# [R] bilinear regression

Christos Hatzis christos at nuverabio.com
Tue Jul 18 20:07:40 CEST 2006

```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 at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Crabb, David
Sent: Tuesday, July 18, 2006 1:36 PM
To: r-help at 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.

David

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

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