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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Cumulative probabilities |

Date |
Wed, 21 Oct 2009 09:44:17 -0400 |

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, >>> >>> 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 * * 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/

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

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

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

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

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