
ggeffects: Marginal Effects and Adjusted Predictions of Regression Models
Daniel Lüdecke
2023-06-09
Source:vignettes/ggeffects.Rmd
ggeffects.Rmd
Aim of the ggeffects-package
Results of regression models are typically presented as tables that are easy to understand. For more complex models that include interaction or quadratic / spline terms, tables with numbers are less helpful and more difficult to interpret. In such cases, the visualization of marginal effects or adjusted predictions is far easier to understand and allows to intuitively get the idea of how predictors and outcome are associated, even for complex models.
ggeffects computes marginal effects and adjusted predictions (or estimated marginal means) at the mean (MEM) or at representative values (MER) of predictors from statistical models, i.e. predictions generated by a model when one holds the non-focal variables constant and varies the focal variable(s). The result is returned as data frame with consistent structure, especially for further use with ggplot. Definitions of “marginal effects” can be found here. Since there is no common language across fields regarding a unique meaning of “marginal effects”, it is recommended to read this vignette to understand what ggeffects actually does, and how this package differs from other packages that calculate “marginal effects”.
Since the focus lies on plotting the data (or the marginal effects/adjusted predictions), at least one model term needs to be specified for which the effects are computed. It is also possible to compute marginal effects for model terms, grouped by the levels of another model’s predictor. The package also allows plotting marginal effects for two-, three- or four-way-interactions, or for specific values of a model term only. Examples are shown below.
Short technical note
ggpredict()
, ggemmeans()
and
ggeffect()
always return predicted values for the
response of a model (or response distribution for
Bayesian models).
Typically, ggpredict()
returns confidence intervals
based on the standard errors as returned by the
predict()
-function, assuming normal distribution
(+/- 1.96 * SE
). If predict()
for a certain
class does not return standard errors (for example,
merMod-objects), these are calculated manually, by following
steps: matrix-multiply X
by the parameter vector
B
to get the predictions, then extract the
variance-covariance matrix V
of the parameters and compute
XVX'
to get the variance-covariance matrix of the
predictions. The square-root of the diagonal of this matrix represent
the standard errors of the predictions, which are then multiplied by
1.96 for the confidence intervals.
For mixed models, if type = "random"
or
type = "zi_random"
, the uncertainty in the random effects
is accounted for when calculating the standard errors. Hence, in such
cases, the intervals may be considered as prediction
intervals.
Consistent and tidy structure
The returned data frames always have the same, consistent structure
and column names, so it’s easy to create ggplot-plots without the need
to re-write the arguments to be mapped in each ggplot-call.
x
and predicted
are the values for the x- and
y-axis. conf.low
and conf.high
could be used
as ymin
and ymax
aesthetics for ribbons to add
confidence bands to the plot. group
can be used as
grouping-aesthetics, or for faceting.
The examples shown here mostly use ggplot2-code for
the plots, however, there is also a plot()
-method, which is
described in the vignette Plotting Marginal Effects.
Marginal effects at the mean
ggpredict()
computes predicted values for all possible
levels and values from a model’s predictors. In the simplest case, a
fitted model is passed as first argument, and the term in question as
second argument. Use the raw name of the variable for the
terms
-argument only - you don’t need to write things like
poly(term, 3)
or I(term^2)
for the
terms
-argument.
library(ggeffects)
data(efc)
fit <- lm(barthtot ~ c12hour + neg_c_7 + c161sex + c172code, data = efc)
ggpredict(fit, terms = "c12hour")
#> # Predicted values of Total score BARTHEL INDEX
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 75.44 | [73.25, 77.63]
#> 20 | 70.38 | [68.56, 72.19]
#> 45 | 64.05 | [62.39, 65.70]
#> 65 | 58.98 | [57.15, 60.80]
#> 85 | 53.91 | [51.71, 56.12]
#> 105 | 48.85 | [46.14, 51.55]
#> 125 | 43.78 | [40.51, 47.05]
#> 170 | 32.38 | [27.73, 37.04]
#>
#> Adjusted for:
#> * neg_c_7 = 11.84
#> * c161sex = 1.76
#> * c172code = 1.97
As you can see, ggpredict()
(and ggeffect()
or ggemmeans()
) has a nice print()
-method,
which takes care of printing not too many rows (but always an equally
spaced range of values, including minimum and maximum value of the term
in question) and giving some extra information. This is especially
useful when predicted values are shown depending on the levels of other
terms (see below).
