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# Re: st: xtmixed with nonrtolerance. What happens?

 From "Lukas Bösch" To statalist@hsphsun2.harvard.edu Subject Re: st: xtmixed with nonrtolerance. What happens? Date Fri, 24 Jun 2011 11:53:58 +0200

```Thank you for your help. I am writing my diploma thesis about the influence of socioeconomic factors on the export of wild species. It took me a long time to recode and transform the original dataset, which comprised about 1 million observations, to a final compact dataset and i did not expect to spend a lot of time with the calculation of the models. But as always, something doesn't work...The work is due end of july and i really didnt expect to take two weeks just to calculate the modells.

1) Concerning the missings, i took care to delete all data i don't have the complete time series for. This means that i had to drop from 130 countries over a 20 years period to 40 countries over a 15 years period. On the other hand, there are deffinitely no missing values.

2) It is the first time i am dealing with mixed modells, so i am not sure about the terminology and the interpretation of the randome effects. In my opinion the structure is not hierarchic as no random effects is nested in another one, like in the always cited example: Students (level one) are nested in classes (level two) and classes nested in schools (level three). This is how i understand the hierarchic structure. In my dataset however, genus is not nested in countries, as the same genus can be exportet by many countries, which is the case for a lot of genus like falco, ursus or crocodylus. This is why i defined the random effects the following way: || _all: R.country || _all: R.genus

3) The dependent variable contains decimals because i had to recode and transform it. In the original dataset, the export was classified in species, categories and units. One countrie can export, products of brown bears, grizzly bears, panda bears and so on (13756 species)... Then the country can export living bears, dead bears, bear fur, bear bones, bear gall, bear teeth and so on (89 categories)... Finally the country can export kg, m, g, units and so on of a given product (24 units). This means that canada exports about 178 different bear products a year in the original dataset. I weighted, deleted and transformed the data, according to theoretical, practical and pragmactic thoughts in order to get one exported product for each genus. In the final dataset, canada exports one bear product a year.

4) If every country had one export a year, then there would be 640 observations. Some countries, however, have many exports a year. For example, Indonesia has 70 exports a year. It exports 70 different genus a year. If i would sum up those 70 export to one export, the whole modell would be much easier, but i thought the mixed model approach was conceived for this kind of problems.

5) It is thrue that there are a lot of zeroes in my dependent variable. In the original dataset, there were so many, that i knew this would become a problem. After transforming the dataset to my final version there were still a lot of zeroes, in this case, 1 stands for zeroes.

null |      Freq.     Percent        Cum.
------------+-----------------------------------
0 |      9,501       24.32       24.32
1 |     29,571       75.68      100.00
------------+-----------------------------------
Total |     39,072      100.00

This is why i decided to analyze only the genus where an export took part in half of the years:

null |      Freq.     Percent        Cum.
------------+-----------------------------------
0 |      4,682       75.61       75.61
1 |      1,510       24.39      100.00
------------+-----------------------------------
Total |      6,192      100.00

null1 |      Freq.     Percent        Cum.
------------+-----------------------------------
0 |      1,216       19.64       19.64
1 |        512        8.27       27.91
2 |        384        6.20       34.11
3 |        608        9.82       43.93
4 |        640       10.34       54.26
5 |        720       11.63       65.89
6 |        688       11.11       77.00
7 |        624       10.08       87.08
8 |        800       12.92      100.00
------------+-----------------------------------
Total |      6,192      100.00

In 1216 cases the genus was exported every year, in 512 cases the genus was not exported in one year, and so on. But there are still a lot of zeros and some really high figures:

. sum quantity

Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
quantity |      6192    8545.829    116704.3          0    4019264

I am going to try the poisson regression if this is better to analyze
data with lot of zeroes. I didn't expect however that the final data still had to many zeroes.

Kind regards

Lukas

-------- Original-Nachricht --------
> Datum: Thu, 23 Jun 2011 22:56:54 -0400
> Von: Joerg Luedicke <joerg.luedicke@gmail.com>
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: xtmixed with nonrtolerance. What happens?

> A couple of points:
>
> 1) You surely assume a hierarchical structure: you have observations
> at Level-1, cross-classified across 2 Level-2 factors.
>
> 2) It is still not clear what your unit of analysis is? What are those
> 6192? They cannot be yearly observations within country as that would
> only result in 640 observations.
