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

Thierry Onkelinx thierry.onkelinx at inbo.be
Tue Jul 21 10:07:20 CEST 2015

Dear Daniel,

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.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht

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 Brinner
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 op 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 that?
> 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,
> rubi
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