.908 10.187328 "EUR" 4 2014 "Belarus" 16 31.914893617021278 6 4 -.224086627364159 5.84 10.12049 "EUR" 4 2016 "Belarus" 16 30.645161290322577 6 4 -.15480200946331 4.76 10.179738 "EUR" 4 2018 "Belarus" 16 25.71428571428572 6 4 -.133964225649834 4.05 10.193598 "EUR" 4 2020 "Belarus" 16 23.958333333333332 6 4 -.57967621088028 3.57 10.185905 "EUR" 4 2022 "Belgium" 17 80.82901554404145 4 4 1.51295030117035 8.52 10.96869 "EUR" 4 2014 "Belgium" 17 81.64556962025317 4 4 1.53148806095123 7.83 10.99063 "EUR" 4 2016 "Belgium" 17 83.33333333333334 4 4 1.42942035198212 5.95 11.016062 "EUR" 4 2018 "Belgium" 17 85.29411764705883 4 4 1.44595634937286 5.55 10.974466 "EUR" 4 2020 "Belgium" 17 72.5 4 4 1.49504864215851 5.56 11.05771 "EUR" 4 2022 "Belize" 18 41.66666666666667 . 2 -.159106820821762 8.24 9.4002905 "AMR" 2 2014 "Belize" 18 41.66666666666667 1 2 -.229891732335091 7 9.390294 "AMR" 2 2016 "Belize" 18 40 1 2 -.169436514377594 7.899 9.343116 "AMR" 2 2018 "Belize" 18 50 1 2 -.193349361419678 10.619 9.203805 "AMR" 2 2020 "Belize" 18 50.391644908616186 1 2 -.237028583884239 8.672 9.426018 "AMR" 2 2022 "Benin" 19 . 2 4 -.669143795967102 1.808 8.040519 "AFR" 1 2014 "Benin" 19 20 2 4 -.529120028018951 1.843 8.031984 "AFR" 1 2016 "Benin" 19 22.5 2 5 -.391388416290283 1.47 8.093288 "AFR" 1 2018 "Benin" 19 47.368421052631575 2 5 -.040327787399292 1.616 8.140294 "AFR" 1 2020 "Benin" 19 . 2 5 -.124255605041981 1.476 8.215443 "AFR" 1 2022 "Bhutan" 20 . . 4 1.30612897872925 2.63 9.345343 "SEA" 5 2014 "Bhutan" 20 . . 4 1.09102046489716 2.747 9.469749 "SEA" 5 2016 "Bhutan" 20 . . 4 1.59051811695099 3.35 9.533319 "SEA" 5 2018 "Bhutan" 20 . . 4 1.61823654174805 5.03 9.467918 "SEA" 5 2020 "Bhutan" 20 . 2 4 1.51425933837891 5.95 . "SEA" 5 2022 end label values TS_ce2 TS_ce2_l label def TS_ce2_l 1 "specific uniform", modify label def TS_ce2_l 2 "adv un NO min", modify label def TS_ce2_l 3 "adv uni WITH min", modify label def TS_ce2_l 4 "mixed uni NO min", modify label def TS_ce2_l 5 "mixed uni WITH min", modify label def TS_ce2_l 6 "specific tiered", modify label values region_id region_id_l label def region_id_l 1 "AFR", modify label def region_id_l 2 "AMR", modify label def region_id_l 3 "EMR", modify label def region_id_l 4 "EUR", modify label def region_id_l 5 "SEA", modify label def region_id_l 6 "WPR", modify
Outside of region dummies, which identify different continents, none of the variables I am interested are time-invariant by definition. So my starting point was to run a Hausman test on the model with the time-varying independent variables only, to see if fixed effects or random effects is the consistent estimator. My understanding is that if I use the fixed effects estimator, I am controlling for the region-specific effects, the effects just aren't estimable because they are absorbed into the fixed component. I ran the Hausman test (with no region dummies) as follows:
