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From |
Evans Jadotte <evans.jadotte@uab.es> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Cumulative probabilities |

Date |
Wed, 21 Oct 2009 16:10:48 +0200 |

Austin Nichols wrote:

Evans Jadotte <evans.jadotte@uab.es> : 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 <evans.jadotte@uab.es> wrote:Austin Nichols wrote:Evans Jadotte <evans.jadotte@uab.es> : 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 <evans.jadotte@uab.es> 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, EvansHi 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* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Cumulative probabilities***From:*Evans Jadotte <evans.jadotte@uab.es>

**Re: st: Cumulative probabilities***From:*Evans Jadotte <evans.jadotte@uab.es>

**Re: st: Cumulative probabilities***From:*Austin Nichols <austinnichols@gmail.com>

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