# Interpreting lmer output with continous fixed effects

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