Code:
xi: xtreg price_dispersion_use i.TS_ce2 E coc unem lnGDPPC i.year, re cluster(id)
i.TS_ce2 _ITS_ce2_1-10 (naturally coded; _ITS_ce2_1 omitted)
i.year _Iyear_2014-2022 (naturally coded; _Iyear_2014 omitted)
Random-effects GLS regression Number of obs = 664
Group variable: id Number of groups = 165
R-squared: Obs per group:
Within = 0.0934 min = 1
Between = 0.5087 avg = 4.0
Overall = 0.4617 max = 5
Wald chi2(15) = 1676.20
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
(Std. err. adjusted for 165 clusters in id)
------------------------------------------------------------------------------
| Robust
price_disp~e | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_ITS_ce2_2 | -14.02557 3.794631 -3.70 0.000 -21.46291 -6.588226
_ITS_ce2_3 | -10.88748 4.686501 -2.32 0.020 -20.07285 -1.702108
_ITS_ce2_4 | 4.796852 3.110406 1.54 0.123 -1.299433 10.89314
_ITS_ce2_5 | -1.795415 4.094529 -0.44 0.661 -9.820545 6.229715
_ITS_ce2_6 | -9.561305 3.260805 -2.93 0.003 -15.95237 -3.170244
_ITS_ce2_8 | -11.07366 3.741402 -2.96 0.003 -18.40668 -3.740649
_ITS_ce2_10 | -21.19221 3.316523 -6.39 0.000 -27.69248 -14.69195
E | -.420992 1.1004 -0.38 0.702 -2.577737 1.735753
coc | 5.599903 1.50856 3.71 0.000 2.643179 8.556627
unem | -.3365144 .1896276 -1.77 0.076 -.7081776 .0351489
lnGDPPC | 4.062827 1.478944 2.75 0.006 1.16415 6.961504
_Iyear_2016 | 1.719148 1.237929 1.39 0.165 -.7071489 4.145445
_Iyear_2018 | 2.422449 1.561346 1.55 0.121 -.6377324 5.48263
_Iyear_2020 | 3.136992 1.555324 2.02 0.044 .0886123 6.185371
_Iyear_2022 | 2.683144 1.712374 1.57 0.117 -.6730476 6.039336
_cons | 21.95015 14.74566 1.49 0.137 -6.950821 50.85112
-------------+----------------------------------------------------------------
sigma_u | 12.909408
sigma_e | 11.049002
rho | .5771861 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. xtoverid
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(id)
Sargan-Hansen statistic 79.296 Chi-sq(15) P-value = 0.0000
Code:
oneway price_dispersion_use region_id, bonferroni
Analysis of variance
Source SS df MS F Prob > F
------------------------------------------------------------------------
Between groups 132305.334 5 26461.0667 65.51 0.0000
Within groups 324737.956 804 403.90293
------------------------------------------------------------------------
Total 457043.29 809 564.948442
Bartlett's equal-variances test: chi2(5) = 15.7086 Prob>chi2 = 0.008
Comparison of price_dispersion_use by group(region)
(Bonferroni)
Row Mean-|
Col Mean | AFR AMR EMR EUR SEA
---------+-------------------------------------------------------
AMR | 18.4197
| 0.000
|
EMR | -2.77116 -21.1908
| 1.000 0.000
|
EUR | 28.7939 10.3743 31.5651
| 0.000 0.000 0.000
|
SEA | -3.69121 -22.1109 -.920047 -32.4851
| 1.000 0.000 1.000 0.000
|
WPR | 18.4931 .073463 21.2643 -10.3008 22.1843
| 0.000 1.000 0.000 0.000 0.000
.
