Re: st: "cmp" command and rho LR test statistic for SUR bivariate probit model

[Maarten buis <maartenbuis@yahoo.co.uk>]

--- On Thu, 3/3/11, David Quinn wrote:
> 1.) The first question is in regards to the command:
> -constraint 1 [atanhrho_12]_cons = `=atanh(0)'-.  When you
> run -cmp-, it reports the value of atanhrho_12 as 
>-.0886333 (and this is the Fisher's z transformed 
> correlation), and the value of rho_12 as -.088402.  So,
> what you are doing with the -constraint- command is telling
> to STATA to set atanhrho_12 to a specific value when running
> the model?  If so, does the value "0" that is in parentheses
> in your example represent the value of rho_12 (i.e., 
> -.088402)?  Am I understanding that correctly?

You asked for a likelihood ratio test. This means you need to
estimate two models, one constrained and one unconstrained, 
and than you compare the likelihoods of these two models. The
first model I estimated is the unconstrained model, i.e. I let
Stata determine whatever value of rho (well, strictly speaking
Fisher's z transformed rho) it liked. The second model I 
constrained rho to be 0, and to make sure that Stata 
understood me I needed to translate that to Fisher's z scores.
I did this by saying `=atanh(0)', the 0 is the rho, and 
whatever `=atanh(0)' evaluates to is the Fisher's z 
transformation of 0 (actualy atanh(0)=0, I just did this for
completeness).
 
> 2.) The second question is in regards to the command: -est
> store a-  and -est store b-. What exactly are these doing?  

Remember a likelihood ratio test compares two models. In 
order to do so, Stata needs to store them somehow. This is 
what -est store- does. 
 
> 3.) To answer the third question, perhaps I first need to
> understand what is going on with the second question.  But
> regardless, I'm not clear exactly what the likelihood-ratio
> test at the end is testing. What are you comparing with 
> "a" and "b"?

It compares model a with model b, so the null hypothesis is
whatever restriction you imposed in model b. In our case that
restriction is that is atanhrho_12 = `=atanh(0)', which is 
just a complicated way of saying rho = 0.
 
Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------


      

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/