>
> 3) If your dependent variable is supposed to represent the number of
> exports (in a given year?), why does it contain decimals and not only
> integers?
>
> 4) Have you ever spent some time looking at the distribution of your
> dependent variable? When you standardize it, it ranges from .07
> standard deviations below the mean to 34 standard deviations above the
> mean!! My guess is that you are looking at some crazy distribution
> like this:
>
> gen x=rgamma(.001,100000)
>
> with some very high values but with the majority of values being zeros
> or close to zero. I suspect that there is either something wrong with
> this variable or with your entire data set-up.
>
> 5) If it turns out that everything in your data is correct, then
> trying to fit a linear model to these data is certainly the wrong
> approach.
>
>
> Joerg
>
>
> On Thu, Jun 23, 2011 at 4:40 PM, "Lukas Bösch" <L.Boesch@gmx.de> wrote:
> > Because i didnt transform the year and the export, named as quantity,
> into z-scores they kept their original names in the first models.
> > I just did the transformation and ran the model again, but it still
> doesnt converge, however seems to work a little better.
> >
> > . xtmixed centquantity2 centyear2 centforestarea2 centgdp2 centlandarea2
> centpopulation2|| _all: R.country || _all: R.genus
> >
> > Performing EM optimization:
> >
> > Iteration 0:   log restricted-likelihood = -4875.1075
> > Iteration 1:   log restricted-likelihood = -4870.6476
> > Iteration 2:   log restricted-likelihood = -4870.5095
> > Iteration 3:   log restricted-likelihood = -4870.4438
> > Iteration 4:   log restricted-likelihood = -4870.4118  (backed up)
> > Iteration 5:   log restricted-likelihood = -4870.4039  (backed up)
> > Iteration 6:   log restricted-likelihood = -4870.3999  (backed up)
> > Iteration 7:   log restricted-likelihood = -4870.3979  (backed up)
> > Iteration 8:   log restricted-likelihood = -4870.3969  (backed up)
> > Iteration 9:   log restricted-likelihood = -4870.3967  (backed up)
> > numerical derivatives are approximate
> > nearby values are missing
> > Iteration 10:  log restricted-likelihood = -4870.3966  (backed up)
> > numerical derivatives are approximate
> > nearby values are missing
> > Iteration 11:  log restricted-likelihood = -4870.3966  (backed up)
> > numerical derivatives are approximate
> > nearby values are missing
> > 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 = -4875.1075          Prob > chi2
>    =    0.0991
> >
> > centquanti~2 |      Coef.   Std. Err.      z    P>|z|
> [95% Conf. Interval]
> >   centyear2 |  -.0169763    .008528    -1.99   0.047
> -.033691   -.0002616
> > centfores~a2 |  -.0846178   .0568262    -1.49   0.136
>  -.1959951    .0267595
> >    centgdp2 |  -.0173484   .0354612    -0.49   0.625
>  -.0868509    .0521542
> > centlandar~2 |  -.4531947   .5468347    -0.83   0.407
>  -1.524971    .6185816
> > centpopul~n2 |   .1910553   .0876979     2.18   0.029
> .0191707      .36294
> >       _cons |   .2434439   .4596746     0.53   0.596
>  -.6575018     1.14439
> >
> >  Random-effects Parameters  |   Estimate   Std. Err.     [95%
> Conf. Interval]
> > _all: Identity               |
> >               sd(R.country) |   2.684813          .
> > _all: Identity               |
> >                 sd(R.genus) |   .0579011          .
> >                sd(Residual) |   .5155702          .