The output shows the predicted values for the response at each value from the term c12hour. The data is already in shape for ggplot:
library(ggplot2)
theme_set(theme_bw())
mydf <- ggpredict(fit, terms = "c12hour")
ggplot(mydf, aes(x, predicted)) + geom_line()
Marginal effects at the mean by other predictors’ levels
The terms
-argument accepts up to four model terms, where
the second to fourth terms indicate grouping levels. This allows
predictions for the term in question at different levels for other model
terms:
ggpredict(fit, terms = c("c12hour", "c172code"))
#> # Predicted values of Total score BARTHEL INDEX
#>
#> # c172code = low level of education
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 74.75 | [71.26, 78.23]
#> 30 | 67.15 | [64.03, 70.26]
#> 55 | 60.81 | [57.77, 63.86]
#> 85 | 53.22 | [49.95, 56.48]
#> 115 | 45.62 | [41.86, 49.37]
#> 170 | 31.69 | [26.59, 36.78]
#>
#> # c172code = intermediate level of education
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 75.46 | [73.28, 77.65]
#> 30 | 67.87 | [66.16, 69.57]
#> 55 | 61.53 | [59.82, 63.25]
#> 85 | 53.93 | [51.72, 56.14]
#> 115 | 46.34 | [43.35, 49.32]
#> 170 | 32.40 | [27.74, 37.07]
#>
#> # c172code = high level of education
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 76.18 | [72.81, 79.55]
#> 30 | 68.58 | [65.41, 71.76]
#> 55 | 62.25 | [59.00, 65.50]
#> 85 | 54.65 | [51.03, 58.27]
#> 115 | 47.05 | [42.85, 51.26]
#> 170 | 33.12 | [27.50, 38.74]
#>
#> Adjusted for:
#> * neg_c_7 = 11.84
#> * c161sex = 1.76
Creating a ggplot is pretty straightforward: the
colour
-aesthetics is mapped with the
group
-column:
mydf <- ggpredict(fit, terms = c("c12hour", "c172code"))
ggplot(mydf, aes(x, predicted, colour = group)) + geom_line()
A second grouping structure can be defined, which will create another
column named facet
, which - as the name implies - might be
used to create a facted plot:
mydf <- ggpredict(fit, terms = c("c12hour", "c172code", "c161sex"))
mydf
#> # Predicted values of Total score BARTHEL INDEX
#>
#> # c172code = low level of education
#> # c161sex = [1] Male
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 73.95 | [69.35, 78.56]
#> 45 | 62.56 | [58.22, 66.89]
#> 85 | 52.42 | [47.89, 56.96]
#> 170 | 30.89 | [24.84, 36.95]
#>
#> # c172code = intermediate level of education
#> # c161sex = [1] Male
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 74.67 | [71.05, 78.29]
#> 45 | 63.27 | [59.88, 66.67]
#> 85 | 53.14 | [49.39, 56.89]
#> 170 | 31.61 | [25.97, 37.25]
#>
#> # c172code = high level of education
#> # c161sex = [1] Male
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 75.39 | [71.03, 79.75]
#> 45 | 63.99 | [59.72, 68.26]
#> 85 | 53.86 | [49.22, 58.50]
#> 170 | 32.33 | [25.94, 38.72]
#>
#> # c172code = low level of education
#> # c161sex = [2] Female
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 75.00 | [71.40, 78.59]
#> 45 | 63.60 | [60.45, 66.74]
#> 85 | 53.46 | [50.12, 56.80]
#> 170 | 31.93 | [26.82, 37.05]
#>
#> # c172code = intermediate level of education
#> # c161sex = [2] Female
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 75.71 | [73.31, 78.12]
#> 45 | 64.32 | [62.41, 66.22]
#> 85 | 54.18 | [51.81, 56.56]
#> 170 | 32.65 | [27.94, 37.37]
#>
#> # c172code = high level of education
#> # c161sex = [2] Female
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 76.43 | [72.88, 79.98]
#> 45 | 65.03 | [61.67, 68.39]
#> 85 | 54.90 | [51.15, 58.65]
#> 170 | 33.37 | [27.69, 39.05]
#>
#> Adjusted for:
#> * neg_c_7 = 11.84
ggplot(mydf, aes(x, predicted, colour = group)) +
geom_line() +
facet_wrap(~facet)
Finally, a third differentation can be defined, creating another
column named panel
. In such cases, you may create multiple
plots (for each value in panel
). ggeffects
takes care of this when you use plot()
and automatically
creates an integrated plot with all panels in one figure.
mydf <- ggpredict(fit, terms = c("c12hour", "c172code", "c161sex", "neg_c_7"))
plot(mydf) + theme(legend.position = "bottom")
Marginal effects for each model term
If the term
argument is either missing or
NULL
, marginal effects for each model term are calculated.
