R help - Sep 2011 - Hysteresis modeling and simulation

Can anyone suggest a package or code for modeling a hysteresis process in R?


I'm currently modeling a certain dataset with a GAM using mgcv, something
like

gam(y~ s(x, by=z) + z, family = Gamma(link=log),data=data)

and getting fits with about 9 estimated degrees of freedom in the smooth for
each value of z.  FWIW, z is a treatment applied to a system which should
have made an improvement, and I'm trying to estimate the magnitude of that
improvement (the aggregated change in y) assuming the x values did not vary.

Looking at plots of y vs. x with lines connecting points in time order makes
it clear that a significant hysteresis process is at work, and I conjecture
I can reduce estimation uncertainty by modeling that hysteresis explicitly.
 I'm looking for a package that


   - can model hysteresis and return estimates of the fit in both the low
   and high states as well as statistics on the upper and lower hysteresis
   thresholds
   - has flexibility in the form of the model in the high and low states
      - While the current model uses GAMs because of the nature of the
      nonlinearity (I tried a number of other models before settling
on this as a
      reasonable compromise), it may be that modeling the hysteresis directly
      would simplify the model a bit.  Still, I'd like the flexibility
to use GAMs
      if called for.
   - produces output that facilitates my using simulation to produce
   estimates of uncertainty in my inferences when I have new data for x, for
   example.

I've searched R-bloggers, R-help, Google, and browsed a number of package
manuals and vignettes.  I've also looked at the cusp package; that and
depmixS4 seem the most attractive so far, but I think it would take a bit of
effort to make those work.  My hysteresis problem is not quite a hidden
Markov model, although the notion of putting covariates on transition
parameters in depmixS4::depmix() seems promising.  I've also thought of
coding the model in JAGS.

Before I go to that work, I thought I'd ask here to see if someone knows a
good, existing solution.

Thanks,

Bill

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Hi Bill,

I once modelled a hysteresis phenomenon (on binary data) with a simple 
logistic model. I am not sure I understand how this pattern appears in 
your data, but in my previous analyses, it appeared as an order effect: 
The response increased in probability later with increasing than with 
decreasing values of the predictor.

I then simply created a binary variable for the decreasing and 
increasing conditions, and the coefficient on this variable was a direct 
and testable measure of hysteresis.

In some cases, you can directly model the bimodal conditional 
distribution of the response. This is what I did here with a beta 
distribution for continuous bounded responses:

http://webcolleges.uva.nl/mediasite/Viewer/?peid=c7a7b041327f4db09dc2fc3a7872aa5a1d

HTH,

Best,

Yvonnick Noel
University of Brittany, Rennes 2
France