> > 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
> >
> >
> >
> > Here the summarize output of all the variables:
> >
> > . sum centquantity2
> >
> >    Variable |       Obs        Mean    Std. Dev.       Min
>        Max
> > -------------+--------------------------------------------------------
> > centquanti~2 |      6192    2.17e-09           1  -.0732263
>    34.3665
> >
> > . sum centyear2
> >
> >    Variable |       Obs        Mean    Std. Dev.       Min
>        Max
> > -------------+--------------------------------------------------------
> >   centyear2 |      6192           0    1.000024  -1.626886
>   1.626886
> >
> > . sum centforestarea2
> >
> >    Variable |       Obs        Mean    Std. Dev.       Min
>        Max
> > -------------+--------------------------------------------------------
> > centfores~a2 |      6192   -.0043667     1.00682 -2.396995
> 2.746216
> >
> > . sum centgdp2
> >
> >    Variable |       Obs        Mean    Std. Dev.       Min
>        Max
> > -------------+--------------------------------------------------------
> >    centgdp2 |      6192   -.0835699    .8318088  -.3333735
> 5.257175
> >
> > . sum centlandarea2
> >
> >    Variable |       Obs        Mean    Std. Dev.       Min
>        Max
> > -------------+--------------------------------------------------------
> > centlandar~2 |      6192   -.0336882    .9528875  -.6987395
> 2.490177
> >
> > . sum centpopulation2
> >
> >    Variable |       Obs        Mean    Std. Dev.       Min
>        Max
> > -------------+--------------------------------------------------------
> > centpopul~n2 |      6192   -.0018452    1.069818  -.6711841
> 8.741787
> >
> > At last a short extract of the dataset, with the original quantity, in
> order to see the structure:
> >
> > quantity country genus   centyear2   centagriculturalland2
> > 0        USA    Tursiops 1.19305        .6379885
> > 0        USA    Tursiops 1.409968       .6239355
> > 6.08     USA    Tursiops 1.626886       .6126072
> > 40.29    USA    Ursus   -1.626886       .7022238
> > 65.375   USA    Ursus   -1.409968       .7022238
> > 140.255  USA    Ursus   -1.19305        .6926397
> >
> > In total 40 countries, 213 genus and 21 independendt variables over a
> period of 16 years with 6192 observations. As there is no hirarchical
> structure, there are no different levels. There is one level for the quantity
> exported and two randome effects at this level, the country and genus.
> > After having transformed the quantity to z-scores, would you still
> recommend dividing it by 100k?
> >
> > Thank you
> >
> > Lukas
> >
> >
> > -------- Original-Nachricht --------
> >> Datum: Thu, 23 Jun 2011 14:41:44 -0400
> >> Von: Joerg Luedicke <joerg.luedicke@gmail.com>
> >> An: statalist@hsphsun2.harvard.edu
> >> Betreff: Re: st: xtmixed with nonrtolerance. What happens?
> >
> >> k stands for 1000 (as in kb=1000 bytes, for instance). What are your
> >> Level 1 observations (i.e., the  6192)? If only 72 bears were exported
> >> from the US in a given year then figures in the ballpark of hundreds
> >> of thousands appear fairly high to me?
> >>
> >> J.
> >>
> >> On Thu, Jun 23, 2011 at 2:14 PM, "Lukas Bösch" <L.Boesch@gmx.de>
> wrote:
> >> > In my opinion the scales dont differ wildly.
> >> > I am not a statistician though, so maybe you have a different
> opinion.
> >> >
> >> >
> >> > . sum centgdp2
> >> >
> >> >    Variable |       Obs        Mean    Std. Dev.
> Min
> >>        Max
> >> >
> -------------+--------------------------------------------------------
> >> >    centgdp2 |      6192   -.0835699    .8318088  -.3333735
> >> 5.257175
> >> >
> >> > . sum centlandarea2
> >> >
> >> >    Variable |       Obs        Mean    Std. Dev.
> Min
> >>        Max
> >> >
> -------------+--------------------------------------------------------
> >> > centlandar~2 |      6192   -.0336882    .9528875  -.6987395
> >> 2.490177
> >> >
> >> > . sum centpopulation2
> >> >
> >> >    Variable |       Obs        Mean    Std. Dev.
> Min
> >>        Max
> >> >
> -------------+--------------------------------------------------------
> >> > centpopul~n2 |      6192   -.0018452    1.069818  -.6711841
> >> 8.741787
> >> >
> >> > . sum centyear2
> >> >
> >> >    Variable |       Obs        Mean    Std. Dev.
> Min
> >>        Max
> >> >
> -------------+--------------------------------------------------------
> >> >   centyear2 |      6192           0    1.000024
>  -1.626886
> >>   1.626886
> >> >
> >> > . sum centforestarea2
> >> >
> >> >    Variable |       Obs        Mean    Std. Dev.
> Min
> >>        Max
> >> >
> -------------+--------------------------------------------------------
> >> > centfores~a2 |      6192   -.0043667     1.00682 -2.396995
> >> 2.746216
> >> >
> >> > The dependent variable is export. The export of wild animal and plant
> >> products from one country to the rest of the world. For example: US
> export of
> >> Bears in 1992: 72.
