Re: [R] bilinear regression

From: Christos Hatzis <christos_at_nuverabio.com>
Date: Wed 19 Jul 2006 - 04:07:40 EST


It appears that you might have a latent (hidden) explanatory variable that causes the two-population appearance. If you have some ideas on what that other factor might be, you could try two separate linear regressions for each value of the latent factor and compare the slopes and intercepts. You can then do some formal tests on the slopes and intercepts to see if you can further simplify the model. Depending on what you find, you can formulate a linear regression model that incorporates such dependence on the slopes or intercepts to fit the "bilinear" trend.

You might find helpful the discussion and example in Ch.10 of Venables & Ripley, 4th ed, that introduces the concepts behind random and mixed effects models.

-Christos

Christos Hatzis, Ph.D.
Vice President, Technology
Nuvera Biosciences, Inc.
400 West Cummings Park
Suite 5350
Woburn, MA 01801
Tel: 781-938-3830
www.nuverabio.com  

-----Original Message-----
From: r-help-bounces@stat.math.ethz.ch
[mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Crabb, David Sent: Tuesday, July 18, 2006 1:36 PM
To: r-help@stat.math.ethz.ch
Subject: [R] bilinear regression

I think this is an easy question, but I would be grateful for any advice on how to implement this in R.

I simply have a response variable (y) that I am trying to predict with one explanatory variable (x) but the shape of the scatter plot is distinctly bilinear. It would be best described by two straight lines. Is there a way of fitting a linear model to give me a bilinear fit and (more importantly) automatically determine the 'cut off' point? I would also want some statistic to convince myself that the bilinear fit is better.

Many thanks for your help.

David

Dr. David Crabb
Department of Optometry and Visual Science, City University, Northampton Square, London EC1V OHB
Tel: 44 207 040 0191 d.crabb@city.ac.uk
http://www.city.ac.uk/optometry/html/david_crabb.html



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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. Received on Wed Jul 19 04:12:20 2006

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