[R] nonmonotonic glm?

[Ben Bolker]

Stanislav Aggerwal <stan.aggerwal <at> gmail.com> writes:

> 
> I have the following problem.
> DV is binomial p
> IV is quantitative variable that goes from negative to positive values.
> 
> The data look like this (need nonproportional font to view):


  [snip to make gmane happy]

> If these data were symmetrical about zero, 
> I could use abs(IV) and do glm(p
> ~ absIV).
> I suppose I could fit two glms, one to positive and one to negative IV
> values. Seems a rather ugly approach.
> 

[snip]


  What's wrong with a GLM with quadratic terms in the predictor variable?

This is perfectly respectable, well-defined, and easy to implement:

  glm(y~poly(x,2),family=binomial,data=...)

or   y~x+I(x^2)  or y~poly(x,2,raw=TRUE)

> (To complicate things further, this is within-subjects design)

glmer, glmmPQL, glmmML, etc. should all support this just fine.