[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 09:59:14 CEST 2019
Hello Patricia,
I think the interpretation of the fixed part is the same as for a
classical glm. See below...
On Sun, Jun 09, 2019 at 09:16:43AM +0200, Patricia Graf wrote:
« Hello,
«
« I have a few questions concering the interpretation of a GLMM output table
« when the model includes an interaction.
«
« We want to analyse bear presence at feeding sites (bear_pres) related to
« the year (two years: 2016, 2017) and the feed supplied at feeding sites
« (carrion, maize). So the response is binary (0 = no bear present, 1 = bear
« present within 5-min intervals over the whole day) and both predictors are
« categorical, we include feeding site ID as random factor.
«
« 1) As I understand, in a model without interaction, the interpretation of
« the results would be as follows:
«
« M1 <- glmer((bear_pres ~ feed + year + (1|Feeding.site), family=binomial,
« data=df10)
«
« Fixed effects:
«
« Estimate Std. Error z value Pr(>|z|)
«
« (Intercept) -4.58524 0.08529 -53.76 <2e-16 ***the intercept is bear
« presence at maize sites in 2016
More exactly, it is the log-odds of bear presence for an average site
where maize is supplied in 2016
« feedcarrion 0.39178 0.02139 18.32 <2e-16 ***bear presence at
« feeding sites in 2017 compared to 2016
«
« year2017 0.23027 0.01978 11.64 <2e-16 ***bear presence at carrion
« feeding sites compared to maize feeding sites
«
You have swapped the two lines. « feedcarrion » is the change in the
log-odds [that is, the log-odds ratio] when replacing maize by carrion
for a given site, both in 2017 and in 2016 since there is no
interaction; « year2017 », the same for 2017 vs 2016.
« Is this interpretation right?
«
« 2) To my knowledge, the output changes when you include an
« interaction:
Yes. Unless you have a perfectly null interaction in the sample, it
has to change, at least with default R coding for factors.
« M2<- glmer(bear_pres ~ year*feed + (1|Feeding.site), family=binomial,
« data=df10)
«
« Fixed effects:
«
« Estimate Std. Error z value Pr(>|z|)
«
« (Intercept) -4.36413 0.10730 -40.67 < 2e-16 ***the intercept is
« bear presence at maize sites in 2016 (baseline)
Same remark as above.
«
« year2017 -0.18010 0.05119 -3.52 0.000434 ***difference in bear
« presence in 2017 compared to 2016 for maize
«
« feedcarrion -0.02933 0.05318 -0.55 0.581222 difference in
« bear presence at carrion sites compared to maize sites in 2016
«
« year2017:feedcarrion 0.85275 0.09953 8.57 < 2e-16 ***difference in
« bear presence at carrion sites 2017 and the sum of ß0+ ß1+ ß2
«
« So to my questions: Is this interpretation right?
Yes.
« What is the coding of the
« model so it does produce this output, e.g. why is the year not comparing
« 2016 to 2017 anymore as in the model without the interaction?
The model is, in the log-odds scale,
y = ß0 + ß1 × 1(year = 2017) + ß2 × 1(feed = carrion)
+ ß3 × 1(year = 2017) × 1(feed = carrion)
where 1(x) is the « indicatrice » of x, that is the function equalling
1 if x is true, 0 otherwise.
« Or why
« doesn’t the model still use the two food types for comparison?
Because the interaction says that the comparison between years is
different for each food type, so a global comparison is (roughly
speaking) meaningless.
« As I understand, when you include an intercation between the two binary
« dummy-coded categorical variables, the interpretation of what was main
« effects before (year, carrion) changes, and so do the betas (these are
« called „simple effects“ afterwards).
The interpretation of what is a main effect does not really change,
but coefficients of the model do not correspond anymore to main
effects. To have main effect evaluation, you should use suited
analysis of variance/deviance tables (see Type I, Type II, Type III
sums of squares and all these kind of things) or coefficients linear
combinations.
« In my group, there is a strong believe that in M2, the year still compares
« the two years (and so does feed), it’s just the coefficient cannot be
« interpreted anymore. Also, there is a believe that the interaction term
« compares to feedmaize in the year 2016.
Not sure to understand, but seems wrong.
« If my interpreation is correct, I need some background on how the algorithm
« works, how simple effects evolve and why the interaction should be
« interpreted as in the output table of M2.
Read more about two-ways, 2×2 crossed factors, analysis of variance:
this is the basic and most simple case to understand interaction. Or
may be, as an alternative, analysis of covariance. Interpretation is
basically the same afterthat for glm/logistic regression, and when
adding random effects. Just a little bit more abstract because of the
change of the modeling scale (log-odds for glm/glmer here, for
instance).
Hope this helps,
Best regards,
--
Emmanuel CURIS
emmanuel.curis using parisdescartes.fr
Page WWW: http://emmanuel.curis.online.fr/index.html
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