Re: st: gllamm, xtmixed, and level-2 standard errors

[Stas Kolenikov <skolenik@gmail.com>]

What if you run -xtreg, re- or -xtreg, mle-? They will give you the
same model, too.

On Tue, Nov 16, 2010 at 4:27 PM, Trey Causey <tcausey@uw.edu> wrote:
> 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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>



-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
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