Technical Details: Difference between ggpredict(), ggemmeans() and ggaverage()

ggpredict() and ggemmeans() compute predicted values for all possible levels or values from a model’s predictor. Basically, ggpredict() wraps the predict()-method for the related model, while ggemmeans() wraps the emmeans()-method from the emmeans-package. Both ggpredict() and ggemmeans() do some data-preparation to bring the data in shape for the newdata-argument (predict()) resp. the at-argument (emmeans()). It is recommended to read the general introduction first, if you haven’t done this yet.

Thus, effects returned by ggpredict() conditional effects (i.e. these are conditioned on certain (reference) levels of factors), while ggemmeans() returns marginal means, since the effects are “marginalized” (or “averaged”) over the levels of factors. However, these differences only apply to non-focal terms, i.e. remaining variables that are not specified in the terms argument.

That means:

For models without categorical predictors, the results from ggpredict() and ggemmeans() are identical (except some slight differences in the associated confidence intervals, which are, however, negligible).
When all categorical predictors are specified in terms and further (non-focal) terms are only numeric, results are also identical (as both ggpredict() and ggemmeans() use the mean value by default to hold non-focal numeric variables constant).

library(magrittr)
library(ggeffects)
data(efc, package = "ggeffects")
fit <- lm(barthtot ~ c12hour + neg_c_7, data = efc)

ggpredict(fit, terms = "c12hour")
#> # Predicted values of Total score BARTHEL INDEX
#> 
#> c12hour | Predicted |         95% CI
#> ------------------------------------
#>       0 |     75.07 | [72.96, 77.19]
#>      20 |     70.15 | [68.40, 71.91]
#>      45 |     64.01 | [62.40, 65.61]
#>      65 |     59.09 | [57.32, 60.86]
#>      85 |     54.17 | [52.04, 56.31]
#>     105 |     49.25 | [46.64, 51.87]
#>     125 |     44.34 | [41.18, 47.49]
#>     170 |     33.27 | [28.78, 37.76]
#> 
#> Adjusted for:
#> * neg_c_7 = 11.83

ggemmeans(fit, terms = "c12hour")
#> # Predicted values of Total score BARTHEL INDEX
#> 
#> c12hour | Predicted |         95% CI
#> ------------------------------------
#>       0 |     75.07 | [72.96, 77.19]
#>      20 |     70.15 | [68.40, 71.91]
#>      45 |     64.01 | [62.40, 65.61]
#>      65 |     59.09 | [57.32, 60.86]
#>      85 |     54.17 | [52.04, 56.31]
#>     105 |     49.25 | [46.64, 51.87]
#>     125 |     44.34 | [41.18, 47.49]
#>     170 |     33.27 | [28.78, 37.76]
#> 
#> Adjusted for:
#> * neg_c_7 = 11.83

As can be seen, the continuous predictor neg_c_7 is held constant at its mean value, 11.83. For categorical predictors, ggpredict() and ggemmeans() behave differently. While ggpredict() uses the reference level of each categorical predictor to hold it constant, ggemmeans() - like ggeffect() - averages over the proportions of the categories of factors.

library(datawizard)
data(efc, package = "ggeffects")
efc$e42dep <- to_factor(efc$e42dep)
fit <- lm(barthtot ~ c12hour + neg_c_7 + e42dep, data = efc)

ggpredict(fit, terms = "c12hour")
#> # Predicted values of Total score BARTHEL INDEX
#> 
#> c12hour | Predicted |         95% CI
#> ------------------------------------
#>       0 |     92.74 | [88.48, 97.01]
#>      20 |     91.32 | [87.06, 95.57]
#>      45 |     89.53 | [85.20, 93.87]
#>      65 |     88.10 | [83.64, 92.57]
#>      85 |     86.68 | [82.03, 91.32]
#>     105 |     85.25 | [80.37, 90.13]
#>     125 |     83.82 | [78.67, 88.98]
#>     170 |     80.61 | [74.71, 86.51]
#> 
#> Adjusted for:
#> * neg_c_7 =       11.83
#> *  e42dep = independent

ggemmeans(fit, terms = "c12hour")
#> # Predicted values of Total score BARTHEL INDEX
#> 
#> c12hour | Predicted |         95% CI
#> ------------------------------------
#>       0 |     73.51 | [71.85, 75.18]
#>      20 |     72.09 | [70.65, 73.53]
#>      45 |     70.30 | [68.89, 71.71]
#>      65 |     68.87 | [67.29, 70.46]
#>      85 |     67.45 | [65.55, 69.34]
#>     105 |     66.02 | [63.74, 68.30]
#>     125 |     64.59 | [61.88, 67.31]
#>     170 |     61.38 | [57.61, 65.15]
#> 
#> Adjusted for:
#> * neg_c_7 = 11.83

