I am trying to interpret the summary output of a linearized mixed effetcs model using the lme4 package in R.

My response variable 'Ratio' as well as the predictors EX and Sex are mean centred and continous variables.The Plate and the individual ID are categorical random effects.

How would you interpret the interaction between EX and Sex ?

Formula: Ratio ~ EX * Sex + (1 | Plate) + (1 | BirdID)
   Data: pn.mv
Control: lmerControl(calc.derivs = F, optCtrl = list(maxfun = 20000))

     AIC      BIC   logLik deviance df.resid 
   154.9    179.0    -70.4    140.9      224 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-4.0471 -0.3552  0.0545  0.5260  2.8547 

Random effects:
 Groups   Name        Variance Std.Dev.
 BirdID   (Intercept) 0.01393  0.1180  
 PlateD4  (Intercept) 0.73933  0.8598  
 Residual             0.06973  0.2641  
Number of obs: 231, groups:  BirdID, 43; Plate, 15

Fixed effects:
            Estimate Std. Error       df t value Pr(>|t|)   
(Intercept) -0.01426    0.22526 15.24635  -0.063  0.95034   
EX          -0.03472    0.02125 39.21815  -1.634  0.11021   
Sex2        -0.02728    0.05351 40.14986  -0.510  0.61295   
EX:Sex2      0.12543    0.04093 39.29658   3.065  0.00393 **
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
        (Intr) EX     Sex2  
EX      -0.030              
Sex2    -0.032  0.062       
EX:Sex2  0.011 -0.122 -0.200````
  • individuals of average size (EX=0) and 'average' Sex (Sex=0) have a fitted/predicted Ratio of -0.014 (unless you are dealing with some system where there are lots of intersex individuals, the intercept is a bit hard to interpret)
  • for individuals of average size (EX=0), a 1-unit increase in Sex (e.g. a change from female to male or vice versa?) is associated with a 0.027-unit decrease in Ratio (main effect of Sex = -0.027)
  • for 'average' Sex individuals (Sex=0), individuals decrease in Ratio by 0.034 for every increase of 1 unit in EX (main effect of EX = -0.034)
  • EX has a different effect on individuals with a greater value of Sex; an increase of 1 unit in sex (e.g. male → female or vice versa?) causes an increase in slope with respect to EX of 0.125 units

Alternatively, the interaction can be interpreted as "an increase of 1 unit in EX causes an increase of 0.125 in the effect of Sex"

The emmeans package can help you make sense of this stuff. Drawing pictures (e.g. with sjPlot::plot_model) also helps.

  • $\begingroup$ My bad! I changed the name of the fixed factor from 'Sex2' to 'Sex' in order to prevent confusion, but i forgot about the output, in which its still named 'Sex2'. That means, Sex is indeed a meancentred numerical value and not a factor. It was originally a factor with the levels.: 1 (female) and 2 (male), but I got told that it's best to meancentre it just as Ratio and EX. $\endgroup$ Aug 8 '21 at 18:54
  • $\begingroup$ It's not terrible, but I would argue that keeping it as a factor and using sum-to-zero contrasts is more interpretable ... $\endgroup$
    – Ben Bolker
    Aug 8 '21 at 19:00
  • $\begingroup$ That would indeed be easier to interpret, thanks for your help! $\endgroup$ Aug 8 '21 at 19:09

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