plogis (and other p* functions), vectorized lower.tail

On 12/9/21 10:03 AM, Martin Maechler wrote:

Matthias Gondan
???? on Wed, 8 Dec 2021 19:37:09 +0100 writes:

???? > Dear R developers,
???? > I have seen that plogis silently ignores vector elements of 
lower.tail,

and also of 'log'.
This is indeed the case for all d*, p*, q* functions.

Yes, this has been on purpose and therefore documented, in the
case of plogis, e.g. in the 'Value' section of ?plogis :

????? The length of the result is determined by ?n? for ?rlogis?, and is
????? the maximum of the lengths of the numerical arguments for the
????? other functions.

? (note: *numerical* arguments: the logical ones are not recycled)

????? The numerical arguments other than ?n? are recycled to the length
????? of the result.? Only the first elements of the logical arguments
????? are used.

? (above, we even explicitly mention the logical arguments ..)


Recycling happens for the first argument (x,p,q) of these
functions and for "parameters" of the distribution, but not for
lower.tail, log.p (or 'log').


???? >> plogis(q=0.5, location=1, lower.tail=TRUE)
???? > [1] 0.3775407
???? >> plogis(q=0.5, location=1, lower.tail=FALSE)
???? > [1] 0.6224593
???? >> plogis(q=c(0.5, 0.5), location=1, lower.tail=c(TRUE, FALSE))
???? > [1] 0.3775407 0.3775407

???? > For those familiar with psychological measurement: A use case 
of the above function is the so-called Rasch model, where the 
probability that a person with some specific ability (q) makes a 
correct (lower.tail=TRUE) or wrong response (lower.tail=FALSE) to an 
item with a specific difficulty (location). A vectorized version of 
plogis would enable to determine the likelihood of an entire response 
vector in a single call. My current workaround is an intermediate 
call to ?Vectorize?.

???? > I am wondering if the logical argument of lower.tail can be 
vectorized (?). I see that this may be a substantial change in many 
places (basically, all p and q functions of probability 
distributions), but in my understanding, it would not break existing 
code which assumes lower.tail to be a single element. If that?s not
???? > possible/feasible, I suggest to issue a warning if a vector of 
length > 1 is given in lower.tail. I am aware that the documentation 
clearly states that lower.tail is a single boolean.

aah ok, here you say you know that the current behavior is documented.

???? > Thank you for your consideration.


As you mention, changing this would be quite a large endeavor.
I had thought about doing that many years ago, not remembering
details, but seeing that in almost all situations you really
only need one of the two tails? (for Gaussian- or t- based confidence
intervals you also only need one, for symmetry reason).

Allowing the recycling there would make the intermediate C code
(which does the recycling) larger and probably slightly
slower because of conceptually two more for loops which would in
99.9% only have one case ..

I'd have found that ugly to add. ... ...
... but of course, if you can prove that the code bloat would not be 
large
and not deteriorate speed in a measurable way and if you'd find
someone to produce a comprehensive and tested patch ...

Martin


???? > With best wishes,
???? > Matthias



???? > [[alternative HTML version deleted]]

???? > ______________________________________________
???? > R-devel at r-project.org mailing list
???? > https://stat.ethz.ch/mailman/listinfo/r-devel

? I agree with everything said above, but think that adding a warning 
when length(lower.tail) > 1 (rather than silently ignoring) might be 
helpful ...? ??

? As for the vectorization, it seems almost trivial to do at the user 
level when needed (albeit it's probably a little bit inefficient):

pv <- Vectorize(plogis, c("q", "location", "scale", "lower.tail"))
pv(q=c(0.5, 0.5), location=1, lower.tail=c(TRUE, FALSE))
[1] 0.3775407 0.6224593