> >> > Because I cannot sum up the export of different species to one export
> >> figure, obviously bears and pearls are not the same, i have to deal
> with
> >> those mixed models. Socioeconomic factors are set as fixed effects and
> the
> >> genus and countries as the variable effects.
> >> > As one species can be exported by different countries, the data is
> not
> >> hierarchic and country and genus are cross-classified. Or i think this
> is
> >> what it means. Two random effects at the same level for all
> observations.
> >> Joerge, can you explain what you mean with dividing by 100k? What does
> the k
> >> stand for?
> >> >
> >> > Thank you
> >> >
> >> > Lukas
> >> >
> >> > mixed modells-------- Original-Nachricht --------
> >> >> Datum: Thu, 23 Jun 2011 09:47:55 -0400
> >> >> Von: Joerg Luedicke <joerg.luedicke@gmail.com>
> >> >> An: statalist@hsphsun2.harvard.edu
> >> >> Betreff: Re: st: xtmixed with nonrtolerance. What happens?
> >> >
> >> >> Your model did not converge using the default convergence criteria
> and
> >> >> with -nonrtolerance- you just turned off that default criteria
> >> >> (though, I do not know what criteria is used instead?). However, you
> >> >> should be very cautious with regard to the results.
> >> >>
> >> >> What is your dependent variable? From your output I gather that its
> >> >> predicted mean is roughly 900k at average values of your covariates.
> >> >> Maybe you should transform your dependent variable and fit the model
> >> >> again (e.g., dividing it by 100k).
> >> >>
> >> >> A question in regards to your random effects: are -country- and
> >> >> -genus- cross-classified?
> >> >>
> >> >> J.
> >> >>
> >> >> On Thu, Jun 23, 2011 at 6:21 AM, "Lukas Bösch" <L.Boesch@gmx.de>
> >> wrote:
> >> >> > I transformed the data to z-scores (score-mean/stdeviation) before
> >> doing
> >> >> the regression.
> >> >> > What do you mean with differing scales? I have either percents,
> for
> >> >> example % forest area, or absolute figures, for example land area,
> in
> >> my
> >> >> dataset, but they are all transformed and should therefore be
> uniform.
> >> >> > What about nonrtolerance?
> >> >> >
> >> >> > Thank you
> >> >> >
> >> >> > Lukas
> >> >> >
> >> >> > -------- Original-Nachricht --------
> >> >> >> Datum: Wed, 22 Jun 2011 18:48:22 -0400
> >> >> >> Von: Stas Kolenikov <skolenik@gmail.com>
> >> >> >> An: statalist@hsphsun2.harvard.edu
> >> >> >> Betreff: Re: st: xtmixed with nonrtolerance. What happens?
> >> >> >
> >> >> >> It looks like you have data with wildly differing scales. I
> >> understand
> >> >> >> that you need to interpret the results in the original scales,
> but
> >> >> >> maybe you could rescale your variables so that all of your
> >> >> >> coefficients would be about 1. Whether that will help convergence
> is
> >> >> >> anybody's telling, of course, but usually differences in the
> scales
> >> >> >> (and hence coefficients) of the order of 1e3-1e4 are detrimental
> to
> >> >> >> numeric convergence.
> >> >> >>
> >> >> >> On Wed, Jun 22, 2011 at 4:33 PM, "Lukas Bösch" <L.Boesch@gmx.de>
> >> >> wrote:
> >> >> >> > 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
> >> >> >> >
> >> >> >> > 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
> >> >> >> >
> >> >> >> > Kind regards
> >> >> >> >
> >> >> >> > Lukas
> >> >> >> >
> >> >> >> > --
> >> >> >> > NEU: FreePhone - kostenlos mobil telefonieren!
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> >> >> >> > *   http://www.stata.com/support/statalist/faq
> >> >> >> > *   http://www.ats.ucla.edu/stat/stata/
> >> >> >> >
> >> >> >>
> >> >> >>
> >> >> >>
> >> >> >> --
> >> >> >> Stas Kolenikov, also found at http://stas.kolenikov.name
> >> >> >> Small print: I use this email account for mailing lists only.
> >> >> >>
> >> >> >> *
> >> >> >> *   For searches and help try:
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> >> >> >
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> >> >> >
> >> >>
> >> >> *
> >> >> *   For searches and help try:
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```