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I want to estimate the Logit function with Maximum Simulated Likelihood with Halton draws.

My program looks very similar to "Estimation of multinomial logit models with unobserved 
heterogeneity using maximum simulated likelihood" by Peter Haan and Arne Uhlendorff, 
Stata Journal 6 (2), 2006; rewritten for 4 alternatives and only the line with beginning * 
changed, because of nonunderstanding.

my programme:

program define sim_mlogit_d0_one_random_cov
	version 9.2

	args todo b lnf
	tempvar etha1 etha2 etha3 random1 random2 random3 pi1 pi2 pi3 pi4 sum lnpi last lj 
L1 L2
								
	tempname lnsig1 lnsig2 lnsig3 rho12 rho13 rho23 sigma1 sigma2 sigma3 cov12 
cov13 cov23

	mleval `etha1' = `b', eq(1)
	mleval `etha2' = `b', eq(2)
	mleval `etha3' = `b', eq(3)
	mleval `lnsig1' = `b', eq(4) scalar
	mleval `lnsig2' = `b', eq(5) scalar
	mleval `lnsig3' = `b', eq(6) scalar
	mleval `rho12' = `b', eq(7) scalar
	mleval `rho13' = `b', eq(8) scalar
	mleval `rho23' = `b', eq(9) scalar


	qui	{

		scalar `sigma1' = (exp(`lnsig1'))^2
		scalar `sigma2' = (exp(`lnsig2'))^2
		scalar `sigma3' = (exp(`lnsig3'))^2
		scalar `cov12' = [exp(2*`rho12')-
1]/[exp(2*`rho12')+1]*(exp(`lnsig2'))*(exp(`lnsig1'))
		scalar `cov13' = [exp(2*`rho13')-
1]/[exp(2*`rho13')+1]*(exp(`lnsig3'))*(exp(`lnsig1'))
		scalar `cov23' = [exp(2*`rho23')-
1]/[exp(2*`rho23')+1]*(exp(`lnsig3'))*(exp(`lnsig2'))

		gen double `random1' = 0
		gen double `random2' = 0
		gen double `random3' = 0

		gen double `lnpi' = 0
		gen double `sum' = 0
		gen double `L1' = 0
		gen double `L2' = 0
	
		by hh: gen byte `last' = (_n==_N)

		gen double `pi1' = 0
		gen double `pi2' = 0
		gen double `pi3' = 0
		gen double `pi4' = 0

		}

	matrix W = (`sigma1' , `cov12' , `cov13' \ `cov12' , `sigma2' , `cov23' \ `cov13' , 
`cov23' , `sigma3')

	capture matrix L = cholesky(W)

	if _rc != 0 {
		di "Warning: cannot do Cholesky factorization of rho matrix" _rc
		}

	local l11=L[1,1]
	local l21=L[2,1]
	local l31=L[3,1]
	local l22=L[2,2]
	local l32=L[3,2]
	local l33=L[3,3]



	local repl=${draws}
	local r = 1

	forvalues r=1/$draws	{
		qui	{
			replace `random1' = random_1`r' * `l11'
			replace `random2' = random_2`r' * `l22'
			replace `random3' = random_3`r' * `l33'

*			replace `random2' = random_2`r'*`l22' + random_1`r'*`l21'

			replace `pi1' = 1/(1+exp(`etha1'+`random1') + exp(`etha2' + 
`random2') + exp(`etha3' + `random3'))
			replace `pi2' = exp(`etha1' + `random1') * `pi1'
			replace `pi3' = exp(`etha2' + `random2') * `pi1'
			replace `pi4' = exp(`etha3' + `random3') * `pi1'

			replace `lnpi' = ln(`pi1'*bet1 + `pi2'*bet2 + `pi3'*bet3 + `pi4'*bet4)

			by hh: replace `sum' = sum(`lnpi')
			by hh: replace `L1' = exp(`sum'[_N]) if _n==_N

			by hh: replace `L2' = `L2' + `L1' if _n==_N
			}
		}

	qui gen `lj' = cond(!`last',0,ln(`L2'/`repl'))
	qui mlsum `lnf' = `lj'
	if (`todo'==0 | `lnf'>=.) exit

end



I tried the same programme as in Haan/Uhlendorf for 3 alternatives, but received the same 
output like for 4 alternatives:



.         ml model d0 sim_mlogit_d0_one_random_cov (dep= indep) (dep= indep) (dep= indep) > /lnsig1 /lnsig2 /lnsig3  /rho12 /rho13 /rho
> 23
r; t=0.10 11:51:27

. 
. 
.         ml search
initial:       log likelihood = -15670.836
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 504
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 506
Warning: cannot do Cholesky factorization of rho matrix 506
improve:       log likelihood =          0
Warning: cannot do Cholesky factorization of rho matrix 504
Warning: cannot do Cholesky factorization of rho matrix 504
rescale:       log likelihood =          0
Warning: cannot do Cholesky factorization of rho matrix 504
Warning: cannot do Cholesky factorization of rho matrix 504
--Break--




My second problem:

How to write the programme for an additional individual varying coefficient vector for some 
variables:




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