Stephen P. Jenkins <[email protected]> asks:
> -_diparm- is a very useful utility for displaying ancillary parameters.
> These parameters are often estimated in a transformed metric, but we are
> interested in the estimate in the original metric. Handily, -_diparm-
> includes several standard transformations as options. My questions are:
> 1. In the example below, why does the value for the standard error of the
> ancillary parameter "rho" that gets pumped out by -_diparm- with the tanh
> option differ from the value that I calculated by hand.
[details omitted]
You had g(t) = (exp(2*t)-1) / (exp(2*t)+1)
g'(t) = 2*sqrt(exp(2*t))/((exp(2*t)+1)
Actually,
g'(t) = 4*exp(2*`t')/((exp(2*`t')+1)^2)
Even thought you are calculating a standard error, you don't take the square
root of g'(t). The variance of the transformation is (old var.)*{g'(t)}^2.
. di " std error of rho = " `set'*4*exp(2*`t')/((exp(2*`t')+1)^2)
std error of rho = .22367534
which agrees with your output from -biprobit-.
> 2. More generally, why does -_diparm- /not/ produce the "z" and "P > z"
> values? ... and yet it produces a c.i.? [I, for one, would like to see "z"
> and "P > z" reported as well.]
Because, generally when you transform a parameter from the estimation using
_diparm, a test of H_o:transformed parameter = 0 is not generally of any
interest. For example, if you exponentiate a parameter, a test of
H_o:exp(beta) = 0 is not as interesting as say a test of H_o:exp(beta)=1,
which is asymptotically equivalent to a test of H_o:beta=0, and that test is
already provided.
In the case of -biprobit-, a test of H_o: rho = 0 is asymptotically equivalent
to a test of H_o: athrho = 0, provided in the line just above -rho-. In this
case, had we wanted to display a test statistic for H_o:rho = 0, we would just
be displaying the "same" information twice, where by "same" I mean
asymptotically the same. Which of the two tests has the better small sample
properties? Who knows? We merely display the version of the test done in the
original estimation metric.
Programmers should note, however, that specifying the -prob- option to
-_diparm- will override the default behavior of not displaying the z-test for
transformed coefficients.
--Bobby
[email protected]
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