# wald test: compare quantile regression estimators from different samples

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## wald test: compare quantile regression estimators from different samples

 Dear all, I am trying to compare the estimated coefficients of a quantile regression model between two different samples. It is a Wald test, but I cannot find one way to do that in R.The samples are collected conditional on a specific characteristic and I would like to test whether such characteristic indeed affect the estimators. The problem in the test anova.rq is that the response variable should be the same, therefore I cannot use different samples. Consider as an example the following: Model 1:Q_y(tau|X,I=2) = X'beta(tau|I=2) Model2;Q_y(tau|X,I=3) = X'beta(tau|I=3) The first sample consider I=2 and the second I=3. I would like to test whether, at the quantile "tau", beta(tau|I=2) = beta(tau|I=3). I have already tried to design a Wald test like: W <- ((beta(tau|I=2)-beta(tau|I=3))^2)/var(beta(tau|I=2)-beta(tau|I=3)) But it doesn't work because var(beta(tau|I=2)-beta(tau|I=3)) is equal to NA. Is there any way to compare those estimators? Thank you very much! Best regards, Julia             [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: wald test: compare quantile regression estimators from different samples

 Dear Julia, One approach would be to fit a combined model for the two samples, with a factor (say, sample) and all interactions between sample and the other predictors -- something like rq(y ~ sample*(x1 + x2 + etc.)) -- and then compare via anova() to the additive model rq(y ~ sample + x1 + x2 + etc.) or, if you're interested in a difference in the intercepts and well as coefficients of the x's (as implied by your formulation), to rq(y ~ x1 + x2 + etc.). I hope this helps,  John -------------------------------- John Fox Senator William McMaster   Professor of Social Statistics Department of Sociology McMaster University Hamilton, Ontario, Canada http://socserv.mcmaster.ca/jfox> -----Original Message----- > From: [hidden email] [mailto:r-help-bounces@r- > project.org] On Behalf Of Julia Lira > Sent: November-19-11 6:49 AM > To: R list > Subject: [R] wald test: compare quantile regression estimators from > different samples > > > Dear all, > I am trying to compare the estimated coefficients of a quantile > regression model between two different samples. It is a Wald test, but > I cannot find one way to do that in R.The samples are collected > conditional on a specific characteristic and I would like to test > whether such characteristic indeed affect the estimators. The problem > in the test anova.rq is that the response variable should be the same, > therefore I cannot use different samples. > Consider as an example the following: > Model 1:Q_y(tau|X,I=2) = X'beta(tau|I=2) > Model2;Q_y(tau|X,I=3) = X'beta(tau|I=3) > The first sample consider I=2 and the second I=3. I would like to test > whether, at the quantile "tau", beta(tau|I=2) = beta(tau|I=3). > I have already tried to design a Wald test like: > W <- ((beta(tau|I=2)-beta(tau|I=3))^2)/var(beta(tau|I=2)-beta(tau|I=3)) > But it doesn't work because var(beta(tau|I=2)-beta(tau|I=3)) is equal > to NA. > Is there any way to compare those estimators? > Thank you very much! > Best regards, > Julia > [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-> guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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