Code:
xtsum price_dispersion_use TS_ce2 E coc unem lnGDPPC year
Variable | Mean Std. dev. Min Max | Observations
-----------------+--------------------------------------------+----------------
price_~e overall | 54.1633 23.68788 4 100 | N = 821
between | 21.47537 7.836111 92.83242 | n = 192
within | 10.13382 16.45002 99.53367 | T-bar = 4.27604
| |
TS_ce2 overall | 3.118182 1.910972 1 10 | N = 770
between | 1.63939 1 7 | n = 176
within | .9785963 -1.131818 9.318182 | T-bar = 4.375
| |
E overall | 3.78359 1.078699 2 5 | N = 975
between | 1.002953 2 5 | n = 195
within | .4022524 1.38359 6.18359 | T = 5
| |
coc overall | -.0858656 .9881318 -1.936706 2.402744 | N = 963
between | .9822009 -1.780401 2.250184 | n = 193
within | .1345866 -.9270451 .4870617 | T-bar = 4.98964
| |
unem overall | 7.565258 5.748101 .11 28.84 | N = 960
between | 5.560955 .146 26.5954 | n = 193
within | 1.455914 .2532579 15.11326 | T-bar = 4.97409
| |
lnGDPPC overall | 9.485856 1.149466 6.753617 11.82817 | N = 918
between | 1.148124 6.810744 11.80229 | n = 185
within | .0820738 9.140171 10.27743 | T = 4.96216
| |
year overall | 2018 2.829879 2014 2022 | N = 975
between | 0 2018 2018 | n = 195
within | 2.829879 2014 2022 | T = 5
According to the authors, country was treated as the level 2 identifier, but the explanation on why and how that they provide is very thin. I have tried to implement it to understand how it is different to the RE regression with clustered standard errors. I used the the Stata help manual on multi-level mixed effects to execute the code for the multi-level/mixed model I show below, but I am no closer to understanding if treating the country (id) as the level 2 identifier in the multilevel model is a similar thing to clustering standard errors at the country level in the random effects regression. If these approaches are not doing the same thing, I am lost on what the difference between the two approaches below is and would greatly appreciate guidance on how 'treating observations as nested in countries in my dataset' is different to clustering standard errors at the country level in the non-hierachical model (xtreg, re cluster(id)).
Code:
xtreg price_dispersion_use i.TS_ce2 E coc unem lnGDPPC i.region_id i.year, re cluster(id)
Random-effects GLS regression Number of obs = 659
Group variable: id Number of groups = 164
R-squared: Obs per group:
Within = 0.0934 min = 1
Between = 0.5542 avg = 4.0
Overall = 0.4828 max = 5
Wald chi2(20) = 1788.60
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
(Std. err. adjusted for 164 clusters in id)
-------------------------------------------------------------------------------------
| Robust
price_dispersion_~e | Coefficient std. err. z P>|z| [95% conf. interval]
--------------------+----------------------------------------------------------------
TS_ce2 |
adv un NO min | -12.40899 3.996279 -3.11 0.002 -20.24155 -4.576423
adv uni WITH min | -8.338264 5.190598 -1.61 0.108 -18.51165 1.835122
mixed uni NO min | 4.808446 3.674408 1.31 0.191 -2.393261 12.01015
mixed uni WITH min | -1.597436 4.06049 -0.39 0.694 -9.55585 6.360977
specific tiered | -8.308067 3.384624 -2.45 0.014 -14.94181 -1.674326
tird adv WITH min | -8.823732 4.080642 -2.16 0.031 -16.82164 -.8258213
mxd trd WITH min | -19.90516 3.876494 -5.13 0.000 -27.50295 -12.30737
|
E | .2397692 1.121628 0.21 0.831 -1.958581 2.438119
