st: another question on the interpretation of rho and atanhrho

["Laura R." <laura.roh@googlemail.com>]

Dear Stata users,

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-.

Rho is the correlation of the error terms, and atanhrho its
arc-hyperbolic tangent.

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.

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

If interpreting atanhrho is better than interpreting rho in terms of
the correlation between the error terms of the two equations in a
model: Do I have to interpret only the coefficient? E.g. atanhrho =
-0.729, or do I have to look for the p-value = whether it is
significant?

Thank you very much for consideration.

LR
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