[Rd] inconsistent handling of factor, character, and logical predictors in lm()
Fox, John
j|ox @end|ng |rom mcm@@ter@c@
Sat Aug 31 19:42:27 CEST 2019
Dear Bill,
Thanks for pointing this difference out -- I was unaware of it.
I think that the difference occurs in model.matrix.default(), which coerces character variables but not logical variables to factors. Later it treats both factors and logical variables as "factors" in that it applies contrasts to both, but unused factor levels are dropped while an unused logical level is not.
I don't see why logical variables shouldn't be treated just as character variables are currently, both with respect to single levels (whether this is considered an error or as collinear with the intercept and thus gets an NA coefficient) and with respect to $levels.
Best,
John
> On Aug 31, 2019, at 1:21 PM, William Dunlap via R-devel <r-devel using r-project.org> wrote:
>
>> Functions like lm() treat logical predictors as factors, *not* as
> numerical variables.
>
> Not quite. A factor with all elements the same causes lm() to give an
> error while a logical of all TRUEs or all FALSEs just omits it from the
> model (it gets a coefficient of NA). This is a fairly common situation
> when you fit models to subsets of a big data.frame. This is an argument
> for fixing the single-valued-factor problem, which would become more
> noticeable if logicals were treated as factors.
>
>> d <- data.frame(Age=c(2,4,6,8,10), Weight=c(878, 890, 930, 800, 750),
> Diseased=c(FALSE,FALSE,FALSE,TRUE,TRUE))
>> coef(lm(data=d, Weight ~ Age + Diseased))
> (Intercept) Age DiseasedTRUE
> 877.7333 5.4000 -151.3333
>> coef(lm(data=d, Weight ~ Age + factor(Diseased)))
> (Intercept) Age factor(Diseased)TRUE
> 877.7333 5.4000 -151.3333
>> coef(lm(data=d, Weight ~ Age + Diseased, subset=Age<7))
> (Intercept) Age DiseasedTRUE
> 847.3333 13.0000 NA
>> coef(lm(data=d, Weight ~ Age + factor(Diseased), subset=Age<7))
> Error in `contrasts<-`(`*tmp*`, value = contr.funs[1 + isOF[nn]]) :
> contrasts can be applied only to factors with 2 or more levels
>> coef(lm(data=d, Weight ~ Age + factor(Diseased, levels=c(FALSE,TRUE)),
> subset=Age<7))
> Error in `contrasts<-`(`*tmp*`, value = contr.funs[1 + isOF[nn]]) :
> contrasts can be applied only to factors with 2 or more levels
>
> Bill Dunlap
> TIBCO Software
> wdunlap tibco.com
>
>
> On Sat, Aug 31, 2019 at 8:54 AM Fox, John <jfox using mcmaster.ca> wrote:
>
>> Dear Abby,
>>
>>> On Aug 30, 2019, at 8:20 PM, Abby Spurdle <spurdle.a using gmail.com> wrote:
>>>
>>>> I think that it would be better to handle factors, character
>> predictors, and logical predictors consistently.
>>>
>>> "logical predictors" can be regarded as categorical or continuous (i.e.
>> 0 or 1).
>>> And the model matrix should be the same, either way.
>>
>> I think that you're mistaking a coincidence for a principle. The
>> coincidence is that FALSE/TRUE coerces to 0/1 and sorts to FALSE, TRUE.
>> Functions like lm() treat logical predictors as factors, *not* as numerical
>> variables.
>>
>> That one would get the same coefficient in either case is a consequence of
>> the coincidence and the fact that the default contrasts for unordered
>> factors are contr.treatment(). For example, if you changed the contrasts
>> option, you'd get a different estimate (though of course a model with the
>> same fit to the data and an equivalent interpretation):
>>
>> ------------ snip --------------
>>
>>> options(contrasts=c("contr.sum", "contr.poly"))
>>> m3 <- lm(Sepal.Length ~ Sepal.Width + I(Species == "setosa"), data=iris)
>>> m3
>>
>> Call:
>> lm(formula = Sepal.Length ~ Sepal.Width + I(Species == "setosa"),
>> data = iris)
>>
>> Coefficients:
>> (Intercept) Sepal.Width I(Species == "setosa")1
>> 2.6672 0.9418 0.8898
>>
>>> head(model.matrix(m3))
>> (Intercept) Sepal.Width I(Species == "setosa")1
>> 1 1 3.5 -1
>> 2 1 3.0 -1
>> 3 1 3.2 -1
>> 4 1 3.1 -1
>> 5 1 3.6 -1
>> 6 1 3.9 -1
>>> tail(model.matrix(m3))
>> (Intercept) Sepal.Width I(Species == "setosa")1
>> 145 1 3.3 1
>> 146 1 3.0 1
>> 147 1 2.5 1
>> 148 1 3.0 1
>> 149 1 3.4 1
>> 150 1 3.0 1
>>
>>> lm(Sepal.Length ~ Sepal.Width + as.numeric(Species == "setosa"),
>> data=iris)
>>
>> Call:
>> lm(formula = Sepal.Length ~ Sepal.Width + as.numeric(Species ==
>> "setosa"), data = iris)
>>
>> Coefficients:
>> (Intercept) Sepal.Width
>> as.numeric(Species == "setosa")
>> 3.5571 0.9418
>> -1.7797
>>
>>> -2*coef(m3)[3]
>> I(Species == "setosa")1
>> -1.779657
>>
>> ------------ snip --------------
>>
>>
>>>
>>> I think the first question to be asked is, which is the best approach,
>>> categorical or continuous?
>>> The continuous approach seems simpler and more efficient to me, but
>>> output from the categorical approach may be more intuitive, for some
>>> people.
>>
>> I think that this misses the point I was trying to make: lm() et al. treat
>> logical variables as factors, not as numerical predictors. One could argue
>> about what's the better approach but not about what lm() does. BTW, I
>> prefer treating a logical predictor as a factor because the predictor is
>> essentially categorical.
>>
>>>
>>> I note that the use factors and characters, doesn't necessarily
>>> produce consistent output, for $xlevels.
>>> (Because factors can have their levels re-ordered).
>>
>> Again, this misses the point: Both factors and character predictors
>> produce elements in $xlevels; logical predictors do not, even though they
>> are treated in the model as factors. That factors have levels that aren't
>> necessarily ordered alphabetically is a reason that I prefer using factors
>> to using character predictors, but this has nothing to do with the point I
>> was trying to make about $xlevels.
>>
>> Best,
>> John
>>
>> -------------------------------------------------
>> John Fox, Professor Emeritus
>> McMaster University
>> Hamilton, Ontario, Canada
>> Web: http::/socserv.mcmaster.ca/jfox
>>
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