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# Re: st: Symmetry Test

 From Alex Olssen To statalist@hsphsun2.harvard.edu Subject Re: st: Symmetry Test Date Thu, 12 May 2011 12:58:09 +1200

```Dear Ana,

I don't really understand what you are asking.

"Based on your routine below, how could I distinguish the parameters fo
interst for the symmetry test (g12 g21 g31 g13...) from the other
parameters of the model?"

What do you mean by "distinguish"?

"Still, sometimes (for other exercises I'm planning to do), I'd like to
keep only some parameters from the model and make some test."

Are you asking about implementing exclusion (zero) restrictions on
some parameters?
You should be able to do this by removing the parameters you want to
exclude from the

scalar `name' = `at'[1,x]

list, and delete the parameter and its associated variable from the

replace w`i' = ...

list.

How can I "view "and "use" the some parameters from the model?
In the case of ther symmetry test (if I only use the unrestricted
model), I tried to use something like [eq_1]g12 = [eq_2]g2, but stata
(actually, me!) always complain with something about: "equation [1]

I don't understand what you are asking?  Do you want to test the
single symmetry constraint g12 = g21 on its own?  That doesn't seem
very sensible.

If you want to test whether symmetry holds overall this should be
simple.  In your second email you presented estimates from the
constrained model, I presume you have the estimates for the
unconstrained model - all you need to do to see if symmetry can be
rejected for your data and model is to look at the likelihood ratio
statistics.

Kind regards,

Alex

On 12 May 2011 05:22, Ana <analunhb@gmail.com> wrote:
> Dear Alex,
> Thank you very much for your prompt response and for your help.
> I'm still with a silly question about the symmetry test.
> Based on your routine below, how could I distinguish the parameters fo
> interst for the symmetry test (g12 g21 g31 g13...) from the other
> parameters of the model?
>
> Still, sometimes (for other exercises I'm planning to do), I'd like to
> keep only some parameters from the model and make some test.
> How can I "view "and "use" the some parameters from the model?
> In the case of ther symmetry test (if I only use the unrestricted
> model), I tried to use something like [eq_1]g12 = [eq_2]g2, but stata
> (actually, me!) always complain with something about: "equation [1]
> Here is the estimates/results I can get from using nlsur quaids based
> on my data:
>
> FGNLS regression
>
> Equation        Obs  Parms       RMSE   R-sq     Constant
>
> 1           w1      26784      .   .4765981     0.7898*      (none)
> 2           w2      26784      .   .5114466     0.3840*      (none)
> 3           w3      26784      .   .4442428     0.3384*      (none)
>
> * Uncentered R-sq
>
>
> Coef.   Std. Err.      z        P>z     [95% Conf. Interval]
>
> /a1    1.461867   .0214499    68.15     0.000     1.419826    1.503908
> /a2     .316065   .0206387    15.31     0.000     .2756139    .3565162
> /a3     .292436   .0186566    15.67     0.000     .2558698    .3290022
> /b1   -.6577555   .0084112   -78.20     0.000    -.6742412   -.6412698
> /b2   -.0759965    .007929    -9.58     0.000     -.091537    -.060456
> /b3   -.1354168   .0072402   -18.70     0.000    -.1496074   -.1212263
> /g11   -1.520055    .045084   -33.72    0.000    -1.608418   -1.431692
> /g12   -.0109163   .0207699    -0.53    0.599    -.0516245     .029792
> /g13    -.399293   .0196141   -20.36    0.000    -.4377359   -.3608502
> /g22   -.0250661   .0151875    -1.65    0.099     -.054833    .0047007
> /g23   -.0521908     .01053    -4.96    0.000    -.0728293   -.0315523
> /g33   -.0643672   .0144734    -4.45    0.000    -.0927346   -.0359998
> /l1    .0855152   .0007695   111.13     0.000      .084007    .0870233
> /l2    .0143847   .0007215    19.94     0.000     .0129705    .0157989
> /l3     .021068   .0006599    31.93     0.000     .0197747    .0223613
>
>
> .
> end of do-file
>
>
> Thanks a lot in advance.Again.
> Best regards,
> Ana.
>
> 2011/5/10 Alex Olssen <alex.olssen@gmail.com>:
>> Dear Ana,
>>
>> I presume you removed the symmetry restriction by adjusting the
>> variables `gij' = `gji' in the nlsurquaids.ado file.
>>
>> To test the symmetry restrictions you could,
>>
>> 1) rename the program without symmetry as nlsurquaids2.ado
>>
>> 2) run the program without symmetry and obtain the log likelihood
>>
>> scalar llnosymmetry = e(ll)
>>
>> 3) run the program with symmetry (the original nlsurquaids) and obtain
>> the log likelihood
>>
>> scalar llsymmetry = e(ll)
>>
>> 4) implement the likelihood ratio test
>>
>> the statistic is given by 2*(llnosymmetry - llsymmetry)
>> which follows a chi-squared distribution with the number of
>> restrictions as the degrees of freedom.
>>
>> Kind regards,
>>
>> Alex Olssen
>>
>> On 11 May 2011 11:37, Ana <analunhb@gmail.com> wrote:
>>> Dear Statalisters,
>>>
>>> I'm using Brian Pois nlsurquaids.ado to estimate a Four Demand Equations.
>>> I've excluded the symmetry restriction from this program in order to
>>> test this restriction.
>>>
>>> My model has the form:
>>> nlsur quaids @ w1 w2 w3 lnp1-lnp4 lnm, ifgnls nequations(3) param(a1
>>> a2 a3 b1 b2 b3 g11 g12 g13 g21 g22 g23 g31 g32 g33 l1 l2 l3) nolog
>>>
>>>
>>> Does anybody know how to test the symmetry restriction?
>>> I want to test if: g12=g21 g13=g31 g23=g32!
>>>
>>> Thanks a lot in advance.
>>> Best regards,
>>> Ana.
>>> *
>>> *   For searches and help try:
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>>> *   http://www.stata.com/support/statalist/faq
>>> *   http://www.ats.ucla.edu/stat/stata/
>>>
>>
>> *
>> *   For searches and help try:
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>> *   http://www.ats.ucla.edu/stat/stata/
>>
>
> *
> *   For searches and help try:
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>

*
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```