Plot random effects

To explore the patterns that your model has identified, it’s often useful to plot the random effects, that is, the group-level adjustments to the fixed effect parameters.

This kind of plot is often nice to include in the appendix of a report or (mini)dissertation.

For the kind of plot that’s best for the Results section, see Plot model-fitted values.

Example: Life satisfaction in Scotland

These data come from 112 people across 12 different Scottish dwellings (cities and towns). Information is captured on their ages and a measure of life satisfaction. The researchers are interested in if there is an association between age and life-satisfaction.

Data are available at https://uoepsy.github.io/data/lmm_lifesatscot.csv.

variable description
age Age (years)
lifesat Life Satisfaction score
dwelling Dwelling (town/city in Scotland)
size Size of Dwelling (> or <100k people) 
lifesatscot <- read_csv("https://uoepsy.github.io/data/lmm_lifesatscot.csv")

Our model is the following (to see how we figured out this random effect structure, see Identify possible random effects).

lifesat_mod <- lmer(
  lifesat ~ age + (1 + age | dwelling),
  data = lifesatscot
)

Plot group-level adjustments

The function dotplot.ranef.mer() will take the model’s group-level adjustments (extracted via ranef(); see Extract estimates from a fitted model) and plot them.

dotplot.ranef.mer(ranef(lifesat_mod))$dwelling

In the plot above, the age adjustments all appear tightly clustered around 0. This is because their magnitude (i.e., the size of the numbers) is a lot smaller than the magnitude of the intercept adjustments.

To “zoom in” on the age adjustments for each dwelling, we can add a bit of extra code that allows the scales of each subplot to vary:

dotplot.ranef.mer(
  ranef(lifesat_mod),
  scales = list(x = list(relation = 'free'))  # allow scales of subplots to vary
)$dwelling

Much better!

Reading random effects plots

In general:

  • Each subplot/panel/facet contains the adjustments to one fixed effect parameter.
  • Each “row” represents one level of the grouping variable.
  • The dots represent the estimated adjustment values for each dwelling place for each fixed effect.
  • The black error bars represent the 95% confidence interval for each adjustment value.

Things to notice about this plot in particular:

  • Dwellings with negative intercept adjustments tend to have positive adjustments to the slope over age. This suggests that the intercept and slope adjustments for each dwelling are negatively correlated. Let’s check:
VarCorr(lifesat_mod)
 Groups   Name        Std.Dev. Corr 
 dwelling (Intercept) 17.795        
          age          0.419   -0.87
 Residual              7.970

Yes indeed: the Corr column shows a correlation between intercept and slope of –0.87 (see Interpret LMM summary > The random effects and Interpret LMM summary > Interpreting the numbers: Correlation).

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