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# Re: st: another question on the interpretation of rho and atanhrho

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: another question on the interpretation of rho and atanhrho Date Mon, 7 May 2012 17:43:30 +0200

```On Mon, May 7, 2012 at 5:20 PM, Laura R. wrote:
> I have a question concerning rho and atanhrho, which you receive
> estimating, e.g. -cmp- models, or Heckman selection models with
> maximum likelihood using -heckman-.
>
> What many people do is, they look at rho, and if it is not zero but
> positive (+) or negative (-), they interpret it as "people who are
> more(+)/less(-) likely to do/have X (dependent variable from the
> selection equation), are more likely to do/have higher Y (dependent
> variable of the main equation)".
>
> First question: Can you say that solely based on the coefficient of
> rho? Because, in the model types I named above, there is no p-value
> reported for rho, i.e., no significance level.

atanhrho is 0 when rho is 0, so the test that atanhrho is 0
corresponds with the test that rho is 0.

> Next, I have read that one should rather interpret atanhrho instead of
> rho, because (1) rho is bounded between -1 and 1, while atanhrho is
> unbounded, (2) rho is very dependend on the covariates included in the
> model.
>

I suspect that comment was part of a discussion of models that
estimated rho directly instead of atanhrho. In those cases using rho
However, unless you want to program your own estimators you can safely
ignore that debate. All you need to know is that both -heckman- and
-cmp- maximize the log likelihood with respect to the atanhrho, and
from that you can derive the rho.

> about (2): why does rho strongly depend on the covariates included,
> but atanhrho not? (if that was a correct information)

It does not.

-- Maarten

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

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