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st: xtnbreg - same results after convergence at 9,000 iterations or limiting to 100 iterations


From   nick klein <nick.auxiliary@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: xtnbreg - same results after convergence at 9,000 iterations or limiting to 100 iterations
Date   Wed, 5 Jun 2013 19:09:40 -0400

Hi-

I have a question about -xtnbreg-

I’m curious if anyone has any thoughts on I am getting the same
results are when I limit the number of iterations to 100 and when I
let the model run until it converges (sometimes after 10,000
iterations).

I have a large panel dataset and am running a series of models. When I
let the models run overnight, the models converge after somewhere
between 50 and 15,000 iterations depending on the model. Looking at
the log, I can see that the models says "(not concave)" through almost
all the iterations but do eventually converge. And the model
coefficients seem to make sense.

However, yesterday I was testing out some my code and ran a model
where I limited the number of iterations to 100 (using the iterate(#)
option). The results for the model were exactly the same in both cases
(100 or >10,000 iterations). I can tell that in the steps right before
fitting the final model, the log likelihood for each iteration become
very similar (I assume if I did a trace, I'd see that they are exactly
the same) - i'm just not sure why this might be or what it means for
my analysis.

Anyone have thoughts on why this might be?

Below are a few of the relevant commands and then part of each log
file - showing the beginning and final iterations for the xtnbreg
model (first without limiting the number of iterations).

-Thanks
Nick


--------------

. xtset
       panel variable:  FIPSblock (strongly balanced)
        time variable:  Year, 1991 to 2008
                delta:  1 unit

. xtsum Firm_Births

Variable         |      Mean   Std. Dev.       Min        Max |    Observations
-----------------+--------------------------------------------+----------------
Firm_B~s overall |  .3413659   2.135944          0        141 |     N =  504072
         between |             1.808005          0   69.05556 |     n =   28004
         within  |             1.137315  -59.71419   94.73025 |     T =      18


. xtnbreg Firm_Births $base_vars $spatial_vars $demographic_vars
$year_vars, re exposure(Acres)

Fitting negative binomial (constant dispersion) model:

Iteration 0:   log likelihood =  -51795942  (not concave)
Iteration 1:   log likelihood =  -49724759  (not concave)
Iteration 2:   log likelihood =  -48730264  (not concave)
Iteration 3:   log likelihood =  -47170895  (not concave)
Iteration 4:   log likelihood =  -45963320  (not concave)
Iteration 5:   log likelihood =  -45021992  (not concave)

....

Iteration 9255:log likelihood = -470774.97  (not concave)
Iteration 9256:log likelihood = -470671.29  (not concave)
Iteration 9257:log likelihood = -470567.37
Iteration 9258:log likelihood = -402031.39  (backed up)
Iteration 9259:log likelihood =  -388353.2
Iteration 9260:log likelihood =  -387803.5
Iteration 9261:log likelihood = -387800.57
Iteration 9262:log likelihood = -387800.57

Iteration 0:   log likelihood = -475132.13
Iteration 1:   log likelihood = -458154.04
Iteration 2:   log likelihood = -457787.12
Iteration 3:   log likelihood =  -457787.1

Iteration 0:   log likelihood = -337007.31
Iteration 1:   log likelihood = -305214.12
Iteration 2:   log likelihood = -303965.91
Iteration 3:   log likelihood = -303963.67
Iteration 4:   log likelihood = -303963.67

Fitting full model:

Iteration 0:   log likelihood = -261858.51
Iteration 1:   log likelihood = -240203.89
Iteration 2:   log likelihood = -238845.87
Iteration 3:   log likelihood = -238800.18
Iteration 4:   log likelihood = -238800.08
Iteration 5:   log likelihood = -238800.08

Random-effects negative binomial regression     Number of obs      =    504072
Group variable: FIPSblock                       Number of groups   =     28004

Random effects u_i ~ Beta                       Obs per group: min =        18
                                                               avg =      18.0
                                                               max =        18

                                                Wald chi2(34)      =  57551.00
Log likelihood  = -238800.08                    Prob > chi2        =    0.0000

