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st: gllamm, xtmixed, and level-2 standard errors
From
Trey Causey <[email protected]>
To
[email protected]
Subject
st: gllamm, xtmixed, and level-2 standard errors
Date
Tue, 16 Nov 2010 14:27:02 -0800
Greetings all. I am estimating a two-level, random-effects linear
model. I know that gllamm is not the most computationally efficient
option for this, but I am running into some very weird problems. I
have ~21,000 individuals nested in 16 countries. I have 9
individual-level predictors (listed as ind1-9) and 2 country-level
predictors (listed as c1 and c2). When I estimate the model using
gllamm, here are my results:
. gllamm DV ind1 ind2 ind3 ind4 ind5 ind6 ind7 ind8 ind9 c1 c2,i(id)
adapt nip(16)
Running adaptive quadrature
Iteration 0: log likelihood = -22865.024
Iteration 1: log likelihood = -22841.735
Iteration 2: log likelihood = -22807.82
Iteration 3: log likelihood = -22797.118
Iteration 4: log likelihood = -22794.274
Iteration 5: log likelihood = -22792.672
Iteration 6: log likelihood = -22791.582
Iteration 7: log likelihood = -22791.557
Iteration 8: log likelihood = -22791.428
Iteration 9: log likelihood = -22791.426
Adaptive quadrature has converged, running Newton-Raphson
Iteration 0: log likelihood = -22791.426 (not concave)
Iteration 1: log likelihood = -22791.426 (not concave)
Iteration 2: log likelihood = -22789.86
Iteration 3: log likelihood = -22789.371
Iteration 4: log likelihood = -22788.767
Iteration 5: log likelihood = -22788.613
Iteration 6: log likelihood = -22788.604
Iteration 7: log likelihood = -22788.604
number of level 1 units = 21360
number of level 2 units = 16
Condition Number = 433.81863
gllamm model
log likelihood = -22788.604
------------------------------------------------------------------------------
DV | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ind1 | -.0020515 .000392 -5.23 0.000 -.0028198 -.0012833
ind2 | -.3839988 .010841 -35.42 0.000 -.4052468 -.3627508
ind3 | -.079134 .0113476 -6.97 0.000 -.1013749 -.0568931
ind4 | .0800358 .0109386 7.32 0.000 .0585966 .101475
ind5 | .0468417 .0048978 9.56 0.000 .0372423
.0564411
ind6 | .1685022 .0149735 11.25 0.000 .1391546 .1978497
ind7 | -.2057474 .0171485 -12.00 0.000 -.2393579 -.1721368
ind8 | -.093775 .0094251 -9.95 0.000 -.1122479 -.0753021
ind9 | -.0080367 .0021554 -3.73 0.000 -.0122613 -.0038122
c1 | .762577 .0802034 9.51 0.000 .6053813 .9197727
c2 | .1763846 .0664327 2.66 0.008 .0461789 .3065903
_cons | 1.265279 .1023452 12.36 0.000 1.064686 1.465872
------------------------------------------------------------------------------
Variance at level 1
------------------------------------------------------------------------------
.49269203 (.00476915)
Variances and covariances of random effects
------------------------------------------------------------------------------
***level 2 (id)
var(1): .09866295 (.01101541)
------------------------------------------------------------------------------
When I estimate the model using xtmixed or xtreg, the output is
essentially the same until I get to the country-level predictors; the
coefficients are slightly different and the standard errors are
approximately *ten* times smaller:
. xtmixed DV ind1 ind2 ind3 ind4 ind5 ind6 ind7 ind8 ind9 c1 c2 || id:,mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -22785.965
Iteration 1: log likelihood = -22785.965
Computing standard errors:
Mixed-effects ML regression Number of obs = 21360
Group variable: id Number of groups = 16
Obs per group: min = 730
avg = 1335.0
max = 2875
Wald chi2(11) = 2296.06
Log likelihood = -22785.965 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
DV | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ind1 | -.0020472 .0003917 -5.23 0.000 -.002815 -.0012794
ind2 | -.3840113 .0108422 -35.42 0.000 -.4052615 -.362761
ind3 | -.0790874 .0113578 -6.96 0.000 -.1013483 -.0568264
ind4 | .0799408 .0109411 7.31 0.000 .0584966 .101385
ind5 | .0468955 .0048961 9.58 0.000 .0372994 .0564916
ind6 | .1686695 .0149734 11.26 0.000 .1393222 .1980167
ind7 | -.2054921 .0172501 -11.91 0.000 -.2393018 -.1716824
ind8 | -.0941011 .0093698 -10.04 0.000 -.1124655 -.0757367
ind9 | -.0079976 .0021584 -3.71 0.000 -.0122279 -.0037672
c1 | .6718781 .2659761 2.53 0.012 .1505744 1.193182
c2 | .1812668 .1083347 1.67 0.094 -.0310652 .3935988
_cons | 1.306302 .2079643 6.28 0.000 .8986998 1.713905
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity |
sd(_cons) | .2033876 .0363049 .1433454 .2885792
-----------------------------+------------------------------------------------
sd(Residual) | .7019342 .0033974 .695307 .7086246
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 1684.50 Prob >= chibar2 = 0.0000
This is obviously a big problem for establishing significance. I have
read previous threads about this problem with xtlogit but have not
seen it mentioned for linear models nor I have a seen a solution. It
is not immediately clear to me why the estimates or standard errors
should differ at all -- as Rabe-Hesketh and Skrondal say in their
book, gllamm is not as computationally efficient for linear models but
the results should be essentially the same. I have replicated this in
Stata 10 and Stata 11.
Thank you very much.
Trey
-----
Trey Causey
Department of Sociology
University of Washington
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