# [R] classification by nls and anova

Maciej.Hoffman-Wecker@evotecoai.com Maciej.Hoffman-Wecker at evotecoai.com
Wed May 29 16:42:30 CEST 2002

```Dear R-users,

I'd appreciate your statistical opinion on the following problem.

I'm fitting the four parameter logistic model [f(x) = a + (b - a)/(1 +
exp((c - x)*d))] to assay data.
We have a lot of samples to fit and my aim is to classify these samples
into following groups:

1. no interrelation
too low concentration

2.   only full saturation
too high concentration

3. only starting interrelation
results going up, not reaching the turning point
too low concentration

4. only starting saturation
results starting above the turning point, going up, reaching the
saturation
hence too high concentration

5. only the linear area
no start and saturation
hence too low concentration range

6. full interrelation
including starting interrelation and saturation

Is there a way to model these classes, and compare their significance by
means of an
analysis of the residuals (ANOVA)?

Something like

model 1 = linear & constant =~ 0 & slope = 0
model 2 = linear & constant =~ 1 & slope = 0
model 3 = ???? some curvature
model 4 = ???? some curvature
model 5 = linear & slope > 0
model 6 = full four parameter logistic model

with the procedure:

Starting with the linear model and testing for any curvature.
-> curvature not significant
==> result = model 1, 2 or 3, depending on significance of slope and
intercept
-> curvature significant
-> testing for full logistic model
-> logistic model significant
==> result = logistic model
-> logistic model not significant
==> result = a curvature model (model 3 or 4), depending on the
parameters

Is this a reasonable and feasible procedure? And if so, what kind of model
might be appropriate
for the classes 3 and 4?

Hope someone has the time to give me an answer or any advice on any other
approach.