# [R-sig-ME] Mixed model interpretation with interaction

Emmanuel Curis emm@nue|@cur|@ @end|ng |rom p@r|@de@c@rte@@|r
Sun Jun 9 19:59:58 CEST 2019

```A small comment on a specific point of the detailed explaination given
by René. Reflecting my understanding, so comments on these are
wellcome especially if I'm wrong.

On Sun, Jun 09, 2019 at 04:57:06PM +0200, René wrote:
« 2) For another (technical) illustration: a test-design matrix as yours with
« (e.g.) 2 feeding sites and 2 years, then it would be a 2(site 1 vs. site 2)
« by 2(year 1 vs year 2) independent measures design; or 2 x 2 for short,
« which could be simply expressed by 4 probabilities or by using means on a
« log scale, one mean for each of the design-cells, which would be the
« "centered" variant of estimation; but usually dummy coding implies a
« non-centered (but mathematically equivalent  - standard) coding:
« If the model is:
« y = site+year (ignoring random effects now), then
« cellmean(site1:year1) = Model_Intercept
« cellmean(site1:year2) = Model_Intercept + year2
« cellmean(site2:year1) = Model_Intercept + site2
« cellmean(site2:year2) = Model_Intercept + site2 + year2
«
« mean(site1) = (2*Model_intercept + year2)/2
« mean(site2) = ( 2(Model_intercept + site2)+year2))/2
« and so on...

Note that these formula for means of each site assume either that
observed sample sizes are exactly the same for both years (if one
wants to obtain the empirical means) or that the two years are equally
probable in the population (if one wants to obtain estimations of the
theoretical mean ; on this specific context, that may seem a weird way
of saying things, but for other experimental designs it should apply).

That may, or may not, be sensible assumptions depending on the
context. For instance, if the bear population has increased between
the two years, it may be expected that more bears are observed on the
second year, so a weighted average may be more sounded. Or not...

« (Where intercept in most estimation methods is by default is defined in
« reference to the first level of the first predictor in the equation; thus
« site1 (+year1, which is 0 in this type of coding); but the reference point
« can be changed manually)

--
Emmanuel CURIS
emmanuel.curis using parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html

```