Hi all! I try to estimate a statistic of the form: (x1-x2)/(y1-y2), where x1,x2,y1,y2 represent variable means, so each has an estimate and standard error associated with it. How is it possible to estimate the mean and the variance of this ratio? Thank you! [[alternative HTML version deleted]]
two options are the Delta method (see, e.g., function deltamethod() in
package 'msm'), and the Bootstrap method (check package 'boot').
I hope it helps.
Best,
Dimitris
----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven
Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
http://www.student.kuleuven.be/~m0390867/dimitris.htm
----- Original Message -----
From: "Irene Mantzouni" <ima at difres.dk>
To: <r-help at stat.math.ethz.ch>
Sent: Monday, February 18, 2008 3:22 PM
Subject: [R] mean and variance of ratio
> Hi all!
>
>
>
> I try to estimate a statistic of the form: (x1-x2)/(y1-y2), where
> x1,x2,y1,y2 represent variable means, so each has an estimate and
> standard error associated with it.
>
> How is it possible to estimate the mean and the variance of this
> ratio?
>
>
>
> Thank you!
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
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Dear Irene, if you have a vector of estimates of x1, x2, y1, y2 and the corresponding estimated variance-covariance matrix (accessible through the method "vcov"), then one possibility is to use the function delta.method() in the package alr3 (on CRAN). This function returns: 1) an estimate of the ratio (which is simply obtained by plugging in the estimates of x1, x2, y1, y2) and 2) an approximate, large-sample standard error of the estimated ratio Christian
Hi Irene, The result depends on the joint distribution of x1,x2,y1,y2. The mean (or the variance) not always exist (if, for example, all of them are independent and normally distributed). One possibility to estimate mean and variance is to use simulation (once you verify that they exist!!!). Regards, Moshe. --- Irene Mantzouni <ima at difres.dk> wrote:> Hi all! > > > > I try to estimate a statistic of the form: > (x1-x2)/(y1-y2), where > x1,x2,y1,y2 represent variable means, so each has an > estimate and > standard error associated with it. > > How is it possible to estimate the mean and the > variance of this ratio? > > > > Thank you! > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org 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. >