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st: LogL of null model in zinb and zip


From   Garry Anderson <g.anderson@unimelb.edu.au>
To   statalist@hsphsun2.harvard.edu
Subject   st: LogL of null model in zinb and zip
Date   Thu, 20 Dec 2007 21:36:54 +1100

Dear Statalist,

I have a query about the calculation of the log-likelihood for the null
model of a zero-inflated negative binomial or zero-inflated Poisson.

I would have expected the null model to be
-webuse fish-
-zinb count ,inf(_cons)-

However, it appears that the null model is
-zinb count ,inf(varlist)-
where varlist is a floating list of variables depending on what
variables are in the model at the time of estimating the two models that
one wishes to compare.

When two models are compared with a likelihood ratio test and they
differ only in the inflate part of the model, the warning message is

. lrtest full .
log likelihood of null models differ: -442.663 vs. -461.7623
r(498);

. lrtest full .,force stat

Likelihood-ratio test                                  LR chi2(1)  =
70.19
(Assumption: . nested in full)                         Prob > chi2 =
0.0000

------------------------------------------------------------------------
-----
       Model |    Obs    ll(null)   ll(model)     df          AIC
BIC
-------------+----------------------------------------------------------
-----
           . |    250   -461.7623   -436.6451      6     885.2902
906.419
        full |    250    -442.663   -401.5478      7     817.0955
841.7457
------------------------------------------------------------------------
-----

The question is why is a ll(null) calculated that differs between the
models?
I think calculation of a null model without any variables in the count
part and inflate part of the model would suppress the warning message.

Further output follows

webuse fish

. zinb count persons livebait,inf(child camper) nolog

Zero-inflated negative binomial regression        Number of obs   =
250
                                                  Nonzero obs     =
108
                                                  Zero obs        =
142

Inflation model = logit                           LR chi2(2)      =
82.23
Log likelihood  = -401.5478                       Prob > chi2     =
0.0000

------------------------------------------------------------------------
------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
count        |
     persons |   .9742984   .1034938     9.41   0.000     .7714543
1.177142
    livebait |   1.557523   .4124424     3.78   0.000     .7491503
2.365895
       _cons |  -2.730064    .476953    -5.72   0.000    -3.664874
-1.795253
-------------+----------------------------------------------------------
------
inflate      |
       child |   3.185999   .7468551     4.27   0.000      1.72219
4.649808
      camper |  -2.020951    .872054    -2.32   0.020    -3.730146
-.3117567
       _cons |  -2.695385   .8929071    -3.02   0.003     -4.44545
-.9453189
-------------+----------------------------------------------------------
------
    /lnalpha |   .5110429   .1816816     2.81   0.005     .1549535
.8671323
-------------+----------------------------------------------------------
------
       alpha |   1.667029   .3028685                      1.167604
2.380076
------------------------------------------------------------------------
------


. est sto full


Delete child from the inflate part of the model

. zinb count persons livebait,inf(camper) nolog

Zero-inflated negative binomial regression        Number of obs   =
250
                                                  Nonzero obs     =
108
                                                  Zero obs        =
142

Inflation model = logit                           LR chi2(2)      =
50.23
Log likelihood  = -436.6451                       Prob > chi2     =
0.0000

------------------------------------------------------------------------
------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
count        |
     persons |   .7979216   .1182117     6.75   0.000      .566231
1.029612
    livebait |   1.636112   .4472886     3.66   0.000     .7594425
2.512782
       _cons |  -2.539434   .5485813    -4.63   0.000    -3.614634
-1.464235
-------------+----------------------------------------------------------
------
inflate      |
      camper |  -3.947683   20.70017    -0.19   0.849    -44.51926
36.6239
       _cons |  -.5245453   .7055834    -0.74   0.457    -1.907463
.8583728
-------------+----------------------------------------------------------
------
    /lnalpha |   1.047034   .4478706     2.34   0.019     .1692237
1.924844
-------------+----------------------------------------------------------
------
       alpha |   2.849188   1.276067                      1.184385
6.85408
------------------------------------------------------------------------
------

. lrtest full .
log likelihood of null models differ: -442.663 vs. -461.7623
r(498);

. lrtest full .,force stat

Likelihood-ratio test                                  LR chi2(1)  =
70.19
(Assumption: . nested in full)                         Prob > chi2 =
0.0000

------------------------------------------------------------------------
-----
       Model |    Obs    ll(null)   ll(model)     df          AIC
BIC
-------------+----------------------------------------------------------
-----
           . |    250   -461.7623   -436.6451      6     885.2902
906.419
        full |    250    -442.663   -401.5478      7     817.0955
841.7457
------------------------------------------------------------------------
-----
               Note:  N=Obs used in calculating BIC; see [R] BIC note



. zinb count ,inf(_cons)

Fitting constant-only model:

Iteration 0:   log likelihood = -519.33992  
Iteration 1:   log likelihood = -473.30482  
Iteration 2:   log likelihood = -466.55445  
Iteration 3:   log likelihood = -465.53667  
Iteration 4:   log likelihood = -464.82369  
Iteration 5:   log likelihood = -464.60737  
Iteration 6:   log likelihood = -464.48975  
Iteration 7:   log likelihood = -464.44921  
Iteration 8:   log likelihood = -464.44138  
Iteration 9:   log likelihood = -464.43977  
Iteration 10:  log likelihood = -464.43942  
Iteration 11:  log likelihood = -464.43934  
Iteration 12:  log likelihood = -464.43932  

Fitting full model:

Iteration 0:   log likelihood = -464.43932  
Iteration 1:   log likelihood = -464.43931  

Zero-inflated negative binomial regression        Number of obs   =
250
                                                  Nonzero obs     =
108
                                                  Zero obs        =
142

Inflation model = logit                           LR chi2(0)      =
0.00
Log likelihood  = -464.4393                       Prob > chi2     =
.

------------------------------------------------------------------------
------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+----------------------------------------------------------
------
count        |
       _cons |   1.192632   .1515535     7.87   0.000     .8955925
1.489671
-------------+----------------------------------------------------------
------
inflate      |
       _cons |  -16.97113   1949.598    -0.01   0.993    -3838.113
3804.17
-------------+----------------------------------------------------------
------
    /lnalpha |   1.693616   .1221088    13.87   0.000     1.454288
1.932945
-------------+----------------------------------------------------------
------
       alpha |   5.439116   .6641637                      4.281433
6.909832
------------------------------------------------------------------------
------

.. estat ic

------------------------------------------------------------------------
-----
       Model |    Obs    ll(null)   ll(model)     df          AIC
BIC
-------------+----------------------------------------------------------
-----
           . |    250   -464.4393   -464.4393      3     934.8786
945.443
------------------------------------------------------------------------
-----
               Note:  N=Obs used in calculating BIC; see [R] BIC note


May I wish Statalist members a happy Christmas.

Best wishes, Garry
Garry Anderson
School of Veterinary Science
University of Melbourne
250 Princes Highway    Ph  03 9731 2221
WERRIBEE    3030       Fax  03 9731 2388
Email:  g.anderson@unimelb.edu.au  





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