st: ml mixture distribution

[Lukas Kornher <lukas.kornher@uni-bonn.de>]

Dear Statalisters,

I am trying to set up a ml model for a mixture distribution function 
with three regimes. Stata cannot find a maximum and returns:
/could not calculate numerical derivatives -- discontinuous region with 
missing values encountered/.
I am quite new to ml in Stata and I find very little on mixture 
distribution on the web and in MLE with Stata. Any comments would be 
really appreciated. Especially how one can constraint the sum of the 
regime probabilities to 1.
Many thanks.

Lukas

STATA CODE:

program define pbm_mixture ;
args todo b lnf;
tempvar lnf_j;
tempname lambda1 lambda2 sigma_1 sigma_2 sigma_3 mu;
scalar `mu' = `b'[1,1];
scalar `sigma_1' = exp(`b'[1,2]);
scalar `sigma_2' = exp(`b'[1,3]);
scalar `sigma_3' = exp(`b'[1,4]);
scalar `lambda1'  = normal(`b'[1,5]);
scalar `lambda2'  = normal(`b'[1,6]);
gen double `lnf_j' =
  `lambda1' * (1/`sigma_1') * normalden(($ML_y1 - `mu')/`sigma_1') +


  `lambda2'*(2/sqrt(`sigma_1'^2+`sigma_2'^2)) * normalden(($ML_y1 - 
`mu')/ sqrt(`sigma_1'^2+`sigma_2'^2))*
  (1-normal((-($ML_y1 - `mu')*(`sigma_1'/`sigma_2'))/ 
sqrt(`sigma_1'^2+`sigma_2'^2)))+
  (1-`lambda1'-`lambda2') * (2/sqrt(`sigma_1'^2+`sigma_3'^2)) * 
normalden(($ML_y1 - `mu')/ sqrt(`sigma_1'^2+`sigma_3'^2))*
  (1-normal((($ML_y1 - `mu')*(`sigma_1'/`sigma_3'))/ 
sqrt(`sigma_1'^2+`sigma_3'^2)));
 mlsum `lnf' = log(`lnf_j');


end;
gen mu = -0.00001;

ml model d0 pbm_mixture (tau = mu, noconst technique(dfp)  ) /ln_sigma_1 
/ln_sigma_2 /ln_sigma_3 /inv_lambda1 /inv_lambda2 ;
ml init mu=0;
ml check;
ml search lambda1 0 1 lambda2 0 1, repeat(250);
ml maximize;

--
Lukas Kornher

Phd Candidate
Department of Economic and Technological Change
Center for Development Research
University of Bonn

Tel.: +49 (0) 228 / 73-1842
Room 1.031



                  

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