[R-sig-ME] Scaling the response of a linear model to different factor groups

Daniel Rubi daniel_rubi at ymail.com
Wed Jul 22 04:17:36 CEST 2015

Thanks a lot.
On Tue, 7/21/15, Thierry Onkelinx <thierry.onkelinx at inbo.be> wrote:

 Subject: Re: [R-sig-ME] Scaling the response of a linear model to different factor groups
 To: "Daniel Rubi" <daniel_rubi at ymail.com>
 Cc: "r-sig-mixed-models at r-project.org" <r-sig-mixed-models at r-project.org>
 Date: Tuesday, July 21, 2015, 4:07 AM
 You answered your
 first question yourself: if you don't add the
 interaction then effect of whisker_row is forced to be
 identical between the species. The interaction seems to be
 required from an ecological point of view.
 I would not standardise the whisker
 lengths. I find that is makes the model harder to interpret.
 Instead, rather think about the whether the effects of
 species and whisker_row is additive of multiplicative. E.g.
 do you want to express the difference between the first and
 second rows to be x mm (additive) or rather as the second
 row is x% of the first row (multiplicative). The additive
 model is plain lmm. You get the multiplicative model by log
 transforming the length or by using a gamma distribution
 with log link.
 ir. Thierry Onkelinx
 Instituut voor natuur- en bosonderzoek /
 Research Institute for Nature and Forest 
 team Biometrie & Kwaliteitszorg / team
 Biometrics & Quality Assurance 
 Kliniekstraat 25
 To call in the statistician after the
 experiment is done may be no more than asking him to perform
 a post-mortem examination: he may be able to say what the
 experiment died of. ~ Sir Ronald Aylmer Fisher
 The plural of anecdote is not data. ~ Roger
 The combination of some data and an
 aching desire for an answer does not ensure that a
 reasonable answer can be extracted from a given body of
 data. ~ John Tukey
 2015-07-18 20:55 GMT+02:00
 Daniel Rubi <daniel_rubi at ymail.com>:
 I hope this question is general
 enough to be of broad interest.
 Here's the abstract explanation of my problem:
 I have two groups for which I measured a certain feature.
 Specifically, this feature can be divided into
 sub-categories, where I am aware that in each group there
 are inherent differences among the sub-categories. I'm
 interested to test if the two groups differ WRT to this
 feature, and if so what is the contribution of each
 sub-category to this feature.
 Now, here's the actual data I'm working with:
 My groups are two species of rodents. The feature is their
 whisker lengths. The whiskers are organized in four rows on
 the faces of each of the species (they are compatible betwen
 the two species).In both species the whiskers at different
 rows have different lengths (e.g., row 1 has the longest
 among all other rows whiskers in both species).
 What would be the correct linear model to test this?
 The simple mixed-effects model I can think of would be:
 whisker_length ~ species + whisker_row + (1|animal)
 where animal is a random effect, since I measure whiske
 lengths for several animals of each species.
 Is this model sufficient?
 My concerns are:
 1. Interpretation - if the result of the model is that both
 species and whisker_row (one or more of the four rows) are
 significant, does this model inform me whether the
 significant whisker rows are different between the two
 species? My impression is that the only interpreation is
 that whisker_row significantly determines whisker length,
 regardless of the species. Hence, should I add an
 interaction term between species and whisker_row to capture
 2. Should I standardize all whisker lengths relative to
 their rows, so that they are on a common scale according to
 their row?
 Thanks a lot,
 R-sig-mixed-models at r-project.org
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