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From |
Stas Kolenikov <[email protected]> |

To |
[email protected] |

Subject |
Re: st: problem with generated regressands and WLS |

Date |
Wed, 13 Oct 2010 15:34:47 -0500 |

Is this a multilevel model with interactions between levels? If yes, you'd want to estimate it as such, probably in -gllamm- or -xtmixed-. If not, you can still run this is the reduced form with all the interactions spelled out as a regular regression, although you'd probably want to correct for heteroskedasticity and/or clustering. 2010/10/13 Arka Roy Chaudhuri <[email protected]>: > I shall repost my earlier mail(using full names for the Greek > characters) as I just learnt that many might not be able to see the > Greek characters.I am extremely sorry for my mistake and the > inconvenience caused. > I wrote: > Thanks for the response. Sorry for not making my notation clearer- I > had used x for the independent variables in both the first and second > stage.Revising my notation: > > 1st stage: > y = alpha + beta1x1+ beta2x2 +................. +betanxn+ rho1z1 + rho2z2 + u > > 2nd stage: > beta= p + deltaq + error > > In the first stage y is the dependent variable and x1...xn, z1,z2 are > the independent variables, beta1-betan and rho1-rho2 are the parameters.alpha > and p are the intercepts in the first and second stage respectively. > The beta's(beta1.....betan) from the first stage constitute my dependent > variable in the second stage-since there are n of them I have n > observations for my dependent variable in the second stage. q is the > independent variable in the second stage and delta is the parameter > to be estimated. I also > have n observations of q. > Yes I do want to improve efficiency although I am not sure how. > Should I use the entire variance-covariance matrix of the beta's from the > first stage as the weighing matrix in the second stage?Or should I > just use the variance(from the first stage) of the betas as analytic > weights in the second stage?If I use the second method should not > non-zero covariances across the observations(beta's) affect my > results?Also if I am to use the entire variance-covariance matrix as > the weighing matrix how should I implement it in Stata?Please > advice.Thanks > > Arka > > 2010/10/12 Arka Roy Chaudhuri <[email protected]>: >> Thanks for the response. Sorry for not making my notation clearer- I >> had used x for the independent variables in both the first and second >> stage.Revising my notation: >> 1st stage: >> y = α + β1x1+ β2x2 +................. +βnxn+ ρ1z1 + ρ2z2 + u >> >> 2nd stage: >> β= p + δq + ε >> >> In the first stage y is the dependent variable and x1...xn, z1,z2 are >> the independent variables.α and p are the intercepts in the first and >> second stage respectively. >> The β's(β1, β2,......βn) from the first stage constitute my dependent >> variable in the second stage-since there are n of them I have n >> observations for my dependent variable in the second stage. q is the >> independent variable in the second stage. I also have n observations >> of them. >> Yes I do want to improve efficiency although I am not sure how. >> Should I use the entire variance-covariance matrix of the β's from the >> first stage as the weighing matrix in the second stage?Or should I >> just use the variance(from the first stage) of the betas as analytic >> weights in the second stage?If I use the second method shouldn't >> non-zero covariances across the observations(β's) affect my >> results?Also if I am to use the entire variance-covariance matrix as >> the weighing matrix how should I implement it in Stata?Please >> advice.Thanks >> >> Arka >> >> 2010/10/12 Austin Nichols <[email protected]>: >>> Arka Roy Chaudhuri <[email protected]>: >>> If you think beta is measured with an independent error, i.e. no >>> endogeneity or other endemic problems, you can ignore the fact that it >>> is generated; measurement error in the depvar is usually not a >>> problem. But perhaps you are looking for improved efficiency, and you >>> want to use the squared SE on beta as a measure of the error >>> variance--but it does not vary by observation--see the manual entry on >>> -vwls- for example. Is your "second stage" in matrix form using the >>> same y and x and so forth, or have you reused notation? >>> > > * > * 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/ > -- Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * 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: problem with generated regressands and WLS***From:*Arka Roy Chaudhuri <[email protected]>

**References**:**st: problem with generated regressands and WLS***From:*Arka Roy Chaudhuri <[email protected]>

**Re: st: problem with generated regressands and WLS***From:*Austin Nichols <[email protected]>

**Re: st: problem with generated regressands and WLS***From:*Arka Roy Chaudhuri <[email protected]>

**Re: st: problem with generated regressands and WLS***From:*Arka Roy Chaudhuri <[email protected]>

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