[R] Interpretation of loess

[Damon Wischik]

I have data on a number of patients. Essentially, for each patient I know
his/her age and whether he/she exhibits certain symptoms:

age  symptom1  symptom2
 50         0         1
 53         0         0
 70         1         1
  ...

I have started off by fitting simple models with forms like
  Prob(patient of age t shows symptom i) = 1 - Exp(-lambda_i * t)
or
  Prob(patient of age t shows symptom i) = 1 - A_i * Exp(-lambda_i * t)

Now, I want to plot my functional forms against the data, to get a rough
idea of how they look. If I do something simple like

  xyplot(symptom1 ~ age)

I get the data points, but it's hard to see what's going on. So I tried to
generate a smooth curve:

  xyplot(symptom1 ~ age,
    panel=function(x,y,...) {
      panel.xyplot(x,y,...)
      panel.loess(x,y,span=.75,...)
      })

This does generate a smooth curve which looks as if it's roughly in the
right place. But I feel uneasy about using a procedure I don't understand,
and I don't understand enough about loess to know if it's appropriate.

Is loess suitable for dealing with this sort of Bernoulli data? Is there a
different smoothing function which it would be "correct" for me to use?
Does anyone have recommendations about good ways to visualise this sort of
data?

Damon Wischik.