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

[David Quinn <dxquinnx@gmail.com>]

Thanks, Maarten.  Sorry, I am kind of new to writing my own STATA
code, so I didn't know what -est store- was doing. I know you're
comparing the two models via a LR test, but I wasn't exactly sure
that's what was going on with the -est store- command.  I now
understand that you were storing the two models.

My last remaining question picks up on the first one I asked.  I know
to do a LR test, you have to compare constrained and unconstrained
models.  I'm used to doing this with typical OLS and logit
regressions, though, where the constraints are something different.
So, for clarification purposes: you will always set rho to 0 for the
constrained model when doing a LR test using heckprob, biprobit, etc.?
 In other words, to do the LR test, the value that goes in parentheses
after atanh will still always be 0, not the value of rho reported by
-cmp- (or -heckprob- or -biprobit-, etc.), right?  Let's say -cmp-
reported the value of rho to be .4567.  In this case, when doing the
LR test, the value that goes in parentheses after atanh will still be
0, not .4567.  Is this correct?

Thanks,
--Dave

On Fri, Mar 4, 2011 at 4:41 AM, Maarten buis <maartenbuis@yahoo.co.uk> wrote:
> --- 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
> --------------------------
>
>
>
>
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