Re: st: Two seemingly similar NL estimations give different results

[Michael Boehm <michael.boehm1@gmail.com>]

Dear Nick,

Thanks for your answer. I am not quite sure I understand it though.
All the parameters we estimate are free to vary in both
implementations of the -nl- command (more detailed code below), but
the estimates are different. Or do I misunderstand something?

program nlexppremia
version 13.1
syntax varlist(min=4 max=4) [aw fw iw] if, at(name)

// Retrieve variables
        local lhs:    word 1 of `varlist'
        local s:       word 2 of `varlist'
        local j:       word 3 of `varlist'
        local e:       word 4 of `varlist'

// Retrieve parameters, stored in "at"
tempname bG pi lambdaL1_0 lambdaL2_0 lambdaEL1_0 lambdaEL2_0
lambdaL1_1 lambdaL2_1 lambdaEL1_1 lambdaEL2_1
    scalar `bG' = `at'[1,1]
    scalar `pi' = `at'[1,2]
    scalar `lambdaL1_0' = `at'[1,3]
    scalar `lambdaL2_0' = `at'[1,4]
    scalar `lambdaEL1_0' = `at'[1,5]
    scalar `lambdaEL2_0' = `at'[1,6]
    scalar `lambdaL1_1' = `at'[1,7]
    scalar `lambdaL2_1' = `at'[1,8]
    scalar `lambdaEL1_1' = `at'[1,9]
    scalar `lambdaEL2_1' = `at'[1,10]

// replace the lhs directly:
    replace `lhs' = `bG'+(`lambdaL1_0'*j+`lambdaL2_0'*j^2) +
log(1+`pi'*exp(`lambdaEL1_0'*j+`lambdaEL2_0'*j^2)*`e') if `s'==0
    replace `lhs' = `bG'+(`lambdaL1_1'*j+`lambdaL2_1'*j^2) +
log(1+`pi'*exp(`lambdaEL1_1'*j+`lambdaEL2_1'*j^2)*`e') if `s'==1
end

nl exppremia @ lhs s j e, nparameters(10)

********************************************************************

program nlexppremia
version 13.1
syntax varlist(min=4 max=4) [aw fw iw] if, at(name)

// Retrieve variables
        local lhs:    word 1 of `varlist'
        local s:       word 2 of `varlist'
        local j:       word 3 of `varlist'
        local e:       word 4 of `varlist'

// Retrieve parameters, stored in "at"
tempname bG pi lambdaL1_0 lambdaL2_0 lambdaEL1_0 lambdaEL2_0
lambdaL1_1 lambdaL2_1 lambdaEL1_1 lambdaEL2_1
    scalar `bG' = `at'[1,1]
    scalar `pi' = `at'[1,2]
    scalar `lambdaL1_0' = `at'[1,3]
    scalar `lambdaL2_0' = `at'[1,4]
    scalar `lambdaEL1_0' = `at'[1,5]
    scalar `lambdaEL2_0' = `at'[1,6]
    scalar `lambdaL1_1' = `at'[1,7]
    scalar `lambdaL2_1' = `at'[1,8]
    scalar `lambdaEL1_1' = `at'[1,9]
    scalar `lambdaEL2_1' = `at'[1,10]

// Compute RHS of regression
    tempvar RHS
    qui gen `RHS'=.
    replace `RHS' = `bG'+(`lambdaL1_0'*j+`lambdaL2_0'*j^2) +
log(1+`pi'*exp(`lambdaEL1_0'*j+`lambdaEL2_0'*j^2)*`e') if `s'==0
    replace `RHS' = `bG'+(`lambdaL1_1'*j+`lambdaL2_1'*j^2) +
log(1+`pi'*exp(`lambdaEL1_1'*j+`lambdaEL2_1'*j^2)*`e') if `s'==1

//Assign lhs=rhs
    replace `lhs' = `RHS'

end

nl exppremia @ lhs s j e, nparameters(10)

********************************************************************

On Thu, Jan 23, 2014 at 9:50 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> The key question is what in your code is free to vary? Only parameters
> that are free to vary can be estimated by -nl-; the others are fixed
> constants.
>
> Nick
> njcoxstata@gmail.com
>
>
> On 23 January 2014 08:44, Michael Boehm <michael.boehm1@gmail.com> wrote:
>> Dear all,
>>
>> We are struggling with nonlinear least square regression with a
>> function evaluator programme. We don’t understand why assigning to the
>> left-hand side variable, lhs, directly an expression for the
>> right-hand side is different to first computing the right-hand side
>> variable, rhs, and then assigning lhs=rhs.
>> Both residual SS and parameter estimates differ across the two
>> scenarios. A sketch of the two codes, which we thought would give the
>> same results are:
>>
>>                 program nltest_1
>>
>>                                 version 13.1
>>                                 syntax varlist(min=4 max=4) [aw fw iw]
>> if, at(name)
>>
>>                                 // Retrieve variables
>>                                 local lhs:    word 1 of `varlist'
>>                                 local s:       word 2 of `varlist'
>>                                 local j:       word 3 of `varlist'
>>                                 local e:       word 4 of `varlist'
>>
>>                                 // replace the lhs directly:
>>                                 replace `lhs'= <Function of Parameters
>> and Variables>  if `s'==0
>>                                 replace `lhs'= <Function of Parameters
>> and Variables>   if `s'==1
>>                 end
>>
>> ********************************************************************
>>                 program nltest_1
>>
>>                                 version 13.1
>>                                 syntax varlist(min=4 max=4) [aw fw iw]
>> if, at(name)
>>
>>                                 // Retrieve variables
>>                                 local lhs:    word 1 of `varlist'
>>                                 local s:       word 2 of `varlist'
>>                                 local j:       word 3 of `varlist'
>>                                 local e:       word 4 of `varlist'
>>
>>                                 // Compute RHS of regression
>>                                 tempvar RHS
>>                                 replace `RHS'= <Function of Parameters
>> and Variables>  if `s'==0
>>                                 replace `RHS'= <Function of Parameters
>> and Variables>   if `s'==1
>>
>>                                 //Assign lhs=rhs.
>>                                 replace `lhs' = `RHS'
>>
>>                 end
>> ********************************************************************
>>
>> *
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>
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