R help - Jan 2015 - nonmonotonic glm?

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):
o                                     o
      o                      o
          o           o
             o     o
                o


----------------------+------------------------
                           0

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.

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

Any suggestions welcome. Thanks!

Bill

	[[alternative HTML version deleted]]

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.

> On Jan 11, 2015, at 4:00 PM, Ben Bolker <bbolker at gmail.com> wrote:
> 
> 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.

As an alternative to Ben's recommendation, consider using a piecewise cubic
spline on the IV. This can be done using glm():

  # splines is part of the Base R distribution
  # I am using 'df = 5' below, but this can be adjusted up or down as
may be apropos
  require(splines)
  glm(DV ~ ns(IV, df = 5), family = binomial, data = YourDataFrame)


and as Ben's notes, is more generally supported in mixed models.

If this was not mixed model, another logistic regression implementation is in
Frank's rms package on CRAN, using his lrm() instead of glm() and rcs()
instead of ns():

# after installing rms from CRAN
require(rms)
lrm(DV ~ rcs(IV, 5), data = YourDataFrame)


Regards,

Marc Schwartz