Plotting
Finally - you can plot the results marginalization to evaluate the effect of the random effect terms graphically.
plot of chunk mfxplot1
One of the most common questions about multilevel models is how much influence grouping terms have on the outcome. One way to explore this is to simulate the predicted values of an observation across the distribution of random effects for a specific grouping variable and term. This can be described as “marginalizing” predictions over the distribution of random effects. This allows you to explore the influence of the grouping term and grouping levels on the outcome scale by simulating predictions for simulated values of each observation across the distribution of effect sizes.
The REmargins() function allows you to do this. Here, we
take the example sleepstudy model and marginalize
predictions for all of the random effect terms (Subject:Intercept,
Subject:Days). By default, the function will marginalize over the
quartiles of the expected rank (see expected rank vignette) of
the effect distribution for each term.
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
mfx <- REmargins(merMod = fm1, newdata = sleepstudy[1:10,])
head(mfx)
#> Reaction Days Subject case grouping_var term breaks original_group_level
#> 1 249.56 0 309 1 Subject Intercept 1 308
#> 2 249.56 0 334 1 Subject Days 1 308
#> 3 249.56 0 350 1 Subject Intercept 2 308
#> 4 249.56 0 330 1 Subject Days 2 308
#> 5 249.56 0 308 1 Subject Intercept 3 308
#> 6 249.56 0 332 1 Subject Days 3 308
#> fit_combined upr_combined lwr_combined fit_Subject upr_Subject lwr_Subject fit_fixed
#> 1 209.3846 250.3619 174.2814 -40.366098 -4.412912 -74.60068 250.4405
#> 2 243.5345 281.7434 204.8201 -6.989358 29.806462 -46.97090 252.7202
#> 3 238.2613 275.8752 199.1572 -13.690991 20.343996 -54.49421 250.8008
#> 4 276.0049 310.5112 237.8415 24.923090 60.486658 -11.80239 252.5914
#> 5 253.5195 292.6832 216.2007 4.515485 39.504991 -32.36923 251.9662
#> 6 259.5311 297.3577 221.2943 9.540808 44.660050 -26.14103 252.0332
#> upr_fixed lwr_fixed
#> 1 286.1343 217.3697
#> 2 287.0427 217.2515
#> 3 286.4434 217.6061
#> 4 286.7899 218.4882
#> 5 287.3253 218.4392
#> 6 287.9647 218.2303The new data frame output from REmargins contains a lot
of information. The first few columns contain the original data passed
to newdata. Each observation in newdata is
identified by a case number, because the function repeats
each observation by the number of random effect terms and number of
breaks to simulate each term over. Then the
grouping_var