In this case, one would obtain the same results for ggpredict() and ggemmeans() again, if condition is used to define specific levels at which variables, in our case the factor e42dep, should be held constant.

ggpredict(fit, terms = "c12hour")
#> # Predicted values of Total score BARTHEL INDEX
#> 
#> c12hour | Predicted |         95% CI
#> ------------------------------------
#>       0 |     92.74 | [88.48, 97.01]
#>      20 |     91.32 | [87.06, 95.57]
#>      45 |     89.53 | [85.20, 93.87]
#>      65 |     88.10 | [83.64, 92.57]
#>      85 |     86.68 | [82.03, 91.32]
#>     105 |     85.25 | [80.37, 90.13]
#>     125 |     83.82 | [78.67, 88.98]
#>     170 |     80.61 | [74.71, 86.51]
#> 
#> Adjusted for:
#> * neg_c_7 =       11.83
#> *  e42dep = independent

ggemmeans(fit, terms = "c12hour", condition = c(e42dep = "independent"))
#> # Predicted values of Total score BARTHEL INDEX
#> 
#> c12hour | Predicted |         95% CI
#> ------------------------------------
#>       0 |     92.74 | [88.48, 97.01]
#>      20 |     91.32 | [87.06, 95.57]
#>      45 |     89.53 | [85.20, 93.87]
#>      65 |     88.10 | [83.64, 92.57]
#>      85 |     86.68 | [82.03, 91.32]
#>     105 |     85.25 | [80.37, 90.13]
#>     125 |     83.82 | [78.67, 88.98]
#>     170 |     80.61 | [74.71, 86.51]
#> 
#> Adjusted for:
#> * neg_c_7 = 11.83

Creating plots is as simple as described in the vignette Plotting Marginal Effects.

ggemmeans(fit, terms = c("c12hour", "e42dep")) %>% plot()

Another option is to use ggaverage() to compute average prediction. This function is a wrapper for the avg_predictions()-method from the marginaleffects-package. The major difference to ggemmeans() is that estimated marginal means, as computed by ggemmeans(), are a special case of predictions, made on a perfectly balanced grid of categorical predictors, with numeric predictors held at their means, and marginalized with respect to some focal variables. ggaverage(), in turn, calculates predicted values for each observation in the data multiple times, each time fixing all values or levels of the focal terms to and then takes the average of these predicted values (aggregated/grouped by the focal terms) - or in other words: ggaverage() duplicates the whole dataset once for every unique value of the focal terms, makes predictions for each observation of the new dataset and take the average of all predictions (grouped by focal terms).

ggaverage(fit, terms = "c12hour")
#> # Average predicted values of Total score BARTHEL INDEX
#> 
#> c12hour | Predicted |         95% CI
#> ------------------------------------
#>       0 |     67.73 | [66.15, 69.31]
#>      20 |     66.30 | [65.03, 67.57]
#>      45 |     64.52 | [63.38, 65.66]
#>      65 |     63.09 | [61.81, 64.37]
#>      85 |     61.66 | [60.07, 63.25]
#>     105 |     60.23 | [58.24, 62.23]
#>     125 |     58.81 | [56.37, 61.25]
#>     170 |     55.59 | [52.08, 59.11]

To explain how ggaverage() works, let’s look at following example. The confidence intervals for the simple means differ from those of ggaverage(), however, the predicted and mean values are identical.

data(iris)
set.seed(123)
# create an unequal distributed factor, used as focal term
iris$x <- as.factor(sample(1:4, nrow(iris), replace = TRUE, prob = c(0.1, 0.2, 0.3, 0.4)))
m <- lm(Sepal.Width ~ Species + x, data = iris)

# average predicted values
ggaverage(m, "x")
#> # Average predicted values of Sepal.Width
#> 
#> x | Predicted |       95% CI
#> ----------------------------
#> 1 |      3.12 | [2.94, 3.31]
#> 2 |      3.11 | [2.99, 3.23]
#> 3 |      2.97 | [2.87, 3.06]
#> 4 |      3.09 | [3.00, 3.17]