The result is returned as a list, which can be plotted manually (or
using the plot()
function).
mydf <- ggpredict(fit)
mydf
#> $c12hour
#> # Predicted values of Total score BARTHEL INDEX
#>
#> c12hour | Predicted | 95% CI
#> ------------------------------------
#> 0 | 75.44 | [73.25, 77.63]
#> 20 | 70.38 | [68.56, 72.19]
#> 45 | 64.05 | [62.39, 65.70]
#> 65 | 58.98 | [57.15, 60.80]
#> 85 | 53.91 | [51.71, 56.12]
#> 105 | 48.85 | [46.14, 51.55]
#> 125 | 43.78 | [40.51, 47.05]
#> 170 | 32.38 | [27.73, 37.04]
#>
#> Adjusted for:
#> * neg_c_7 = 11.84
#> * c161sex = 1.76
#> * c172code = 1.97
#>
#> $neg_c_7
#> # Predicted values of Total score BARTHEL INDEX
#>
#> neg_c_7 | Predicted | 95% CI
#> ------------------------------------
#> 6 | 78.17 | [75.10, 81.23]
#> 8 | 73.57 | [71.20, 75.94]
#> 12 | 64.38 | [62.73, 66.04]
#> 14 | 59.79 | [57.88, 61.70]
#> 16 | 55.19 | [52.72, 57.67]
#> 20 | 46.00 | [42.04, 49.97]
#> 22 | 41.41 | [36.63, 46.20]
#> 28 | 27.63 | [20.30, 34.96]
#>
#> Adjusted for:
#> * c12hour = 42.20
#> * c161sex = 1.76
#> * c172code = 1.97
#>
#> $c161sex
#> # Predicted values of Total score BARTHEL INDEX
#>
#> c161sex | Predicted | 95% CI
#> ------------------------------------
#> 1 | 63.96 | [60.57, 67.35]
#> 2 | 65.00 | [63.11, 66.90]
#>
#> Adjusted for:
#> * c12hour = 42.20
#> * neg_c_7 = 11.84
#> * c172code = 1.97
#>
#> $c172code
#> # Predicted values of Total score BARTHEL INDEX
#>
#> c172code | Predicted | 95% CI
#> -------------------------------------
#> 1 | 64.06 | [61.01, 67.11]
#> 2 | 64.78 | [63.12, 66.43]
#> 3 | 65.49 | [62.31, 68.68]
#>
#> Adjusted for:
#> * c12hour = 42.20
#> * neg_c_7 = 11.84
#> * c161sex = 1.76
#>
#> attr(,"class")
#> [1] "ggalleffects" "list"
#> attr(,"model.name")
#> [1] "fit"
Two-Way, Three-Way- and Four-Way-Interactions
To plot the marginal effects of interaction terms, simply specify
these terms in the terms
-argument.
library(sjmisc)
data(efc)
# make categorical
efc$c161sex <- to_factor(efc$c161sex)
# fit model with interaction
fit <- lm(neg_c_7 ~ c12hour + barthtot * c161sex, data = efc)
# select only levels 30, 50 and 70 from continuous variable Barthel-Index
mydf <- ggpredict(fit, terms = c("barthtot [30,50,70]", "c161sex"))
ggplot(mydf, aes(x, predicted, colour = group)) + geom_line()
Since the terms
-argument accepts up to four model terms,
you can also compute marginal effects for a 3-way-interaction or
4-way-interaction. To plot the marginal effects of three interaction
terms, just like before, specify all three terms in the
terms
-argument.
# fit model with 3-way-interaction
fit <- lm(neg_c_7 ~ c12hour * barthtot * c161sex, data = efc)
# select only levels 30, 50 and 70 from continuous variable Barthel-Index
mydf <- ggpredict(fit, terms = c("c12hour", "barthtot [30,50,70]", "c161sex"))
ggplot(mydf, aes(x, predicted, colour = group)) +
geom_line() +
facet_wrap(~facet)
4-way-interactions are rather confusing to print and plot. When
plotting, multiple plots (for each level of the fourth interaction term)
are plotted for the remaining three interaction terms. This can easily
be done using the plot()
-method.
# fit model with 4-way-interaction
fit <- lm(neg_c_7 ~ c12hour * barthtot * c161sex * c172code, data = efc)
# marginal effects for all 4 interaction terms
pr <- ggpredict(fit, c("c12hour", "barthtot", "c161sex", "c172code"))
# use plot() method, easier than own ggplot-code from scratch
plot(pr) + theme(legend.position = "bottom")
Polynomial terms and splines
ggpredict()
also works for models with polynomial terms
or splines. Following code reproduces the plot from
?splines::bs
:
library(splines)
data(women)
fm1 <- lm(weight ~ bs(height, df = 5), data = women)
dat <- ggpredict(fm1, "height")
ggplot(dat, aes(x, predicted)) +
geom_line() +
geom_point()
Survival models
ggpredict()
also supports coxph
-models from
the survival-package and is able to either plot
risk-scores (the default), probabilities of survival
(type = "survival"
) or cumulative hazards
(type = "cumulative_hazard"
).
