[R] interaction terms in regression analysis

[John S. Walker]

G'day,

My problem is I'm not sure how to extract effect sizes from a nonlinear 
regression model with a significant interaction term.

My data sets are multiple measurements of force response to an agonist 
with two superimposed treatments each having two levels.
This is very similar to the Ludbrook example in Venables and Ripley.

The experiment is that a muscle is exposed to an agonist and the force 
response is measured. The resulting data is fit to a logistic fit (a 
three parameter rather than the four parameter used by Ludbrook) . This 
is done for each combination of two factors (treatmentA and Treatment 
B) each having two levels (- and +). Each set of measurements is 
obtained on a muscle from a different animal (i.e. each dose response 
curve represents an independent experiment).

The data are stored as follows:

expt	treatA treatB dose force

I use a groupedData object mydata=groupedData(force ~ dose | expt)

I used an nlme obect to model the data as follows (pseudocode):

myfit <- nlme(force ~ ssThreeParLogistic(dose, upper, ed50,slope), 
fixed=list(ed50~factor(treatmentA)*factor(treatmentC)))


The ThreeParLogistic is a properly debugged and fully functional 
selfstarting object that I wrote- no problem here. I also included 
terms for the other terms; upper and slope, but my main focus is on the 
ed50 so that's all I've included here

Running an anova on the resulting object I found theA -/B- (control) to 
be significantly different from zero, treatment A had no significant 
effect, treatment B was significantly different and there was a 
significant interaction between treatment A and treatment B.

  The interaction term is likely to be real. The treatments are on 
sequential steps in a pathway and treatment A may be blocking the 
effect of treatment B, i.e. treatment A alone has no effect because it 
blocks a pathway that is not active, treatment B reduces force via this 
pathway and treament A therefore blocks the effect of treatment B when 
used together.

So back to my question
How do I extract estimates of the parameters from my model object for a 
specific combination of factors including the interaction term.
  i.e. what is the ed50 (and std err) for A-/B-, A+/B-, A-/B+, A+/B+ ?


Regards



John S. Walker, PhD
Department of Physiology & Biophysics
University of Illinois at Chicago
835 Sth Wolcott Ave MC 901
Chicago IL 60612
USA

email: jsw9c at uic.edu
phone: 1 312 355 0150
fax: 1 312 355 0261

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