# replicate the dataset for each level of "x", i.e. 4 times
d <- do.call(rbind, replicate(4, iris, simplify = FALSE))
# for each data set, we set our focal term "x" to one of the four unique values
d$x <- as.factor(rep(1:4, each = 150))
# we calculate predicted values for each "dataset", i.e. we predict our outcome
# for observations, for all levels of "x"
d$predicted <- predict(m, newdata = d)
# now we compute the average predicted values for each level of "x"
datawizard::means_by_group(d, "predicted", "x")
#> # Mean of predicted by x
#> 
#> Category | Mean |   N |   SD |       95% CI |      p
#> ----------------------------------------------------
#> 1        | 3.12 | 150 | 0.28 | [3.08, 3.17] | 0.017 
#> 2        | 3.11 | 150 | 0.28 | [3.07, 3.16] | 0.059 
#> 3        | 2.97 | 150 | 0.28 | [2.92, 3.01] | < .001
#> 4        | 3.09 | 150 | 0.28 | [3.04, 3.13] | 0.468 
#> Total    | 3.07 | 600 | 0.28 |              |       
#> 
#> Anova: R2=0.048; adj.R2=0.044; F=10.094; p<.001

But when should I use ggemmeans(), ggpredict() or ggaverage()?

When you are interested in the strength of association, it usually doesn’t matter. as you can see in the plots below. The slope of our focal term, c12hour, is the same for all four plots:

library(see)
p1 <- plot(ggpredict(fit, terms = "c12hour"), show_ci = FALSE, show_title = FALSE, show_x_title = FALSE, show_y_title = FALSE)
p2 <- plot(ggemmeans(fit, terms = "c12hour"), show_ci = FALSE, show_title = FALSE, show_x_title = FALSE, show_y_title = FALSE)
p3 <- plot(ggemmeans(fit, terms = "c12hour", condition = c(e42dep = "independent")), show_ci = FALSE, show_title = FALSE, show_x_title = FALSE, show_y_title = FALSE)
p4 <- plot(ggaverage(fit, terms = "c12hour"), show_ci = FALSE, show_title = FALSE, show_x_title = FALSE, show_y_title = FALSE)

plots(p1, p2, p3, p4, n_rows = 2)

However, the predicted outcome varies. This gives an impression when ggemmeans(), i.e. marginal effects, matter: when you want to predict your outcome, marginalized over the different levels of factors, i.e. “generalized” to the population (of your sample) on a balanced grid of focal terms. ggpredict() would give a predicted outcome for a subgroup (or: specific group) of your sample, i.e. conditioned on specific levels of factors. Hence, the predicted outcome from ggpredict() does not necessarily generalize to the “population” (always keeping in mind that we assume having a “representative sample” of a “population” as data in our model). Finally, ggaverage() gives you predictions averaged across your sample and aggregated by the focal terms.

What is the most apparent difference from ggaverage() to the other functions in ggeffects?

The most apparent difference from ggaverage() compared to the other methods occurs when you have categorical co-variates (non-focal terms) with unequally distributed levels. ggemmeans() will “average” over the levels of non-focal factors, while ggaverage() will average over the observations in your sample.

Let’s show this with a very simple example:

data(iris)
set.seed(123)
# create an unequal distributed factor, used as non-focal term
iris$x <- as.factor(sample(1:4, nrow(iris), replace = TRUE, prob = c(0.1, 0.2, 0.3, 0.4)))
m <- lm(Sepal.Width ~ Species + x, data = iris)

# predicted values, conditioned on x = 1
ggpredict(m, "Species")
#> # Predicted values of Sepal.Width
#> 
#> Species    | Predicted |       95% CI
#> -------------------------------------
#> setosa     |      3.50 | [3.30, 3.69]
#> versicolor |      2.84 | [2.63, 3.04]
#> virginica  |      3.04 | [2.85, 3.23]
#> 
#> Adjusted for:
#> * x = 1

# predicted values, conditioned on weighted average of x
ggemmeans(m, "Species")
#> # Predicted values of Sepal.Width
#> 
#> Species    | Predicted |       95% CI
#> -------------------------------------
#> setosa     |      3.45 | [3.35, 3.54]
#> versicolor |      2.78 | [2.68, 2.89]
#> virginica  |      2.99 | [2.89, 3.09]

# average predicted values, averaged over the sample and aggregated by "Species"
ggaverage(m, "Species")
#> # Average predicted values of Sepal.Width
#> 
#> Species    | Predicted |       95% CI
#> -------------------------------------
#> setosa     |      3.43 | [3.34, 3.52]
#> versicolor |      2.77 | [2.67, 2.86]
#> virginica  |      2.97 | [2.88, 3.07]

There is no rule of thumb which approach is better; it depends on the characteristics of the sample and the population to which should be generalized. Consulting the marginaleffects-website might help to decide which approach is more appropriate.