Since probabilities of survival and cumulative hazards are changing
across time, the time-variable is automatically used as x-axis in such
cases, so the terms
-argument only needs up to
two variables for type = "survival"
or
type = "cumulative_hazard"
.
library(survival)
data("lung2")
m <- coxph(Surv(time, status) ~ sex + age + ph.ecog, data = lung2)
# predicted risk-scores
ggpredict(m, c("sex", "ph.ecog"))
#> # Predicted risk scores
#>
#> # ph.ecog = good
#>
#> sex | Predicted | 95% CI
#> ---------------------------------
#> male | 1.00 | [1.00, 1.00]
#> female | 0.58 | [0.42, 0.81]
#>
#> # ph.ecog = ok
#>
#> sex | Predicted | 95% CI
#> ---------------------------------
#> male | 1.51 | [1.02, 2.23]
#> female | 0.87 | [0.53, 1.43]
#>
#> # ph.ecog = limited
#>
#> sex | Predicted | 95% CI
#> ---------------------------------
#> male | 2.47 | [1.58, 3.86]
#> female | 1.43 | [0.83, 2.45]
#>
#> Adjusted for:
#> * age = 62.42
# probability of survival
ggpredict(m, c("sex", "ph.ecog"), type = "survival")
#> # Probability of Survival
#>
#> # sex = male
#> # ph.ecog = good
#>
#> time | Predicted | 95% CI
#> -------------------------------
#> 1 | 1.00 | [1.00, 1.00]
#> 180 | 0.78 | [0.69, 0.87]
#> 276 | 0.65 | [0.54, 0.78]
#> 1022 | 0.09 | [0.03, 0.26]
#>
#> # sex = female
#> # ph.ecog = good
#>
#> time | Predicted | 95% CI
#> -------------------------------
#> 1 | 1.00 | [1.00, 1.00]
#> 180 | 0.87 | [0.80, 0.93]
#> 276 | 0.78 | [0.68, 0.88]
#> 1022 | 0.24 | [0.11, 0.51]
#>
#> # sex = male
#> # ph.ecog = limited
#>
#> time | Predicted | 95% CI
#> -------------------------------
#> 1 | 1.00 | [1.00, 1.00]
#> 180 | 0.54 | [0.42, 0.70]
#> 276 | 0.34 | [0.22, 0.52]
#> 1022 | 0.00 | [0.00, 0.04]
#>
#> # sex = female
#> # ph.ecog = limited
#>
#> time | Predicted | 95% CI
#> -------------------------------
#> 1 | 1.00 | [1.00, 1.00]
#> 180 | 0.70 | [0.59, 0.83]
#> 276 | 0.53 | [0.40, 0.71]
#> 1022 | 0.03 | [0.00, 0.19]
#>
#> # sex = male
#> # ph.ecog = ok
#>
#> time | Predicted | 95% CI
#> -------------------------------
#> 1 | 1.00 | [1.00, 1.00]
#> 180 | 0.69 | [0.60, 0.79]
#> 276 | 0.52 | [0.42, 0.64]
#> 1022 | 0.02 | [0.01, 0.11]
#>
#> # sex = female
#> # ph.ecog = ok
#>
#> time | Predicted | 95% CI
#> -------------------------------
#> 1 | 1.00 | [1.00, 1.00]
#> 180 | 0.80 | [0.73, 0.88]
#> 276 | 0.68 | [0.59, 0.79]
#> 1022 | 0.12 | [0.04, 0.31]
#>
#> Adjusted for:
#> * age = 62.42
Labelling the data
ggeffects makes use of the sjlabelled-package
and supports labelled
data. If the data from the fitted models is labelled, the value and
variable label attributes are usually copied to the model frame stored
in the model object. ggeffects provides various
getter-functions to access these labels, which are returned as
character vector and can be used in ggplot’s lab()
- or
scale_*()
-functions.
-
get_title()
- a generic title for the plot, based on the model family, like “predicted values” or “predicted probabilities” -
get_x_title()
- the variable label of the first model term interms
. -
get_y_title()
- the variable label of the response. -
get_legend_title()
- the variable label of the second model term interms
. -
get_x_labels()
- value labels of the first model term interms
. -
get_legend_labels()
- value labels of the second model term interms
.
The data frame returned by ggpredict()
,
ggemmeans()
or ggeffect()
must be used as
argument to one of the above function calls.
get_x_title(mydf)
#> [1] "average number of hours of care per week"
get_y_title(mydf)
#> [1] "Negative impact with 7 items"
ggplot(mydf, aes(x, predicted, colour = group)) +
geom_line() +
facet_wrap(~facet) +
labs(
x = get_x_title(mydf),
y = get_y_title(mydf),
colour = get_legend_title(mydf)
)