[R-sig-ME] Mixed model interpretation with interaction
René
b|mono@om @end|ng |rom gm@||@com
Mon Jun 10 10:17:19 CEST 2019
@Emmanuel
Good point, and just to add some clarity from my side: these mean formulas
are, indeed, not a descriptive statistic, but estimated marginal means,
which reflect the assumption that there is a "true" population mean
regardless of the number of observations in the design cells (if they are
not weighted within the model, which might be worth thinking about in terms
of related problems of variance assumptions in likelihood ratio testing;
see internet discussions about type 1 vs. type 3 LRT's with unbalanced
sample sizes).
Am So., 9. Juni 2019 um 20:26 Uhr schrieb <d.luedecke using uke.de>:
> If you have multiple (repeated) measurements from both bears and feeding
> site, you may even have a nested or cross classified design. In such case,
> bears might be nested within feeding sites, and both bear and feeding site
> might be modelled as random intercept. Here’s a very short gist showing the
> difference between nested and cross classified design and how to write this
> in lme4-notation:
>
>
>
>
> http://htmlpreview.github.io/?https://github.com/strengejacke/mixed-models-snippets/blob/master/nested_fully-crossed_cross-classified_models.html
>
>
>
> Best
>
> Daniel
>
>
>
> *Von:* René <bimonosom using gmail.com>
> *Gesendet:* Sonntag, 9. Juni 2019 17:29
> *An:* d.luedecke using uke.de
> *Cc:* Patricia Graf <patricia.graf03 using gmail.com>; r-sig-mixed-models <
> r-sig-mixed-models using r-project.org>
> *Betreff:* Re: [R-sig-ME] Mixed model interpretation with interaction
>
>
>
> Ps:
>
>
>
> I also agree with Daniel to take care of repeated measurements of the same
> bears coming to the sites in both years.
>
> However, the main problem I guess, will be that not every bear comes back
> in the second year. This means, having random slopes for bears that were
> observed only once, will bias the effect estimate (i.e. the random slopes
> for year will not be separable from the fixed effect of year).
>
> A solution to this, however would be, to use an extra variable (lets call
> it 'repeat') that codes, whether a bear has there in both years (=1) or not
> (=0; numeric coding - not factored). Then you the following should work:
>
>
>
> model<-(y~site*year+(0+repeat*year| bearID))
>
> Which will estimate random slopes for year for all bears that were there
> at least twice, but not for others, where the term before the | becomes 0
> (and nothing happens)).
>
>
>
> Best, René
>
>
>
> Pps: You can tell your colleagues that:
>
> the Model-intercept is the only direct mean that the model estimates
> directly (i.e. the reference cell) and all other deviations (including
> other means) are linear combinations from that intercept (for any factor)
> ... And ... of course, the parameters still can be interpreted this way
> (as illustrated above) ... but you need to know some details how to do so
> :)) (you can impress them now...)
>
>
>
> The easiest way to let a function reconstruct the model outputs is using
> emmeans()
>
> e.g.
>
> emmeans(model1, ~Site) should give the marginal estimates of the - site
> main effect - (site 1 and site 2 means) on the log scale
>
> and
>
> emmeans(model1, ~Site, type = "response") will give the estimates on the
> actual response (probability) scale. I find this often very helpful (also
> for plotting).
>
>
>
>
>
>
>
> Am So., 9. Juni 2019 um 16:57 Uhr schrieb René <bimonosom using gmail.com>:
>
> Hi,
>
>
>
> I don't know if this adds anything new but the most direct answers that
> come into my mind would be.
>
> 1) It seems you use dummy coding, and this defines the interpretation of
> the estimated coefficients, which would be different from (often preferred
> because more easy to interpret) effect / or contrast coding (dummy coding
> has some 'fitting' advantages which are mainly discussed with respected to
> centered vs. non-centered likelihood (or least-square-mean) estimation
> processes, which might be insightful for you to look up in the internet);
> but any coding design you use will eventually simply try to estimate
> cell-means (in your case on a log scale), and you need to check how to get
> these cell means out of your coefficients (via back-transformation). One
> way of doing this is by using marginal predictions, as Daniel points out.
>
>
>
> 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...
