[R] nonmonotonic glm?

[Vito M. R. Muggeo]

dear Stanislav,
Your data show two slopes with a kink at around 0. Thus, yet another 
approach would be to use segmented regression to fit a piecewise linear 
relationship with unknown breakpoint (being estimated as part of model 
fitting). While the resulting fitting is likely to be (slightly) worse 
than the one coming from splines, the advantage is that you get 
interpretable parameter estimates, left and right slopes and breakpoint. 
Relevant syntax is

library(segmented)
o<-glm(DV~IV, data= YourDataFrame, family=binomial)
os<-segmented(o, ~IV, psi=0)

vito


Il 12/01/2015 13.45, Stanislav Aggerwal ha scritto:
> Thanks very much Marc and Ben for the helpful suggestions
>
> Stan
>
> On Sun, Jan 11, 2015 at 10:28 PM, Ben Bolker <bbolker at gmail.com> wrote:
>
>> If you're going to use splines, another possibility is mgcv::gam (also
>> part of standard R installation)
>>
>>    require(mgcv)
>>    gam(DV ~ s(IV), data= YourDataFrame, family=binomial)
>>
>> this has the advantage that the complexity of the spline is
>> automatically adjusted/selected by the fitting algorithm (although
>> occasionally you need to use s(IV,k=something_bigger) to adjust the
>> default *maximum* complexity chosen by the code)
>>
>>
>> On Sun, Jan 11, 2015 at 5:23 PM, Marc Schwartz <marc_schwartz at me.com>
>> wrote:
>>>
>>>> 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
>>>
>>>
>>
>
> 	[[alternative HTML version deleted]]
>
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-- 
==============================================
Vito M.R. Muggeo
Dip.to Sc Statist e Matem `Vianelli'
Università di Palermo
viale delle Scienze, edificio 13
90128 Palermo - ITALY
tel: 091 23895240
fax: 091 485726
http://dssm.unipa.it/vmuggeo

28th IWSM
International Workshop on Statistical Modelling
July 8-12, 2013, Palermo
http://iwsm2013.unipa.it