coc | 5.508633 1.577934 3.49 0.000 2.41594 8.601326
unem | -.2725512 .1849838 -1.47 0.141 -.6351129 .0900104
lnGDPPC | 2.830525 1.64612 1.72 0.086 -.3958122 6.056861
|
region_id |
AMR | 8.763069 4.040908 2.17 0.030 .8430354 16.6831
EMR | -4.99006 5.627373 -0.89 0.375 -16.01951 6.039388
EUR | 6.148668 4.709602 1.31 0.192 -3.081982 15.37932
SEA | -6.283476 6.768348 -0.93 0.353 -19.54919 6.982243
WPR | 6.940622 5.036833 1.38 0.168 -2.931389 16.81263
|
year |
2016 | 1.931037 1.249372 1.55 0.122 -.5176866 4.379761
2018 | 2.56888 1.583531 1.62 0.105 -.534783 5.672544
2020 | 3.320599 1.587323 2.09 0.036 .2095038 6.431694
2022 | 3.046376 1.754632 1.74 0.083 -.3926392 6.485391
|
_cons | 26.26522 15.42733 1.70 0.089 -3.971789 56.50223
--------------------+----------------------------------------------------------------
sigma_u | 12.469835
sigma_e | 11.083854
rho | .55864045 (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
Code:
xtmixed price_dispersion_use i.TS_ce2 E coc unem lnGDPPC i.region_id i.year || id:
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2657.2751
Iteration 1: log likelihood = -2657.2751
Computing standard errors:
Mixed-effects ML regression Number of obs = 659
Group variable: id Number of groups = 164
Obs per group:
min = 1
avg = 4.0
max = 5
Wald chi2(20) = 267.79
Log likelihood = -2657.2751 Prob > chi2 = 0.0000
--------------------------------------------------------------------------------------
price_dispersion_use | Coefficient Std. err. z P>|z| [95% conf. interval]
---------------------+----------------------------------------------------------------
TS_ce2 |
adv un NO min | -12.49909 2.729109 -4.58 0.000 -17.84805 -7.150137
adv uni WITH min | -8.384119 3.86549 -2.17 0.030 -15.96034 -.8078988
mixed uni NO min | 5.015721 3.225648 1.55 0.120 -1.306432 11.33787
mixed uni WITH min | -1.830149 2.964851 -0.62 0.537 -7.64115 3.980852
specific tiered | -8.339198 2.554442 -3.26 0.001 -13.34581 -3.332584
tird adv WITH min | -8.622508 12.77176 -0.68 0.500 -33.65469 16.40967
mxd trd WITH min | -19.78572 5.321532 -3.72 0.000 -30.21573 -9.355705
|
E | .2622187 .8506864 0.31 0.758 -1.405096 1.929533
coc | 5.498374 1.530339 3.59 0.000 2.498964 8.497784
unem | -.2666603 .1678856 -1.59 0.112 -.59571 .0623893
lnGDPPC | 2.855437 1.628536 1.75 0.080 -.336435 6.047309
|
region_id |
AMR | 8.716485 3.774297 2.31 0.021 1.318999 16.11397
EMR | -5.048147 4.628445 -1.09 0.275 -14.11973 4.023439
EUR | 5.882058 4.439661 1.32 0.185 -2.819518 14.58363
SEA | -6.389057 6.032405 -1.06 0.290 -18.21235 5.43424
WPR | 6.907721 4.138175 1.67 0.095 -1.202953 15.01839
|
year |
2016 | 1.928479 1.407243 1.37 0.171 -.8296663 4.686624
2018 | 2.582868 1.459202 1.77 0.077 -.2771154 5.442851
2020 | 3.31731 1.456869 2.28 0.023 .4618988 6.172721
2022 | 3.048146 1.504786 2.03 0.043 .0988195 5.997472
|
_cons | 25.99444 14.52699 1.79 0.074 -2.477937 54.46682
--------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
id: Identity |
sd(_cons) | 11.90176 .8518652 10.34396 13.69417
-----------------------------+------------------------------------------------
sd(Residual) | 11.06389 .3550944 10.38936 11.78222
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 207.65 Prob >= chibar2 = 0.0000
Thank you!
Sam
References:
StataCorp. 2023. Stata 18 Multilevel Mixed-Effects Reference Manual. College Station, TX: Stata Press.
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