st: xtmixed with nonrtolerance. What happens?

["Lukas Bösch" <L.Boesch@gmx.de>]

Dear Statalist community.

I am using Stata 10.0 and doing a mixed model analysis of export data.
After trying different options and always having trouble to get a propper output i finally found a way to get to my results. I however could not find any information about why it works and if it is allright. But let us first start with the problem:

1) This is the command i enter and the output stata creates:

xtmixed quantity year centforestarea2 centgdp2 centlandarea2 centpopulation2 || _all: R.country || _all: R.genus

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -77051.164  
Iteration 1:   log restricted-likelihood = -77046.704  
Iteration 2:   log restricted-likelihood = -77046.565  
Iteration 3:   log restricted-likelihood =   -77046.5  
Iteration 4:   log restricted-likelihood = -77046.468  (backed up)
Iteration 5:   log restricted-likelihood =  -77046.46  (backed up)
Iteration 6:   log restricted-likelihood = -77046.456  (backed up)
Iteration 7:   log restricted-likelihood = -77046.454  (backed up)
numerical derivatives are approximate
nearby values are missing
Iteration 8:   log restricted-likelihood = -77046.453  (backed up)
numerical derivatives are approximate
nearby values are missing
Hessian has become unstable or asymmetric

Mixed-effects REML regression                   Number of obs      =      6192
Group variable: _all                            Number of groups   =         1

                                                Obs per group: min =      6192
                                                               avg =    6192.0
                                                               max =      6192
                                                Wald chi2(5)       =      9.26
Log restricted-likelihood = -77051.164          Prob > chi2        =    0.0991
    quantity |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
        year |  -429.7599   215.8898    -1.99   0.047    -852.8961   -6.623654
centfores~a2 |  -9875.264   6631.861    -1.49   0.136    -22873.47    3122.945
    centgdp2 |  -2024.629   4138.469    -0.49   0.625    -10135.88    6086.621
centlandar~2 |  -52889.76   63817.96    -0.83   0.407    -177970.7    72191.13
centpopul~n2 |   22296.98   10234.72     2.18   0.029     2237.304    42356.66
       _cons |   895402.2   433369.4     2.07   0.039     46013.74     1744791

  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]

_all: Identity               |
               sd(R.country) |   313329.2          .             
_all: Identity               |
                 sd(R.genus) |   6757.304          .             
                sd(Residual) |   60169.26          .             
LR test vs. linear regression:       chi2(2) =  7810.42   Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference.
Warning: convergence not achieved; estimates are based on iterated EM

Obviously Stata has a problem and can't calculate the standard errors of the random factors.

2) With the option nonrtolerance it works however:

xtmixed quantity year centforestarea2 centgdp2 centlandarea2 centpopulation2 || _all: R.country || _all: R.genus, nonrtolerance

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log restricted-likelihood = -77051.164  
Iteration 1:   log restricted-likelihood = -77046.704  
Iteration 2:   log restricted-likelihood = -77046.565  
Iteration 3:   log restricted-likelihood =   -77046.5  
Iteration 4:   log restricted-likelihood = -77046.468  (backed up)
Iteration 5:   log restricted-likelihood =  -77046.46  (backed up)
Iteration 6:   log restricted-likelihood = -77046.456  (backed up)

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      6192
Group variable: _all                            Number of groups   =         1

                                                Obs per group: min =      6192
                                                               avg =    6192.0
                                                               max =      6192


                                                Wald chi2(5)       =      9.22
Log restricted-likelihood = -77046.456          Prob > chi2        =    0.1008
    quantity |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
        year |  -429.7645   216.4073    -1.99   0.047     -853.915   -5.614053
centfores~a2 |  -9885.307    6647.52    -1.49   0.137    -22914.21    3143.592
    centgdp2 |  -2021.312   4148.464    -0.49   0.626    -10152.15    6109.527
centlandar~2 |  -52859.75   63778.66    -0.83   0.407    -177863.6    72144.12
centpopul~n2 |   22276.96   10257.46     2.17   0.030     2172.715     42381.2
       _cons |   895338.1   434389.3     2.06   0.039     43950.68     1746726

  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
_all: Identity               |
               sd(R.country) |   313133.2    36075.6      249840.9    392459.4
_all: Identity               |
                 sd(R.genus) |   3440.288   1355.694      1589.157    7447.712
                sd(Residual) |   60315.87   545.9681      59255.23     61395.5
LR test vs. linear regression:       chi2(2) =  7819.83   Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.

Can someone explain to me why it works with nonrtolerance and tell me if these outputs are as reliable as if they were created without nonrtolerance. I searched in the stata help and on stata.com but could not find more information about this.

Kind regards

Lukas

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