Mean-centering variables in glmer

Question

I have the following model in r that compares the differences between dives where whales fed and dives where whales didn't fed (distribution is binomial: presence of feeding (foraging) = 1, abscence = 0). Whale (18 individuals) is used as random factor.

I included several metrics in the model: dive duration, maximum depth, descent/ascent rate, etc... and used scale on all numerical metrics (scale())

g_model <- glmer(foraging~max_depths*diel_2+duration+pd_times+d_rate+a_rate+bottom_prop+(1|whale),
                      data=data, control=glmerControl(optimizer="bobyqa",optCtrl=list(maxfun=2e5)),
                      family="binomial", na.action = na.fail)



summary(g_model)

Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: foraging ~ max_depths * diel_2 + duration + pd_times + d_rate +  
    a_rate + bottom_prop + (1 | whale)
   Data: data
Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))

     AIC      BIC   logLik deviance df.resid 
  1244.6   1301.4   -612.3   1224.6     2164 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-99.364  -0.195   0.083   0.285   4.311 

Random effects:
 Groups Name        Variance Std.Dev.
 whale  (Intercept) 0.2201   0.4692  
Number of obs: 2174, groups:  whale, 18

Fixed effects:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)              0.5621     0.1600   3.514 0.000441 ***
max_depths               1.9123     0.1863  10.266  < 2e-16 ***
diel_2Night              1.5491     0.2577   6.012 1.83e-09 ***
duration                -0.3535     0.1516  -2.331 0.019739 *  
pd_times                -0.6118     0.1531  -3.996 6.45e-05 ***
d_rate                   0.6536     0.1099   5.949 2.70e-09 ***
a_rate                  -0.3688     0.1248  -2.955 0.003122 ** 
bottom_prop              2.8876     0.1343  21.502  < 2e-16 ***
max_depths:diel_2Night   1.9049     0.3184   5.984 2.18e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) mx_dpt dl_2Ng duratn pd_tms d_rate a_rate bttm_p
max_depths  -0.083                                                 
diel_2Night -0.313  0.206                                          
duration    -0.115 -0.678  0.066                                   
pd_times     0.034 -0.037 -0.020 -0.098                            
d_rate       0.079 -0.131 -0.042  0.409 -0.015                     
a_rate       0.095 -0.659 -0.139  0.423  0.093 -0.134              
bottom_prop  0.086  0.628  0.158 -0.449 -0.083  0.078 -0.248       
mx_dpth:_2N  0.065  0.034  0.600 -0.165  0.066 -0.138 -0.081  0.168

Two of the values do not make sense at all: duration and pd_times (post-dive duration).

Feeding dives are usually longer and since they have a high energetic cost whales usually rest for a while after at surface. Nevertheless, estimates are negative for both metrics. I know that just because that's common knowledge it doesn't mean my data will follow those assumptions but when I make boxplots of the data, duration is quite higher in feeding dives, contrary to what the model says (graph below). The post-dive duration graph is just weird (I suppose it is because of the outliers) and I can't really figure out anything out of it (also if you know what I should do to correct this boxplot it would be awesome! Graph below as well).

It was suggested that I should mean-center the variables, how can I do it? Or did I already did that by scaling? I already looked for correlation between variables and found nothing. Looked at differences between individuals (only one individual in 18 performed longer non-feeding dives than feeding dives, and thats because it only had 2 long non-feeding dives). I can't really figure it out.

F = feeding dives/ NF = non-feeding dives

DURATION

PD_TIMES

Thank you!

Answer 1

When you use the scale function on a variable, this will apply to the whole variable.

That is not what you want here.

You need to try to disentangle the within-whale associations from the between-whale associations. One good way to do this is by mean-centering the variable(s) in question by group - that is, by whale in your case. Then you ALSO have to include the mean variable in the model. In R I would suggest using the dplyr package to create the whale means, and the built-in merge function to add the means to your data. Then you simply create the whale mean-centred variable by duducting the whale mean from it. For example:

mydata <- merge(mydata, mydata %>% group_by(id) %>% summarise(duration_whale_mean = mean(duration)))
mydata$duration_mean_cent <- mydata$duration - mydata$duration_whale_mean

Then in your model you will have:

foraging ~ duration_mean_cent + duration_whale_mean + ...

(and you will not use the duration variable in the model.