Adjusted Predictions

In the context of this package, an “Adjusted Prediction” is defined as:

The response predicted by a model for some combination of the regressors’ values, such as their means or factor levels (a.k.a. “reference grid”).

An adjusted prediction is thus the regression-adjusted response variable (or link, or other fitted value), for a given combination (or grid) of predictors. This grid may or may not correspond to the actual observations in a dataset.

By default, predictions calculates the regression-adjusted predicted values for a single hypothetical unit of observation with all regressors set at their means or modes:

library(marginaleffects)

mod <- lm(mpg ~ hp + factor(cyl), data = mtcars)

predictions(mod)
#>          type predicted std.error conf.low conf.high       hp cyl
#> 1 expectation  16.60307  1.278754 13.98366  19.22248 146.6875   8

In many cases, this is too limiting, and researchers will want to specify a grid of “typical” values over which to compute adjusted predictions.

Typical Predictions

There are two main ways to select the reference grid over which we want to compute adjusted predictions. The first is using the variables argument. The second is with the newdata argument and the typical() function that we already introduced in the marginal effects vignette.

variables: Levels and Tukey’s 5 numbers

The variables argument is a handy shortcut to create grids of predictors. Each of the levels of factor/logical/character variables listed in the variables argument will be displayed. For numeric variables, predictions will compute adjusted predictions at Tukey’s 5 summary numbers. All other variables will be set at their means or modes.

predictions(mod, variables = c("cyl", "hp"))
#>           type predicted std.error  conf.low conf.high cyl  hp
#> 1  expectation  21.43244 1.6083883 18.137810  24.72708   6  52
#> 2  expectation  27.40010 1.0595843 25.229639  29.57056   4  52
#> 3  expectation  18.87925 2.5641372 13.626851  24.13165   8  52
#> 4  expectation  20.37474 1.2562453 17.801433  22.94804   6  96
#> 5  expectation  26.34239 0.9707174 24.353966  28.33081   4  96
#> 6  expectation  17.82154 1.9364843 13.854831  21.78825   8  96
#> 7  expectation  19.72569 1.1892191 17.289682  22.16169   6 123
#> 8  expectation  25.69334 1.1343184 23.369796  28.01689   4 123
#> 9  expectation  17.17249 1.5721502 13.952087  20.39289   8 123
#> 10 expectation  18.35547 1.4848895 15.313815  21.39713   6 180
#> 11 expectation  24.32313 1.7749372 20.687334  27.95892   4 180
#> 12 expectation  15.80228 0.9537705 13.848567  17.75599   8 180
#> 13 expectation  14.62945 3.4865450  7.487590  21.77132   6 335
#> 14 expectation  20.59711 4.0024363 12.398490  28.79573   4 335
#> 15 expectation  12.07626 2.1126445  7.748702  16.40381   8 335

The data.frame produced by predictions is “tidy”, which makes it easy to manipulate with other R packages and functions:

library(kableExtra)
library(tidyverse)

predictions(mod, variables = c("cyl", "hp")) %>%
    select(hp, cyl, predicted) %>%
    pivot_wider(values_from = predicted, names_from = cyl) %>%
    kbl(caption = "A table of Adjusted Predictions") %>%
    kable_styling() %>%
    add_header_above(header = c(" " = 1, "cyl" = 3))
A table of Adjusted Predictions
cyl
hp 6 4 8
52 21.43244 27.40010 18.87925
96 20.37474 26.34239 17.82154
123 19.72569 25.69334 17.17249
180 18.35547 24.32313 15.80228
335 14.62945 20.59711 12.07626

newdata and typical

A second strategy to construct grids of predictors for adjusted predictions is to combine the newdata argument and the typical function. Recall that this function creates a “typical” dataset with all variables at their means or modes, except those we explicitly define:

typical(cyl = c(4, 6, 8), model = mod)
#>         hp cyl
#> 1 146.6875   4
#> 2 146.6875   6
#> 3 146.6875   8

We can also use this typical function in a predictions call (omitting the model argument):

predictions(mod, newdata = typical(cyl = c(4, 6, 8)))
#>          type predicted std.error conf.low conf.high       hp cyl
#> 1 expectation  25.12392  1.368888 22.31988  27.92796 146.6875   4
#> 2 expectation  19.15627  1.247190 16.60151  21.71102 146.6875   6
#> 3 expectation  16.60307  1.278754 13.98366  19.22248 146.6875   8

Plot: Conditional Predictions

First, we download the ggplot2movies dataset from the RDatasets archive. Then, we create a variable called certified_fresh for movies with a rating of at least 8. Finally, we discard some outliers and fit a logistic regression model:

library(tidyverse)
dat <- read.csv("https://vincentarelbundock.github.io/Rdatasets/csv/ggplot2movies/movies.csv") %>%
    mutate(style = case_when(Action == 1 ~ "Action",
                             Comedy == 1 ~ "Comedy",
                             Drama == 1 ~ "Drama",
                             TRUE ~ "Other"),
           style = factor(style),
           certified_fresh = rating >= 8) %>%
    filter(length < 240)

mod <- glm(certified_fresh ~ length * style, data = dat, family = binomial)

We can plot adjusted predictions, conditional on the length variable using the plot_cap function:

mod <- glm(certified_fresh ~ length, data = dat, family = binomial)

plot_cap(mod, condition = "length")

We can also introduce another condition which will display a categorical variable like style in different colors. This can be useful in models with interactions:

mod <- glm(certified_fresh ~ length * style, data = dat, family = binomial)

plot_cap(mod, condition = c("length", "style"))

Of course, you can also design your own plots or tables by working with the predictions output directly:

predictions(mod, 
              type = c("response", "link"),
              newdata = typical(length = 90:120,
                                style = c("Action", "Comedy"))) %>%
    ggplot(aes(length, predicted, color = style))  +
    geom_line() +
    facet_wrap(~type, scales = "free_y")

Prediction types

The predictions function computes model-adjusted means on the scale of the output of the predict(model) function. By default, predict produces predictions on the "response" scale, so the adjusted predictions should be interpreted on that scale. However, users can pass a string or a vector of strings to the type argument, and predictions will consider different outcomes.

Typical values include "response" and "link", but users should refer to the documentation of the predict of the package they used to fit the model to know what values are allowable. documentation.

mod <- glm(am ~ mpg, family = binomial, data = mtcars)
predictions(mod, type = c("response", "link"))
#>          type predicted std.error  conf.low conf.high      mpg
#> 1 expectation    0.3929 0.1083666 0.2098929 0.6118973 20.09062

Users who need more control over the type of adjusted predictions to compute, including a host of options for back-transformation, may want to consider the emmeans package.