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

From   Maarten Buis <>
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.
> about (1): why is this a disadvantage?

I suspect that comment was part of a discussion of models that
estimated rho directly instead of atanhrho. In those cases using rho
instead of atanhrho can be a disadvantage for estimation algorithms.
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
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