{smcl}
{com}{sf}{ul off}{txt}{.-}
       log:  {res}C:\Documents and Settings\jli2\My Documents\Log\MLE_log\negative_binomial.smcl
  {txt}log type:  {res}smcl
 {txt}opened on:  {res}29 Sep 2004, 22:08:30
{txt}
{com}. * count data_negative binomial model
. * we use the data from stata official website
. use http://www.stata-press.com/data/r8/rod93
{txt}
{com}. * to generate relevant variables
. quietly tab cohort, gen(coh)
{txt}
{com}. * first run the canned "nbreg" routine
. nbreg  deaths coh2 coh3

{txt}Fitting Poisson model:

Iteration 0:   log likelihood = {res} -325.7993{txt}  
Iteration 1:   log likelihood = {res} -325.7993{txt}  

Fitting constant-only model:

Iteration 0:   log likelihood = {res}-114.33669{txt}  
Iteration 1:   log likelihood = {res}-110.33038{txt}  
Iteration 2:   log likelihood = {res}-108.56521{txt}  
Iteration 3:   log likelihood = {res}-108.56018{txt}  
Iteration 4:   log likelihood = {res}-108.56018{txt}  

Fitting full model:

Iteration 0:   log likelihood = {res}-108.48867{txt}  
Iteration 1:   log likelihood = {res}-108.48841{txt}  
Iteration 2:   log likelihood = {res}-108.48841{txt}  

Negative binomial regression{col 51}Number of obs{col 67}= {res}        21
{col 51}{txt}LR chi2({res}2{txt}){col 67}= {res}      0.14
{col 51}{txt}Prob > chi2{col 67}= {res}    0.9307
{txt}Log likelihood = {res}-108.48841{col 51}{txt}Pseudo R2{col 67}= {res}    0.0007

{txt}{hline 13}{c TT}{hline 64}
      deaths {c |}      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
{hline 13}{c +}{hline 64}
        coh2 {c |}  {res} .0591305   .2978419     0.20   0.843    -.5246289      .64289
        {txt}coh3 {c |}  {res}-.0538792   .2981621    -0.18   0.857    -.6382662    .5305077
       {txt}_cons {c |}  {res} 4.435906   .2107213    21.05   0.000       4.0229    4.848912
{txt}{hline 13}{c +}{hline 64}
    /lnalpha {c |}  {res}-1.207379   .3108622{col 58}-1.816657   -.5980999
{txt}{hline 13}{c +}{hline 64}
       alpha {c |}  {res}   .29898   .0929416{col 58} .1625683    .5498555
{txt}{hline 13}{c BT}{hline 64}
Likelihood-ratio test of alpha=0:  {help j_chibar:chibar2(01) =}{res}  434.62{txt} Prob>=chibar2 = {res}0.000
{txt}
{com}. * user-define MLE procedure
. program drop _all
{txt}
{com}. program define neg_bin_stata
{txt}  1{com}. args lnf theta1 theta2
{txt}  2{com}. quietly replace `lnf'=lngamma((1/`theta2')+$ML_y1)-lngamma($ML_y1+1)-lngamma(1/`theta2')+(1/`theta2')*ln(1/(1+`theta2'*exp(`theta1')))+$ML_y1*ln(1-1/(1+`theta2'*exp(`theta1')))
{txt}  3{com}. end
{txt}
{com}. ml model lf neg_bin_stata ( deaths= coh2 coh3) ()
{txt}
{com}. ml maximize

{txt}initial:       log likelihood = {res}    -<inf>{txt}  (could not be evaluated)
feasible:      log likelihood = {res}-1347.5967
{txt}rescale:       log likelihood = {res}-130.77236
{txt}rescale eq:    log likelihood = {res}-114.30781
{txt}Iteration 0:   log likelihood = {res}-114.30781{txt}  
Iteration 1:   log likelihood = {res}-109.97715{txt}  
Iteration 2:   log likelihood = {res}-108.54119{txt}  
Iteration 3:   log likelihood = {res}-108.48846{txt}  
Iteration 4:   log likelihood = {res}-108.48841{txt}  
Iteration 5:   log likelihood = {res}-108.48841{txt}  

{col 51}Number of obs{col 67}= {res}        21
{col 51}{txt}Wald chi2({res}2{txt}){col 67}= {res}      0.14
{txt}Log likelihood = {res}-108.48841{col 51}{txt}Prob > chi2{col 67}= {res}    0.9306

{txt}{hline 13}{c TT}{hline 64}
      deaths {c |}      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
{hline 13}{c +}{hline 64}
{res}eq1          {txt}{c |}
        coh2 {c |}  {res} .0591305   .2978419     0.20   0.843     -.524629      .64289
        {txt}coh3 {c |}  {res}-.0538792   .2981621    -0.18   0.857    -.6382662    .5305078
       {txt}_cons {c |}  {res} 4.435906   .2107214    21.05   0.000       4.0229    4.848912
{txt}{hline 13}{c +}{hline 64}
{res}eq2          {txt}{c |}
       _cons {c |}  {res} .2989801   .0929416     3.22   0.001     .1168179    .4811423
{txt}{hline 13}{c BT}{hline 64}

{com}. * we get the same result
. * the unconditional pdf is given in the description of nbreg command in stata manual 
. log close
       {txt}log:  {res}C:\Documents and Settings\jli2\My Documents\Log\MLE_log\negative_binomial.smcl
  {txt}log type:  {res}smcl
 {txt}closed on:  {res}29 Sep 2004, 22:11:25
{txt}{.-}
{smcl}
{txt}{sf}{ul off}