st: Parameter Restrictions on ML model

[Dev Vencappa <Dev.Vencappa@nottingham.ac.uk>]

Dear Stata users, 

 I am trying to maximise a log likelihood function using method d0 and I need to impose restrictions on the parameters. Basically, in the codes below, I need to estimate parameters d, beta and T (through lnd,lnbeta,lnT).   The only variables are t and set, where set is a censoring indicator, and t is survival time taking values between  0.3 to 400 inclusive. As this is a complicated log-likelihood, I need to restrict the parameters of interest otherwise the log-likelihood returns missing values and stops. Having experimented with this in Excel (plugging in different values of d,beta,T), I calculated that to produce non-missing log-likelihood values, the following restrictions need to be applied:

0.67<d<0.998
beta> 328.9
1<T< 12.7

I experimented with these codes below and get the message: 


. ml maximize, tech(nr bhhh dfp bfgs) tol(1e-12) gtol(1e-12) force

initial:       log likelihood = -1527.7258
rescale:       log likelihood = -1527.7258
rescale eq:    log likelihood = -1527.6898
numerical derivatives are approximate
flat or discontinuous region encountered could not calculate numerical derivatives -- discontinuous region with missing values encountered could not calculate numerical derivatives -- discontinuous region with missing values encountered r(430);


I was wondering if I am doing something wrong here especially in the way I am imposing the parameter range of values?

Any help/suggestion would be very much appreciated.

Thanks and regards
Dev

capture program drop ej_d0_3het
program ej_d0_3het
	version 13.0
	args todo b lnf
	tempname d lnd beta lnbeta T lnT c0 c1 c2 c3
	tempvar  theta h1 h2 H1 H2 A
	mleval `lnd'=`b',eq(1) scalar
	mleval `lnbeta'=`b',eq(2) scalar
	mleval `lnT'=`b',eq(3) scalar
	quietly{
	scalar `d'=0.67+0.328*invlogit(`lnd')
	scalar `beta'=328.9+exp(`lnbeta')
	scalar `T'=1+11.7*invlogit(`lnT')
	scalar `c0' =(1-`d')*(`d'^-`T')
	scalar `c1'=(1-`d')*`beta'-(`d'^(1-`T'))
	scalar `c2'=`d'^(-`T')
	scalar `c3'= (1-`d')*`beta' 
	local t $ML_y1
	local set $ML_y2
	gen double `h1'=(`c0'*(`d'^`t'))/(`c1'+`c2'*(`d'^`t'))
	gen double `h2'=(`c0'*`c3'*(`d'^`t')) / ( (`c1'+`c2'*(`d'^`t'))^2)
	gen double `H1'=`c0'*(ln(`c1'+`c2'*(`d'^`t'))-ln(`c1'+`c2'))/(`c2'*ln(`d'))
	gen double `H2'=(`c0'*`c3'*((`d'^`t')-1) ) / ((`c1'+`c2'*(`d'^`t'))*(`c1'+`c2')*ln(`d'))
	gen double `A'= ( (`h1'+`h2')^`set')*exp(-(`H1'+`H2'))
	mlsum `lnf'=ln(`A')
		}
end

ml model d0 ej_d0_3het (dsetw settled = ) (lnd:) (lnbeta:) (lnT:) ml check ml graph ml maximize, tech(nr bhhh dfp bfgs) tol(1e-12) gtol(1e-12) force ml query

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