After fitting a model, it is useful generate model-based estimates (expected values, or adjusted predictions) of the response variable for different combinations of predictor values. Such estimates can be used to make inferences about relationships between variables.
The ggeffects package computes marginal means and adjusted predicted
values for the response, at the margin of specific values or levels from
certain model terms. The package is built around three core functions:
predict_response() (understanding results), test_predictions() (importance
of results) and plot() (communicate results).
By default, adjusted predictions or marginal means are returned on the
response scale, which is the easiest and most intuitive scale to interpret
the results. There are other options for specific models as well, e.g. with
zero-inflation component (see documentation of the type-argument). The
result is returned as structured data frame, which is nicely printed by
default. plot() can be used to easily create figures.
The main function to calculate marginal means and adjusted predictions is
predict_response(), which returns adjusted predictions, marginal means
or averaged counterfactual predictions depending on value of the
margin-argument.
In previous versions of ggeffects, the functions ggpredict(), ggemmeans(),
ggeffect() and ggaverage() were used to calculate marginal means and
adjusted predictions. These functions are still available, but predict_response()
as a "wrapper" around these functions is the preferred way to calculate marginal
means and adjusted predictions now.
predict_response(
model,
terms,
margin = "mean_reference",
ci_level = 0.95,
type = "fixed",
condition = NULL,
back_transform = TRUE,
vcov_fun = NULL,
vcov_type = NULL,
vcov_args = NULL,
weights = NULL,
interval,
bias_correction = FALSE,
verbose = TRUE,
...
)A data frame (with ggeffects class attribute) with consistent data columns:
"x": the values of the first term in terms, used as x-position in plots.
"predicted": the predicted values of the response, used as y-position in plots.
"std.error": the standard error of the predictions. Note that the standard
errors are always on the link-scale, and not back-transformed for non-Gaussian
models!
"conf.low": the lower bound of the confidence interval for the predicted values.
"conf.high": the upper bound of the confidence interval for the predicted values.
"group": the grouping level from the second term in terms, used as
grouping-aesthetics in plots.
"facet": the grouping level from the third term in terms, used to indicate
facets in plots.
The estimated marginal means (or predicted values) are always on the response scale!
For proportional odds logistic regression (see ?MASS::polr)
resp. cumulative link models (e.g., see ?ordinal::clm),
an additional column "response.level" is returned, which indicates
the grouping of predictions based on the level of the model's response.
Note that for convenience reasons, the columns for the intervals
are always named "conf.low" and "conf.high", even though
for Bayesian models credible or highest posterior density intervals
are returned.
There is an as.data.frame() method for objects of class ggeffects,
which has an terms_to_colnames argument, to use the term names as column
names instead of the standardized names "x" etc.
A model object.
Names of those terms from model, for which predictions should
be displayed (so called focal terms). Can be:
A character vector, specifying the names of the focal terms. This is the
preferred and probably most flexible way to specify focal terms, e.g.
terms = "x [40:60]", to calculate predictions for the values 40 to 60.
A list, where each element is a named vector, specifying the focal terms
and their values. This is the "classical" R way to specify focal terms,
e.g. list(x = 40:60).
A formula, e.g. terms = ~ x + z, which is internally converted to a
character vector. This is probably the least flexible way, as you cannot
specify representative values for the focal terms.
A data frame representing a "data grid" or "reference grid". Predictions are then made for all combinations of the variables in the data frame.
terms at least requires one variable name. The maximum length is four terms,
where the second to fourth term indicate the groups, i.e. predictions of the first
term are grouped at meaningful values or levels of the remaining terms (see
values_at()). It is also possible to define specific values for focal
terms, at which adjusted predictions should be calculated (see details below).
All remaining covariates that are not specified in terms are "marginalized",
see the margin argument in ?predict_response. See also argument condition
to fix non-focal terms to specific values, and argument typical for
ggpredict() or ggemmeans().
Character string, indicating how to marginalize over the
non-focal predictors, i.e. those variables that are not specified in
terms. Possible values are "mean_reference", "mean_mode",
"marginalmeans" and "empirical" (or "counterfactual", aka average
"counterfactual" predictions). You can set a default-option for the margin
argument via options(), e.g. options(ggeffects_margin = "empirical"),
so you don't have to specify your preferred marginalization method each time
you call predict_response(). See details in the documentation below.
Numeric, the level of the confidence intervals. Use
ci_level = NA if confidence intervals should not be calculated
(for instance, due to computation time). Typically, confidence intervals are
based on the returned standard errors for the predictions, assuming a t- or
normal distribution (based on the model and the available degrees of freedom,
i.e. roughly +/- 1.96 * SE). See introduction of
this vignette
for more details.
Character, indicating whether predictions should be conditioned
on specific model components or not. Consequently, most options only apply
for survival models, mixed effects models and/or models with zero-inflation
(and their Bayesian counter-parts); only exception is type = "simulate",
which is available for some other model classes as well (which respond to
simulate()).