Showing the difference between ggemmeans() and ggaverage()

A code example, where we compute the average predicted values the estimated marginal means manually, shows the differences between these two ways of averaging in detail.

data(iris)
set.seed(123)
iris$x <- as.factor(sample(1:4, nrow(iris), replace = TRUE, prob = c(0.1, 0.2, 0.3, 0.4)))
m <- lm(Sepal.Width ~ Species + x, data = iris)

# average predicted values
ggaverage(m, "Species")
#> # Average predicted values of Sepal.Width
#> 
#> Species    | Predicted |       95% CI
#> -------------------------------------
#> setosa     |      3.43 | [3.34, 3.52]
#> versicolor |      2.77 | [2.67, 2.86]
#> virginica  |      2.97 | [2.88, 3.07]

# replicate the dataset for each level of "Species", i.e. 3 times
d <- do.call(rbind, replicate(3, iris, simplify = FALSE))
# for each data set, we set our focal term to one of the three levels
d$Species <- as.factor(rep(levels(iris$Species), each = 150))
# we calculate predicted values for each "dataset", i.e. we predict our outcome
# for observations, for all levels of "Species"
d$predicted <- predict(m, newdata = d)
# now we compute the average predicted values by levels of "Species"
datawizard::means_by_group(d, "predicted", "Species")
#> # Mean of predicted by Species
#> 
#> Category   | Mean |   N |   SD |       95% CI |      p
#> ------------------------------------------------------
#> setosa     | 3.43 | 150 | 0.06 | [3.42, 3.44] | < .001
#> versicolor | 2.77 | 150 | 0.06 | [2.76, 2.78] | < .001
#> virginica  | 2.97 | 150 | 0.06 | [2.96, 2.98] | < .001
#> Total      | 3.06 | 450 | 0.28 |              |       
#> 
#> Anova: R2=0.951; adj.R2=0.951; F=4320.998; p<.001

# estimated marginal means, in turn, differ from the above, because they are
# averaged across balanced reference grids for all focal terms, thereby non-focal
# are hold constant at a "weighted average".

# estimated marginal means, from `ggemmeans()`
ggemmeans(m, "Species")
#> # Predicted values of Sepal.Width
#> 
#> Species    | Predicted |       95% CI
#> -------------------------------------
#> setosa     |      3.45 | [3.35, 3.54]
#> versicolor |      2.78 | [2.68, 2.89]
#> virginica  |      2.99 | [2.89, 3.09]

d <- rbind(
  data_grid(m, "Species", condition = c(x = "1")),
  data_grid(m, "Species", condition = c(x = "2")),
  data_grid(m, "Species", condition = c(x = "3")),
  data_grid(m, "Species", condition = c(x = "4"))
)
d$predicted <- predict(m, newdata = d)
# means calculated manually
datawizard::means_by_group(d, "predicted", "Species")
#> # Mean of predicted by Species
#> 
#> Category   | Mean |  N |   SD |       95% CI |      p
#> -----------------------------------------------------
#> setosa     | 3.45 |  4 | 0.07 | [3.36, 3.53] | < .001
#> versicolor | 2.78 |  4 | 0.07 | [2.70, 2.87] | < .001
#> virginica  | 2.99 |  4 | 0.07 | [2.91, 3.07] | 0.019 
#> Total      | 3.07 | 12 | 0.30 |              |       
#> 
#> Anova: R2=0.952; adj.R2=0.941; F=88.566; p<.001

When should I use ggpredict(), ggemmeans() or ggaverage()?

The strength of the association should not be affected by the way of averaging. You can see this when comparing the differences between the predicted values, which are the same. If you’re interested in differences between specific levels (or values) of your predictors, it shouldn’t matter which function you use.

What is different is the predicted outcome, and therefore the conclusions you would draw from the results. ggpredict() predicts your outcome for certain characteristics of your sample (for “subgroups”, if you like). ggaverage() and ggemmeans() predict your outcome for an “average observation” of your sample, with slightly different approaches of averaging.

# check that the difference between the predicted value, average predicted values
#  estimated marginal means is the same
out1 <- ggaverage(m, "Species")
out2 <- ggemmeans(m, "Species")
out3 <- ggpredict(m, "Species")
all.equal(diff(out1$predicted), diff(out2$predicted))
#> [1] TRUE
all.equal(diff(out1$predicted), diff(out3$predicted))
#> [1] TRUE

Some models are not yet supported by the emmeans package, thus, for certain models, only ggpredict() works, not ggemmeans() nor ggeffect(). ggaverage() should support the same (or more) models as ggpredict(), but averages predictions from the sample, and thus may not be the quantity of interest. Sometimes, robust variance-covariance estimation is required for confidence intervals of predictions. In such cases, you have to rely on ggpredict() or ggaverage(). If you have no categorical predictors as non-focal terms (i.e. no factor needs to be held constant), then - as shown above - ggpredict() and ggemmeans() yield the same results.

Daniel Lüdecke

2023-11-29