Solved – Origin and spelling of (multi)collinear/colinear

Multicollinear and multicolinear both appear to be used in scientific literature, although the former appears to be a lot more popular and is also the name of the tag here. I figured there must be a single spelling of colinear/collinear which is more correct, but that is also spelled both ways.

Two questions about this:

  1. Which is more correct? Is there some different meaning implied by the extra L?
  2. If not, why is multicollinear used more frequently?

It doesn't seem intuitive to me that the double L version is more popular. I interpreted its definition as 'sharing linearity' with the outcome and hence the 'co-' prefix. What did the statistician who coined the term have to say about this?

Collinear follows the model of collaborate, collide, &c.: the m of the Latin prefix com- ("together") is assimilated to the initial l of the Latinate stem (cf. commiserate, contemporary, coæval, corrode). It's pronounced with the stress on the second syllable, & therefore an indeterminate vowel or at most a short o.

An excuse for colinear might be that you're treating linear as a native word, following the model of copilot, co-worker, &c.—cases in which the prefix is reduced to co- irrespective of the initial letter of the stem. I imagine people who write it thus also pronounce it with at least a secondary stress on the first syllable, & with a long o.

Pace @Carl I don't think a general predilection among the British for writing double l has much to do with it, though a preference for more traditional word-forms might. Counts of occurrences in published works from Google Ngrams suggest that colinear & its derivatives are disfavoured only slightly less in U.S. than in British English (an odds ratio of 1.4 over 1999 – 2008).

library(ngramr) #define word list & corpora words <- "collinear, colinear, collinearity, colinearity, multicollinear, multicolinear, multicollinearity, multicolinearity" corpora <- c("eng_gb_2012", "eng_us_2012") # fetch word counts dd <- ngram(words, corpora, year_start = 1999, smoothing = 0,  count = T, tag = NULL, case_ins = TRUE) # reduce derivatives dd$stem <- factor(gsub("multi|ity", "", tolower(dd$Phrase))) # tabulate xtabs(Count~stem+Corpus, data=dd) -> tb 

What may well be muddying the waters, however, is that there are more recent coinings of the word with different senses from the geometric one "together in a line" (first known use in 1863 according to my dictionary); in these we'd naturally expect the form colinear just because people don't make up Latin words any more. Wikipedia has an article on colinear maps & the on-line Merriam-Webster dictionary gives a second sense of colinear (but not collinear), "having corresponding parts arranged in the same linear order", that finds its use in Genetics & Molecular Biology.

† If you really want to write colinear & anyone's picking on you because of it, ask them if they write complanar.

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