Hello everyone,

I am trying to model some data regarding a predator prey interaction
experiment (n=26). Predation rate is my response variable and I have 4
explanatory variables: predator density (1,2,3,4 5), predator size, prey
density (5,10,15,20,25,30) and prey type (3 categories). I started with
several linear models (glm) and found (as expected) that prey and predator
density were non-linear related to predation rates. If I use a log
transformation on these variables I get really nice curves and an adjusted
R2 of 0.82, but it is not really the right approach for modelling
non-linear relationships. Therefore I switched to non-linear least square
regression (nls). I have several predator-prey models based on existing
ecological literature e.g.:

model1 <- nls(rates ~ (a * prey)/(1 + b * prey), start = list(a = 0.27,b =
0.13), trace = TRUE) ### Holling's type II functional response

model2 <- nls(rates ~ (a*prey)/(1+ (b * prey) + c * (pred -1 )), start =
list(a=0.22451, b=-0.18938, c=1.06941), trace=TRUE, subset=I1) ###
Beddington-**DeAngelis functional response

These models work perfectly, but now I want to add prey type as well. In
the linear models prey type was the most important variable so I don't want
to leave it out. I understand that you can't add categorical variables in
nls, so I thought I try a generalized additive model (gam).

The problem with the gam models is that the smoothers (both spline and
loess) don't work on both variables because there are only a very
restricted number of values for prey density and predator density. I can
manage to get a model with a single variable smoothed using loess. But for
two variables it is simply not working. The spline function does not work
at all because I have so few values (5) for my variables (see model 4).

model3 <- gam(rates~ lo(pred, span=0.9)+prey) ## this one is actually
working but does not include a smoother for prey.

model4 <- gam(rates~ s(pred)+prey) ## this one gives problems:
*A term has fewer unique covariate combinations than specified maximum
degrees of freedom*

My question is: are there any other possibilities to model data with 2
non-linear related variables in which I can also include a categorical
variable. I would prefer to use nls (model2) with for example different
intercepts for each category but I'm not sure how to get this sorted, if it
is possible at all. The dataset is too small to split it up into the three
categories, moreover, one of the categories only contains 5 data points.

Any help would be really appreciated.

With kind regards,
-- 
Robbie Weterings
*Project Manager Cat Drop Thailand

** Tel: +66(0)890176087
*
65/13 Mooban Chakangrao, Naimuang Muang
Kamphaeng Phet 62000, Thailand
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