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# Re: st: Wald chi-square and ml with multiple equations

 From "E. Paul Wileyto" To statalist@hsphsun2.harvard.edu Subject Re: st: Wald chi-square and ml with multiple equations Date Thu, 13 Nov 2008 07:51:48 -0500

Nobody answered, so I dug around and got an answer myself. Here it is for anyone who is curious about it.
```
```
Any ml procedure will, by default, report the Wald test for the first equation. From the call to -zinb-, we see a table entry for the Wald chi2 with 9 degrees of freedom. I want an overall test that covers equations 1 and 2, with 18 degrees of freedom. If I were writing the routine, I could add an option to the ml max statement (or model statement for non-interactive) specifying waldtest(-2), which would make the table report the test for the first two equations. However, you cannot mess around with the other people's code to do this, especially stock Stata commands.
```
```
The alternative is to use -test- afterwards, and the most efficient way to call it is:
```
test [#2]
test [#1], a

```
The first call will report a test for equation 2, and the second call, with the "a" option will give a cumulative test of equation 1 and prior test.
```
Results look like this:

. test [#2]

( 1)  [inflate]drug = 0
( 2)  [inflate]sex = 0
( 3)  [inflate]wk_1 = 0
( 4)  [inflate]wk_2 = 0
( 5)  [inflate]wk_3 = 0
( 6)  [inflate]wk_4 = 0
( 7)  [inflate]wk_5 = 0
( 8)  [inflate]wk_6 = 0
( 9)  [inflate]wk_7 = 0

chi2(  9) =   52.06
Prob > chi2 =    0.0000

. test [#1],a

( 1)  [inflate]drug = 0
( 2)  [inflate]sex = 0
( 3)  [inflate]wk_1 = 0
( 4)  [inflate]wk_2 = 0
( 5)  [inflate]wk_3 = 0
( 6)  [inflate]wk_4 = 0
( 7)  [inflate]wk_5 = 0
( 8)  [inflate]wk_6 = 0
( 9)  [inflate]wk_7 = 0
(10)  [cignums]drug = 0
(11)  [cignums]sex = 0
(12)  [cignums]wk_1 = 0
(13)  [cignums]wk_2 = 0
(14)  [cignums]wk_3 = 0
(15)  [cignums]wk_4 = 0
(16)  [cignums]wk_5 = 0
(17)  [cignums]wk_6 = 0
(18)  [cignums]wk_7 = 0

chi2( 18) =  137.09
Prob > chi2 =    0.0000

E. Paul Wileyto wrote:
```
When I am using ml with a multiple equation model, for instance <zinb>, the Wald chi-square seems only to reflect the first equation. Is this correct? Is there any way to specify that the Wald chi-square should refer to equations 1 and 2?
```
Example, from our smoking data..

. zinb cignums drug sex wk_*, inflate(drug sex wk_*) vce(cluster subject)

```
Zero-inflated negative binomial regression Number of obs = 61187 Nonzero obs = 25293 Zero obs = 35894
```
```
Inflation model = logit Wald chi2(9) = 14.20 Log pseudolikelihood = -140745.3 Prob > chi2 = 0.1152
```
```
(Std. Err. adjusted for 1108 clusters in subject) ------------------------------------------------------------------------------
```            |               Robust
```
| Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+----------------------------------------------------------------
```cignums      |
```
drug | -.0456683 .3742062 -0.12 0.903 -.7790989 .6877623 sex | -.6529265 .3798595 -1.72 0.086 -1.397437 .0915844 wk_1 | .3787082 .2037435 1.86 0.063 -.0206218 .7780381 wk_2 | .1070914 .2334659 0.46 0.646 -.3504934 .5646762 wk_3 | .0697002 .194177 0.36 0.720 -.3108797 .4502802 wk_4 | .0677434 .1862907 0.36 0.716 -.2973796 .4328664 wk_5 | .0437185 .0350697 1.25 0.213 -.0250169 .1124539 wk_6 | .00758 .0215772 0.35 0.725 -.0347106 .0498706 wk_7 | .0017718 .0107169 0.17 0.869 -.019233 .0227766 _cons | 3.153936 .3848694 8.19 0.000 2.399606 3.908266 -------------+----------------------------------------------------------------
```inflate      |
```
drug | 1.237415 .2633714 4.70 0.000 .7212164 1.753613 sex | -.645983 .2127249 -3.04 0.002 -1.062916 -.2290497 wk_1 | 1.210853 .2290275 5.29 0.000 .7619678 1.659739 wk_2 | 1.012303 .190464 5.31 0.000 .639 1.385605 wk_3 | .839768 .1582912 5.31 0.000 .5295229 1.150013 wk_4 | .6872417 .1480842 4.64 0.000 .3970019 .9774815 wk_5 | .4740839 .1026852 4.62 0.000 .2728246 .6753432 wk_6 | .2748173 .0671609 4.09 0.000 .1431844 .4064501 wk_7 | .1148675 .0404778 2.84 0.005 .0355325 .1942025 _cons | -1.463269 .5311934 -2.75 0.006 -2.504389 -.4221496 -------------+---------------------------------------------------------------- /lnalpha | 1.38432 .1631759 8.48 0.000 1.064501 1.704139 -------------+---------------------------------------------------------------- alpha | 3.992112 .6514166 2.899393 5.496653 ------------------------------------------------------------------------------
```

Thanks

Paul

```
```
--
E. Paul Wileyto, Ph.D.
Assistant Professor of Biostatistics
Tobacco Use Research Center
School of Medicine, U. of Pennsylvania
3535 Market Street, Suite 4100
Philadelphia, PA  19104-3309

215-746-7147
Fax: 215-746-7140
epw@mail.med.upenn.edu

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```

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