---------------------------------------------------------------------------------------------
                Firm_Births |      Coef.   Std. Err.      z    P>|z|
  [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
...
                      _cons |  -2.502535   .0503268   -49.73   0.000
 -2.601174   -2.403897
                  ln(Acres) |          1  (exposure)
----------------------------+----------------------------------------------------------------
                      /ln_r |   2.151578   .0221937
  2.108079    2.195077
                      /ln_s |  -.3551327   .0117288
 -.3781207   -.3321448
----------------------------+----------------------------------------------------------------
                          r |   8.598419   .1908308
  8.232415    8.980694
                          s |   .7010804   .0082228
  .6851478    .7173835
---------------------------------------------------------------------------------------------
Likelihood-ratio test vs. pooled: chibar2(01) =  1.3e+05 Prob>=chibar2 = 0.000
(est1 stored)

. xtnbreg Firm_Births $base_vars $spatial_vars $demographic_vars
$year_vars, re exposure(Acres) iterate(100)

Fitting negative binomial (constant dispersion) model:

Iteration 0:   log likelihood =  -51795942  (not concave)
Iteration 1:   log likelihood =  -49724759  (not concave)
Iteration 2:   log likelihood =  -48730264  (not concave)
Iteration 3:   log likelihood =  -47170895  (not concave)
Iteration 4:   log likelihood =  -45963320  (not concave)
Iteration 5:   log likelihood =  -45021992  (not concave)

....

Iteration 97:  log likelihood = -6911325.4  (not concave)
Iteration 98:  log likelihood = -6837625.2  (not concave)
Iteration 99:  log likelihood = -6480527.6  (not concave)
Iteration 100: log likelihood = -6375502.1  (not concave)
convergence not achieved

Iteration 0:   log likelihood = -475132.13
Iteration 1:   log likelihood = -458154.04
Iteration 2:   log likelihood = -457787.12
Iteration 3:   log likelihood =  -457787.1

Iteration 0:   log likelihood =  -457787.1  (not concave)
Iteration 1:   log likelihood = -447149.68  (not concave)
Iteration 2:   log likelihood = -433018.99
Iteration 3:   log likelihood = -374195.22
Iteration 4:   log likelihood = -343626.28
Iteration 5:   log likelihood = -325391.13
Iteration 6:   log likelihood = -308563.02
Iteration 7:   log likelihood = -304292.41
Iteration 8:   log likelihood = -303973.76
Iteration 9:   log likelihood = -303963.67
Iteration 10:  log likelihood = -303963.67

Fitting full model:

Iteration 0:   log likelihood = -261858.51
Iteration 1:   log likelihood = -240203.89
Iteration 2:   log likelihood = -238845.87
Iteration 3:   log likelihood = -238800.18
Iteration 4:   log likelihood = -238800.08
Iteration 5:   log likelihood = -238800.08

Random-effects negative binomial regression     Number of obs      =    504072
Group variable: FIPSblock                       Number of groups   =     28004

Random effects u_i ~ Beta                       Obs per group: min =        18
                                                               avg =      18.0
                                                               max =        18

                                                Wald chi2(34)      =  57551.00
Log likelihood  = -238800.08                    Prob > chi2        =    0.0000

---------------------------------------------------------------------------------------------
                Firm_Births |      Coef.   Std. Err.      z    P>|z|
  [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
...
                      _cons |  -2.502535   .0503268   -49.73   0.000
 -2.601174   -2.403897
                  ln(Acres) |          1  (exposure)
----------------------------+----------------------------------------------------------------
                      /ln_r |   2.151578   .0221937
  2.108079    2.195077
                      /ln_s |  -.3551327   .0117288
 -.3781207   -.3321448
----------------------------+----------------------------------------------------------------
                          r |   8.598419   .1908308
  8.232415    8.980694
                          s |   .7010804   .0082228
  .6851478    .7173835
---------------------------------------------------------------------------------------------
Likelihood-ratio test vs. pooled: chibar2(01) =  1.3e+05 Prob>=chibar2 = 0.000
(est1 stored)

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