Mark Schaffer <[email protected]> asks about what appear to be multiple
offset variables with a single equation in -ml-:
> The likelihood function that I want to minimize has the form of, say, one
> dependent variable y and 3 independent variables w, x and z. However, of
> the independent variables, only x has a coefficient associated with it.
> The other two variables, w and z, are needed for calculating the
> likelihood but don't have coefficients.
>
> My question - what's the best way of passing w and z to the likelihood
> function?
>
> I can think of 3 ways, but all seem pretty hacky:
>
> 1. Save "w z" as a string in a global macro called, say, MyMLvars. The
> likelihood program mymlprog knows to look in $MyMLvars to find them.
>
> 2. In the ml model command, list w and z as additional endogenous
> variables, e.g.,
>
> ml model d0 mymlprog (y w z = x)
>
> Then mymlprog can find w and z as $ML_y2 and $ML_y3.
>
> 3. The hackiest of all - list w and z as indep vars, but constrain the
> coeffs to be zero:
>
> constraint 1 w=0
> constraint 2 z=0
> ml model d0 mymlprog (y = x w z)
>
> Is there a better way? Or, if there isn't, which of these is to be
> preferred?
This will depend upon the form of the likelihood, but if the variables -w- and
-z- are part of the likelihood but are not necessarily part of -xb- for the
first equation, I would most definitely use constraints and extra equations.
Here is an overly simple example:
***** BEGIN:
clear
program drop _all
program myll
version 8.2
args lnf xb1 xb2 xb3
quietly replace `lnf' = - ($ML_y1-`xb1')^2 - (`xb2')^2 - (`xb3')^2
end
global xx
sysuse auto
const 1 [eq2]trunk = 1
const 2 [eq3]displacement = 1
ml model lf myll ///
(eq1: mpg = turn) ///
(eq2: trunk, noconstant) ///
(eq3: displ, noconstant) ///
, constr(1 2) max
ml display, first
***** END:
Here are the results from the -ml display-:
***** BEGIN:
initial: log likelihood = -36008
alternative: log likelihood = -34482.631
rescale: log likelihood = -23753.635
rescale eq: log likelihood = -4520
Iteration 0: log likelihood = -3516088
Iteration 1: log likelihood = -3512747.6
Iteration 2: log likelihood = -3512747.6
. ml display, first
Number of obs = 74
Wald chi2(1) = 2527.66
Log likelihood = -3512747.6 Prob > chi2 = 0.0000
( 1) [eq2]trunk = 1
( 2) [eq3]displacement = 1
------------------------------------------------------------------------------
mpg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
turn | -.9457877 .018812 -50.28 0.000 -.9826586 -.9089169
_cons | 58.7965 .7503857 78.36 0.000 57.32577 60.26723
------------------------------------------------------------------------------
***** END:
--Jeff
[email protected]
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