Stephen P. Jenkins <[email protected]> asks about using -ml- to optimize
functions:
> I'm thinking about updating my -smfit- and -dagumfit- programs written
> in Stata version 4 (sic!) to version 8.1, but am unclear about to
> convert one key aspect of the -ml- program. These programs, fitting
> parametric functional forms to distributions of data, are a little
> unusual because they don't have a dependent variable with explanatory
> variables in the way a regression model usually does, and fitting in
> version 4 involved a particular "depv(000)" statement, thus:
> ~~~~~ado code extract ~~~~~~~~~~~~~~~~~~~
> ml begin
> ml func sm_ll
> ml method deriv0
> eq p1 :
> eq p2 :
> eq p3 :
> ml model c = p1 p2 p3, depv(000) from(c0)
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> What is the version 8.1 equivalent of the "trick" used here, please?
> The "depv" option no longer exists.
> [Note: the original programs simply fitted 3 parameter functional
> forms. In the update, I would also like to make each parameter
> optionally a function of covariates. The original programs are
> available using -ssc-.]
I've constructed an (admittedly silly) example to illustrate how Stephen may
go about using -ml- in Stata 8 to optimize his "functional forms".
Here is a -d0- "likelihood evaluator" that return the sum of two "upside-down"
parabolas:
***** BEGIN: parab_d0.ado
program parab_d0
version 8.1
args todo b lnf
tempname x y
mleval `x' = `b', scalar
mleval `y' = `b', scalar eq(2)
quietly mlsum `lnf' = 1 - (`x'-15)^2 - (`y'-10)^2
end
***** END: parab_d0.ado
We can now use -ml- to find the values x=15 and y=10, the only requirement is
that we have some data in memory (at least one observation to work with).
Here is a log of -parab_d0- in action:
***** BEGIN:
. clear
. sysuse auto
(1978 Automobile Data)
. keep in 1
(73 observations deleted)
. ml model d0 parab_d0 (x:) (y:)
. ml max
initial: log likelihood = -324
alternative: log likelihood = -299.5
rescale: log likelihood = -36
rescale eq: log likelihood = -4
Iteration 0: log likelihood = -4
Iteration 1: log likelihood = 1
Iteration 2: log likelihood = 1
Number of obs = 1
Wald chi2(0) = .
Log likelihood = 1 Prob > chi2 = .
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
_cons | 15 .7071068 21.21 0.000 13.6141 16.3859
-------------+----------------------------------------------------------------
y |
_cons | 10 .7071068 14.14 0.000 8.614096 11.3859
------------------------------------------------------------------------------
***** END:
We could also make each parameter optionally a function of covariates. In the
following example, we include -mpg- in the first equation and -turn- in the
second:
***** BEGIN:
. clear
. sysuse auto
(1978 Automobile Data)
. ml model d0 parab_d0 (x: mpg) (y: turn)
. ml max
initial: log likelihood = -23976
alternative: log likelihood = -22163
rescale: log likelihood = -2664
rescale eq: log likelihood = -296
Iteration 0: log likelihood = -296
Iteration 1: log likelihood = 74
Iteration 2: log likelihood = 74
Number of obs = 74
Wald chi2(1) = 0.00
Log likelihood = 74 Prob > chi2 = 1.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
mpg | -1.24e-13 .0143048 -0.00 1.000 -.0280369 .0280369
_cons | 15 .3155484 47.54 0.000 14.38154 15.61846
-------------+----------------------------------------------------------------
y |
turn | -3.16e-13 .018812 -0.00 1.000 -.0368708 .0368708
_cons | 10 .7503857 13.33 0.000 8.529271 11.47073
------------------------------------------------------------------------------
***** END:
--Jeff
[email protected]
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
