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

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

Dear Maarten,

thanks for the quick response.

So in one of my estimations, atanhrho is -2.489 and rho is -0.244, but
the p-value of atanhrho is > 0.100, which means not significant based
on at least 10%-significance. Now which of the 2 interpretations are
correct:

(1) "persons who are less likely to do/have X, are more likely to
do/have (more of) Y, because the error terms are correlated, shown by
a negative rho and atanhrho"

or

(2) "no significant correlation between the error terms because for
atanrho p>0.100, so no result regarding the dependent variables
(despite that rho and atanrho not equal to 0.000)"


Thinking about interpreting atanrho, not rho, came from Roodman's
(2009) working paper, p. 26, but maybe I missunderstood it.
http://www.cgdev.org/files/1421516_file_Roodman_cmp_FINAL.pdf

LR



2012/5/7 Maarten Buis <maartenlbuis@gmail.com>:
> 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
> Germany
>
>
> http://www.maartenbuis.nl
> --------------------------
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