inconsistent handling of factor, character, and logical predictors in lm()

Functions like lm() treat logical predictors as factors, *not* as

coef(lm(data=d, Weight ~ Age + Diseased))

coef(lm(data=d, Weight ~ Age + factor(Diseased)))

coef(lm(data=d, Weight ~ Age + Diseased, subset=Age<7))

coef(lm(data=d, Weight ~ Age + factor(Diseased), subset=Age<7))

coef(lm(data=d, Weight ~ Age + factor(Diseased, levels=c(FALSE,TRUE)),

Dear Abby,

On Aug 30, 2019, at 8:20 PM, Abby Spurdle <spurdle.a at 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