# st: ml command and chi-square tests

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject st: ml command and chi-square tests Date Fri, 25 Mar 2005 13:51:32 -0500

According to the documentation, the -ml- command will provide a Wald test (rather than an LR test) when you specify robust, cluster or pweights. However, I am finding that it also provides a Wald test when you use the -constraint- option. Why? This isn't mentioned in the documentation. Is there some mathematical reason for this, or is it a bug/limitation of the software, or what? The log likelihood is being reported for the constrained model (not a pseudo log likelihood) so I don't understand why it can't give me a LR chi-square instead of a Wald chi-square for the model.

Here is a simple example. The program for the likelihood function is

program define mylogit
args lnf Xb
replace `lnf' = -ln(1+exp(-`Xb')) if \$ML_y1==1
replace `lnf' = -`Xb' - ln(1+exp(-`Xb')) if \$ML_y1==0
end

Using this program, I
(a) estimate a constant only model. This gives me the info the subsequent model needs to compute a LR chi-square
(b) run an unconstrained model. LR chi-square is reported
(c) run the constant-only model again
(d) run a constrained model where the effect of 1 variable is constrained to be 0. It reports Wald chi-square instead of LR chi-square. Why? I can get an LR chi-square by rerunning the variable dropped, and LL is being reported (and it is correct) so why can't I get LR chi-square in the output? (A workaround is to use -estimates store- and -lrtest- but I'd rather save all that trouble.)

------------------------
. webuse auto
(1978 Automobile Data)

. * Null model
. ml model lf mylogit (foreign=)
. quietly ml maximize

. * Unconstrained Model
. ml model lf mylogit (foreign=mpg weight), continue
. ml maximize, nolog

Number of obs = 74
LR chi2(2) = 35.72
Log likelihood = -27.175156 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
foreign | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg | -.1685869 .0919175 -1.83 0.067 -.3487418 .011568
weight | -.0039067 .0010116 -3.86 0.000 -.0058894 -.001924
_cons | 13.70837 4.518709 3.03 0.002 4.851859 22.56487
------------------------------------------------------------------------------

. * Null model again
. ml model lf mylogit (foreign=)
. quietly ml maximize

. * Constrained Model
. constraint define 1 mpg=0
. ml model lf mylogit (foreign=mpg weight), continue constraint(1)
. ml maximize, nolog

Number of obs = 74
Wald chi2(1) = 18.03
Log likelihood = -29.054002 Prob > chi2 = 0.0000

( 1) [eq1]mpg = 0
------------------------------------------------------------------------------
foreign | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg | (dropped)
weight | -.0025874 .0006094 -4.25 0.000 -.0037817 -.001393
_cons | 6.282599 1.603967 3.92 0.000 3.138882 9.426317
------------------------------------------------------------------------------

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