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Different results in Stata and MLwiN for random intercept linear regression
Posted: Wed Jul 15, 2015 2:17 pm
by kjetilwel
Dear all,
I am using runmlwin to estimate a simple 2-level linear random intercept model. While the Stata commands xtreg and xtmixed produce comparable results, the MlwiN results differ dramatically. Compared to the Stata results the fixed effects are similar, but the coefficients for the level2 variable is different and with a much larger standard error. Furthermore, while xtmixed report a variance of 0.19, the level2 variance in MLwiN is 55.99, which does not make sense! This is puzzling because the runmlwin help file says that the command I am using should be analogue to xtreg.
These are the commands I am running:
runmlwin depvar Level2var level1covars , level2(groupvar: cons) level1(PID: cons) nopause
xtreg depvar Level2var level1covars, i(groupvar)
xtmixed depvar Level2var level1covars || groupvar: , mle
Does anyone have an explanation?
Many thanks,
Kjetil van der Wel
Re: Different results in Stata and MLwiN for random intercept linear regression
Posted: Wed Jul 15, 2015 8:09 pm
by ChrisCharlton
By default xtmixed (and presumably xtreg) display random effects as standard deviations, whereas runmlwin reports these as variances. Both commands have options to change this.
Code: Select all
. use http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial, clear
Code: Select all
. xtreg normexam standlrt, i(school)
Random-effects GLS regression Number of obs = 4,059
Group variable: school Number of groups = 65
R-sq: Obs per group:
within = 0.3329 min = 2
between = 0.4794 avg = 62.4
overall = 0.3500 max = 198
Wald chi2(1) = 2042.68
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
standlrt | .5636107 .0124704 45.20 0.000 .5391692 .5880522
_cons | .0026355 .0388987 0.07 0.946 -.0736046 .0788756
-------------+----------------------------------------------------------------
sigma_u | .29374257
sigma_e | .75211121
rho | .13234743 (fraction of variance due to u_i)
------------------------------------------------------------------------------
Code: Select all
. xtmixed normexam standlrt || school: , mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -4678.6211
Iteration 1: log likelihood = -4678.6211
Computing standard errors:
Mixed-effects ML regression Number of obs = 4,059
Group variable: school Number of groups = 65
Obs per group:
min = 2
avg = 62.4
max = 198
Wald chi2(1) = 2042.57
Log likelihood = -4678.6211 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
standlrt | .5633711 .0124654 45.19 0.000 .5389394 .5878029
_cons | .0023907 .0400227 0.06 0.952 -.0760524 .0808338
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
school: Identity |
sd(_cons) | .3035282 .0305253 .2492271 .3696603
-----------------------------+------------------------------------------------
sd(Residual) | .7521508 .0084176 .7358322 .7688313
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 403.27 Prob >= chibar2 = 0.0000
Code: Select all
. runmlwin normexam cons standlrt, level2(school: cons) level1(student: cons) nopause sd
MLwiN 2.34 multilevel model Number of obs = 4059
Normal response model
Estimation algorithm: IGLS
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 65 2 62.4 198
-----------------------------------------------------------
Run time (seconds) = 2.09
Number of iterations = 4
Log likelihood = -4678.6211
Deviance = 9357.2422
------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | .0023908 .0400224 0.06 0.952 -.0760516 .0808332
standlrt | .5633712 .0124654 45.19 0.000 .5389394 .5878029
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: school |
sd(cons) | .3035252 .0298946 .2378215 .3573458
-----------------------------+------------------------------------------------
Level 1: student |
sd(cons) | .7521509 .0084149 .7354732 .7684668
------------------------------------------------------------------------------
Code: Select all
. xtmixed normexam standlrt || school: , mle var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -4678.6211
Iteration 1: log likelihood = -4678.6211
Computing standard errors:
Mixed-effects ML regression Number of obs = 4,059
Group variable: school Number of groups = 65
Obs per group:
min = 2
avg = 62.4
max = 198
Wald chi2(1) = 2042.57
Log likelihood = -4678.6211 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
standlrt | .5633711 .0124654 45.19 0.000 .5389394 .5878029
_cons | .0023907 .0400227 0.06 0.952 -.0760524 .0808338
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
school: Identity |
var(_cons) | .0921294 .0185306 .0621141 .1366488
-----------------------------+------------------------------------------------
var(Residual) | .5657309 .0126626 .5414491 .5911016
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 403.27 Prob >= chibar2 = 0.0000
Code: Select all
. runmlwin normexam cons standlrt, level2(school: cons) level1(student: cons) nopause
MLwiN 2.34 multilevel model Number of obs = 4059
Normal response model
Estimation algorithm: IGLS
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 65 2 62.4 198
-----------------------------------------------------------
Run time (seconds) = 2.40
Number of iterations = 4
Log likelihood = -4678.6211
Deviance = 9357.2422
------------------------------------------------------------------------------
normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | .0023908 .0400224 0.06 0.952 -.0760516 .0808332
standlrt | .5633712 .0124654 45.19 0.000 .5389394 .5878029
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: school |
var(cons) | .0921275 .0181475 .0565591 .127696
-----------------------------+------------------------------------------------
Level 1: student |
var(cons) | .565731 .0126585 .5409209 .5905412
------------------------------------------------------------------------------
Would this explain what you were seeing?
Re: Different results in Stata and MLwiN for random intercept linear regression
Posted: Thu Jul 16, 2015 9:49 am
by kjetilwel
Dear Chris,
Thanks for your reply. I did know about the difference in the xtmixed and MLwiN reporting. Your code did however help me anyway because it made me realise that I (embarrassingly) had overlooked that the constant term needs be included explicitly in the code!
Thanks,
Kjetil