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st: non-linear least squares
A colleague of mine has asked for help with the following stata query:
Working with non-linear least squares regression, Stata 8 includes a couple of non-linear functions already programmed. The logistic function:
nl log3 Y = b1/(1 + exp(-b2*(X-b3)))
and the Gompertz:
nl gom3 Y = b1*exp(-exp(-b2*(X-b3)))
However, looking at various econometric manuals, these functions are normally of the form:
log Y = b1/(1+(b2*exp(-b3*X)))
gom Y = b1*exp(-b2*exp(-b3*X)))
I can't find a mathematical way to move between the two; are the functions programmed into Stata a recognised alternative form, or is the help file incorrect?
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