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---
title: "Using merTools to Marginalize Over Random Effect Levels"
author: "Jared Knowles and Carl Frederick"
date: "2020-06-22"
output: rmarkdown::html_vignette
vignette: >
%\VignetteEngine{knitr::rmarkdown}
%\VignetteIndexEntry{Marginalizing Random Effect Levels}
%\VignetteEncoding{UTF-8}
---
# Marginalizing Random Effects
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.
```r
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 218.2303
```
The 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`
# Summarizing
# Plotting
Finally - you can plot the results marginalization to evaluate the effect of the random effect terms
graphically.
```r
ggplot(mfx) + aes(x = breaks, y = fit_Subject, group = case) +
geom_line() +
facet_wrap(~term)
```
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