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Re: st: Cumulative probabilities
Austin Nichols wrote:
Evans Jadotte <[email protected]> :
Rabe-Hesketh and Skrondal (2005: 167) are not predicting in that
equation--they are describing a model of unit-specific variance in e
with common cut points in an ordered probit framework. Presumably,
this is not related to your desideratum. I can't see Gunther and
Harttgen (July 2009. "Estimating Vulnerability to Idiosyncratic and
Covariate Shocks." World Development 37(7):1222-1234) so maybe you can
describe what they are actually doing.
On Wed, Oct 21, 2009 at 9:08 AM, Evans Jadotte <[email protected]> wrote:
Austin Nichols wrote:
Evans Jadotte <[email protected]> :
What's z in (z-xb-...) below? If you are calculating an estimate of e
in the numerator, and dividing by the estimate of the SD of e, then
you are calculating the Z score of the idiosyncratic error, and
Phi(Z). What is this for? Can you provide refs for what "some books
suggest" ?
On Tue, Oct 20, 2009 at 11:16 AM, Evans Jadotte <[email protected]>
wrote:
Hello listers,
Sorry for sending this message again but I realized some characters did
not
appear too well.
I am estimating cumulative probabilities of the following function:
Yijk = b0 +b1Xijk + eijk + u.jk + u..k
where u.jk and u..k are two random intercepts with variance Sigma^2
(u.jk)
and Sigma^2 (u..k). The variance of my raw residuals is Sigma^2 (eijk).
The
cumulative probabilities I want to calculate are of the form:
Phi((z-xb-uhat.jk - uhat../k/)/sqrt(?))
where Phi denotes the standard normal cumulative density. My question is:
should the square root, sqrt, in the denominator contain just the
variance
of the raw residuals, i.e. Sigma^2 (eijk), as some books suggest? Or
should
it bear, according to my logic, the total variance of the model, which
would
be the sum Sigma^2 (e ijk) + Sigma^2 (u.jk) + Sigma^2 (u..k)? And
finally,
what would be the statistics rationale for using the former instead of
the
latter formula?
Thanks in advance,
Evans
Hi Austin,
z is a threshold (e.g. a deprivation line) and xb are the fitted values
(yhat) of the fixed part of the estimation. The Phi is to calculate the
cumulative probabilities of the function:
Pr(Yijk < z) = Phi((z-xb-uhat.jk - uhat..k)/sqrt(?))
For instance, in their book "Multilevel and Longitudinal Modelling Using
Stata", Rabe-Hesketh and Skrondal (2005: 167), section 5.11, use only the SD
of e in the denominator, other papers adopt the same stance (e.g.
"Estimating Vulnerability to Idiosyncratic and Covariate Shocks": Gunther
and Harttgen (2009)). I am trying to understand the statistics rationale for
not accounting for the variances of the random intercepts Sigma^2 (u.jk)
and Sigma^2 (u..k) in the denominator.
Thanks!
Evans
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Yes indeed, Rabe-Hesketh and Skrondal (2005: 167)is not directly related to my desideratum. However, the method should be standard I suppose. And what Gunther and Harttgen (2009)are doing is estimating a vulnerability index with the Pr(Yijk < z). My model is an extension of theirs though since they do not have the two random intercepts I incorporated in the numerator (in fact I believe they should have one random intercept in the numerator Phi (.) for consistency of their model. I would send the Gunther and Harttgen (2009)but I was suggested not to attach files in this thread.
Thanks,
Evans
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* http://www.stata.com/support/statalist/faq
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