Hi, all. I'm trying to use some linear regression models in which both the dependent and independent variables are measured with some error. To make things worse, while the errors in the dependent variable are uniform, the errors in the independent (or explanatory, or "x") variables can be heteroskedastic. I've been looking at the book _Measurement Error Models_ by Fuller (1987). I'm wondering whether anybody knows any other references on the subject, and whether anyone has written S or R code that handles these kinds of problems. (As far as I can tell, the usual lm and glm functions don't; if I'm wrong, that's great.) Thanks for any pointers. Matt Wiener Laboratory of Neuropsychology NIMH, NIH Bethesda, MD USA -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
regression with uncertainty in both variables
3 messages · Matthew Wiener, Brian Ripley, Stuart Luppescu
[I don't think blanketing both S and R help on this is a good idea.]
On Wed, 14 Apr 1999, Matthew Wiener wrote:
I'm trying to use some linear regression models in which both the dependent and independent variables are measured with some error. To
Notation: that is not a `regression' model.
make things worse, while the errors in the dependent variable are uniform, the errors in the independent (or explanatory, or "x") variables can be heteroskedastic. I've been looking at the book _Measurement Error Models_ by Fuller (1987). I'm wondering whether anybody knows any other references on the subject, and whether anyone has written S or R code that handles these kinds of problems. (As far as I can tell, the usual lm and glm functions don't; if I'm wrong, that's great.)
Well, there are of lots of other references, even one by me, but that is
the main book. If lm and glm did this they would be wrong: it is a
different statistical model. There are several Fortran solutions on statlib
in multi/leiv?
1. Programs for best line fitting with errors in both coordinates.
2. D. York, "Least squares fitting of a straight line", Canadian
Journal of Physics, 44, 1079-1086, 1986.
G. Fasano and R. Vio, "Fitting straight lines with errors on both
coordinates", Newsletter of Working Group for Modern
Astronomical Methodology, No. 7, 2-7, Sept. 1988.
B.D. Ripley and M. Thompson, "Regression techniques for the
detection of analytical bias", Analyst, 112, 377-383,
1987.
and I have seen an S interface somewhere (multiv?). Today, I would take the
algorithm in the last of those papers and re-write it in S in a few
minutes. A project that has, several times, nearly made the MASS library
and one I set as a exercise in my linear models course.
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
On 15-Apr-99 Matthew Wiener wrote:
Hi, all. I'm trying to use some linear regression models in which both the dependent and independent variables are measured with some error. To make things worse, while the errors in the dependent variable are uniform, the errors in the independent (or explanatory, or "x") variables can be heteroskedastic. I've been looking at the book _Measurement Error Models_ by Fuller (1987). I'm wondering whether anybody knows any other references on the subject, and whether anyone has written S or R code that handles these kinds of problems. (As far as I can tell, the usual lm and glm functions don't; if I'm wrong, that's great.)
This really has nothing to do with R (I don't think, anyway -- could it be done with lme?), but we do this kind of thing all the time using the HLM program (Bryk, Raudenbush and Congden). At level 1, the outcome is the measure divided by the standard error, and a series of dummies, one for each type of measure, divided by the standard error. The level 1 variance is fixed at 1.0. These 1/s.e., come down to level 2, where they can be considered ``true score'' estimates of the measures, as outcomes, or as predictors, if you use the latent variable regression capability of HLM. I believe this capability is in the latest version of the HLM program (maybe not -- we use a pre-release version here), and the procedure should be detailed in the 2nd edition of Bryk and Raudenbush, _Hierarchical Linear Models_, to be published (by Sage again?) this summer or fall. ______________________________________________________________________ Stuart Luppescu -=-=- University of Chicago ºÃʸ ¤ÈÃÒÆà Èþ¤ÎÉã(EUC) -=-=- s-luppescu at uchicago.edu http://www.consortium-chicago.org/people/sl/sl.html ICQ #21172047 AIM: psycho7070 "Ubi non accusator, ibi non judex." (Where there is no police, there is no speed limit.) -- Roman Law, trans. Petr Beckmann (1971)
Sent on 15-Apr-99 at 09:22:12 with xfmail
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