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# Re: st: RE: nl-function log4-formula

 From Jennyfer Wolf To statalist@hsphsun2.harvard.edu Subject Re: st: RE: nl-function log4-formula Date Wed, 16 Nov 2011 16:10:17 +0100

```Dear Nick, dear Brian,

thanks a lot for your answers which were of big help!

Jennyfer

2011/11/16 Brian P. Poi <bpoi@stata.com>:
> Jennyfer Wolf wrote:
>>
>> Dear Nick,
>>
>> I tried with the parantheses outside:
>>
>> 2. nl(VAR1={b0}+{b1}/(1+exp(-{b2}*(VAR2-{b3})))) if VAR3=="xxx"
>>
>> It does not change anything. Still I don't get same reults as with
>> log4 and only an estimate for b0.
>> Would you have another idea?
>>
>> Thank you!
>> Jennyfer
>
> The difference between using -nl-'s log4 routine and typing in the
> substitutable expression yourself lies with the starting values that -nl-
> uses in its optimization routine.  The logistic function that -nl- calls
> log4 is somewhat sensitive to the starting values you use.  When you type in
> your own substitutable expression, unless you specify your own starting
> values, -nl- initializes all the parameters to zero.  On the other hand,
> -nl-'s log4 routine examines your data to come up with better starting
> values.  With sensitive nonlinear functions, it's not unheard of for the
> optimizer to find a different value for the constant term but leave all the
> other parameters at zero; "strange" results like that are usually a good
> indication that you should try different starting values.
>
> For the log4 function y = b0 + b1/(1 + exp(-b2*(x-b3))), -nl- sets b0 to
> slightly less than the smallest value of y in your data and sets b1 to
> slightly more than the difference between the largest and smallest values of
> y.  b2 and b3 are initialized based on a linear regression that uses a
> transformation of y as the dependent variable.  To see the nitty gritty
> details, you can type in
>
>   . viewsource nllog4.ado
>
> The program code in between the -quietly- braces gets the initial values.
>
>
> Brian P. Poi
> Senior Economist
> StataCorp LP
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>

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```