nonmonotonic glm?

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nonmonotonic glm?

Stanislav Aggerwal
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]]

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Re: nonmonotonic glm?

bbolker
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.

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Re: nonmonotonic glm?

Marc Schwartz-3

> On Jan 11, 2015, at 4:00 PM, Ben Bolker <[hidden email]> 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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Re: nonmonotonic glm?

bbolker
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 <[hidden email]> wrote:

>
>> On Jan 11, 2015, at 4:00 PM, Ben Bolker <[hidden email]> 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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Re: nonmonotonic glm?

Stanislav Aggerwal
Thanks very much Marc and Ben for the helpful suggestions

Stan

On Sun, Jan 11, 2015 at 10:28 PM, Ben Bolker <[hidden email]> 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 <[hidden email]>
> wrote:
> >
> >> On Jan 11, 2015, at 4:00 PM, Ben Bolker <[hidden email]> 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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Re: nonmonotonic glm?

Vito Michele Rosario 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 <[hidden email]> 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 <[hidden email]>
>> wrote:
>>>
>>>> On Jan 11, 2015, at 4:00 PM, Ben Bolker <[hidden email]> 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]]
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--
==============================================
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

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Re: nonmonotonic glm?

Michael Dewey
Comments in line

On 12/01/2015 13:13, Vito M. R. Muggeo wrote:
> 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.

Dear Stanislav
You might also want to search for 'broken stick', another name for this
sort of model. I suppose it is also a linear spline. If you know on
scientific grounds where the breakpoint is you can force its position.

I am not sure how relevant this is but in your original example the
slopes would have been constrained to be equal although I wonder whether
that was really what you intended.

Michael

> 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 <[hidden email]> 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 <[hidden email]>
>>> wrote:
>>>>
>>>>> On Jan 11, 2015, at 4:00 PM, Ben Bolker <[hidden email]> 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]]
>>
>> ______________________________________________
>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>

--
Michael
http://www.dewey.myzen.co.uk

______________________________________________
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Re: nonmonotonic glm?

Bert Gunter
...
but do realize that after you have looked at the data to determine the
appropriate modeling approach, no statistical inference (significance
tests, confidence intervals, etc.) should be done on the model used.
Or more precisely, any that is done is wrong.

Cheers,
Bert

Bert Gunter
Genentech Nonclinical Biostatistics
(650) 467-7374

"Data is not information. Information is not knowledge. And knowledge
is certainly not wisdom."
Clifford Stoll




On Mon, Jan 12, 2015 at 7:26 AM, Michael Dewey <[hidden email]> wrote:

> Comments in line
>
> On 12/01/2015 13:13, Vito M. R. Muggeo wrote:
>>
>> 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.
>
>
> Dear Stanislav
> You might also want to search for 'broken stick', another name for this sort
> of model. I suppose it is also a linear spline. If you know on scientific
> grounds where the breakpoint is you can force its position.
>
> I am not sure how relevant this is but in your original example the slopes
> would have been constrained to be equal although I wonder whether that was
> really what you intended.
>
> Michael
>
>> 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 <[hidden email]> 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 <[hidden email]>
>>>> wrote:
>>>>>
>>>>>
>>>>>> On Jan 11, 2015, at 4:00 PM, Ben Bolker <[hidden email]> 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]]
>>>
>>> ______________________________________________
>>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>
> --
> Michael
> http://www.dewey.myzen.co.uk
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
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