# [R] nonmonotonic glm?

Marc Schwartz marc_schwartz at me.com
Sun Jan 11 23:23:19 CET 2015

```> 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

```

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