>
> (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)
>
>
>
> If the model is:
>
> y=site+year+site:year, 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 + site2:year2
>
>
>
> Where only the fourth equation changes, which nontheless can have a huge
> impact on the estimation of the other parameters
>
>
>
> (usually R outputs the reference levels for the intercept and the
> coefficients, which you can easily identify)
>
> In case there are more sites than two... e.g.. 4 of them, then:
>
> cellmean(site1:year1) = Model_Intercept
>
> cellmean(site2:year1) = Model_Intercept + site2
>
> cellmean(site3:year1) = Model_Intercept + site3
>
> cellmean(site4:year1) = Model_Intercept + site4
>
>
>
> You might get the gist :)
>
>
>
> Finally, if you actually want to test for an overall interaction in this
> way (or main effects), looking at these coefficients is not meaningful,
> which you can tell by just looking at the formulas above..., So you might
> want to do it differently (correctly), namely by using likelihood ratio
> tests:
>
> (in R like coding)
>
>
>
> Model1<- y=site+year+site:year
>
> vs
>
> Model2<- y=site+year
>
>
>
> with
>
> anova(Model1,Model2) (I think aov() should work as well)
>
> If the interaction of both variables is significant (i.e. the anova()
> output gives a * for the comparison between Model 1 and Model 2... :)))
> then the interaction effect explains some 'significant' amount of variance.
> (If there is no *, you can consider the models as equal in terms of
> explained variance). Same for other effects (e.g. full model vs. model a
> specific main effect).
>
> Maybe Check whether the "afex::mixed" function which does this for you in
> a sensible way (there are different ways of doing LRT tests...)
>
> ;))
>
>
>
> Having done this in the first place, is often viewed as prerequisite for
> 'digging' into the model estimates (as discussed above) to find out, what
> significant then actually means in terms of 'mean-changes' :)
>
>
>
> Hope this helps,
>
> Best, René
>
>
>
>
>
>
>
> Am So., 9. Juni 2019 um 12:45 Uhr schrieb <d.luedecke using uke.de>:
>
> Dear Patricia,
>
> when you include an interaction, your assumption is that the relationship
> between an independent X1 and the dependent variable Y varies *depending on
> the values of another independent variable X2*. Indeed, for logistic
> regression models (as well as for many models with non-Gaussian families),
> the interpretation of interaction terms can be tricky. In such cases, I
> would recommend to compute (at least additionally) marginal effects, which
> give you an intuitive output of your results.
>
> You can do so e.g. with the "ggeffects" package (
> https://strengejacke.github.io/ggeffects/), and there is also an example
> for a logistic mixed effects model (
> https://strengejacke.github.io/ggeffects/articles/practical_logisticmixedmodel.html),
> which might help you.
>
> In your case, the code would be
> ggpredict(M1, c("feed", "year")) for the model with interaction. If you
> want to plot the results, simply call
> me <- ggpredict(M1, c("feed", "year"))
> plot(me)
>
> A comment on your model: I'm not sure, but if you compare subjects (or
> feeding sites) at two time points, you might want to model the
> auto-correlation of subjects / feeding site ("repeated measure") using your
> time variable as random slope:
>
> M1 <- glmer((bear_pres ~ feed * year + (1 + year | Feeding.site), family
> = binomial, data = df10)
>
> Computing marginal effects than would be the same function call:
> ggpredict(M1, c("feed", "year"))
>
>
> Best
> Daniel
>
>
> -----Ursprüngliche Nachricht-----
> Von: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> Im
> Auftrag von Patricia Graf
> Gesendet: Sonntag, 9. Juni 2019 09:17
> An: r-sig-mixed-models using r-project.org
> Betreff: [R-sig-ME] Mixed model interpretation with interaction
>
> 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.
>
>
>
> The model includes some other variables too but for simplicity I just use
> those two variables for explanation.
>
>
>
> 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
>
> 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
>
>
>
> Is this interpretation right?
>
>
>
>
>
> 2) To my knowledge, the output changes when you include an interaction:
>
>
>
> 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)
>
> 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? 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? Or why
> doesn’t the model still use the two food types for comparison?
>
>
>
> 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).
>
>
>
> 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.
>
>
>
> 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.
>
>
>
> Thank you for your help in advance!
>
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> Vorstandsmitglieder: Prof. Dr. Burkhard Göke (Vorsitzender), Prof. Dr. Dr.
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