Note 1: For brmsfit-models with zero-inflation component, there is no
type = "zero_inflated" nor type = "zi_random"; predicted values for these
models always condition on the zero-inflation part of the model. The same
is true for MixMod-models from GLMMadaptive with zero-inflation
component (see 'Details').
Note 2: If margin = "empirical", or when calling ggaverage() respectively,
(i.e. counterfactual predictions), the type argument is handled differently.
It is set to "response" by default, but usually accepts all possible options
from the type-argument of the model's respective predict() method. E.g.,
passing a glm object would allow the options "response", "link", and
"terms". For models with zero-inflation component, the below mentioned
options "fixed", "zero_inflated" and "zi_prob" can also be used and will
be "translated" into the corresponding type option of the model's respective
predict()-method.
"fixed" (or "count")
Predicted values are conditioned on the fixed effects or conditional
model only (for mixed models: predicted values are on the population-level
and confidence intervals are returned, i.e. re.form = NA when calling
predict()). For instance, for models fitted with zeroinfl from pscl,
this would return the predicted mean from the count component (without
zero-inflation). For models with zero-inflation component, this type calls
predict(..., type = "link") (however, predicted values are
back-transformed to the response scale, i.e. the conditional mean of the
response).
"random"
This only applies to mixed models, and type = "random" does not condition
on the zero-inflation component of the model. type = "random" still
returns population-level predictions, however, conditioned on random effects
and considering individual level predictions, i.e. re.form = NULL when
calling predict(). This may affect the returned predicted values, depending
on whether REML = TRUE or REML = FALSE was used for model fitting.
Furthermore, unlike type = "fixed", intervals also consider the uncertainty
in the variance parameters (the mean random effect variance, see Johnson
et al. 2014 for details) and hence can be considered as prediction intervals.
For models with zero-inflation component, this type calls
predict(..., type = "link") (however, predicted values are back-transformed
to the response scale).
To get predicted values for each level of the random effects groups, add the
name of the related random effect term to the terms-argument
(for more details, see
this vignette).
"zero_inflated" (or "zi")
Predicted values are conditioned on the fixed effects and the zero-inflation
component. For instance, for models fitted with zeroinfl from pscl,
this would return the predicted (or expected) response (mu*(1-p)),
and for glmmTMB, this would return the expected response mu*(1-p)
without conditioning on random effects (i.e. random effect variances
are not taken into account for the confidence intervals). For models with
zero-inflation component, this type calls predict(..., type = "response").
See 'Details'.
"zi_random" (or "zero_inflated_random")
Predicted values are conditioned on the zero-inflation component and
take the random effects uncertainty into account. For models fitted with
glmmTMB(), hurdle() or zeroinfl(), this would return the
expected value mu*(1-p). For glmmTMB, prediction intervals
also consider the uncertainty in the random effects variances. This
type calls predict(..., type = "response"). See 'Details'.
"zi_prob"
Predicted zero-inflation probability. For glmmTMB models with
zero-inflation component, this type calls predict(..., type = "zlink");
models from pscl call predict(..., type = "zero") and for
GLMMadaptive, predict(..., type = "zero_part") is called.
"simulate"
Predicted values and confidence resp. prediction intervals are
based on simulations, i.e. calls to simulate(). This type
of prediction takes all model uncertainty into account, including
random effects variances. Currently supported models are objects of
class lm, glm, glmmTMB, wbm, MixMod and merMod.
See ... for details on number of simulations.
"survival" and "cumulative_hazard"
Applies only to coxph-objects from the survial-package and
calculates the survival probability or the cumulative hazard of an event.
When margin = "empirical" (or when calling ggaverage()), the type
argument accepts all values from the type-argument of the model's respective
predict()-method.
Named character vector, which indicates covariates that
should be held constant at specific values. Unlike typical, which
applies a function to the covariates to determine the value that is used
to hold these covariates constant, condition can be used to define
exact values, for instance condition = c(covariate1 = 20, covariate2 = 5).
See 'Examples'.
Logical, if TRUE (the default), predicted values for
log-, log-log, exp, sqrt and similar transformed responses will be
back-transformed to original response-scale. See
insight::find_transformation() for more details.
Variance-covariance matrix used to compute uncertainty estimates (e.g., for confidence intervals based on robust standard errors). This argument accepts a covariance matrix, a function which returns a covariance matrix, or a string which identifies the function to be used to compute the covariance matrix.
A (variance-covariance) matrix
A function which returns a covariance matrix (e.g., stats::vcov())
A string which indicates the estimation type for the heteroscedasticity-consistent
variance-covariance matrix, e.g. vcov_fun = "HC0". Possible values are
"HC0", "HC1", "HC2", "HC3", "HC4", "HC4m", and "HC5", which
will then call the vcovHC()-function from the sandwich package, using
the specified type. Further possible values are "CR0", "CR1", "CR1p",
"CR1S", "CR2", and "CR3", which will call the vcovCR()-function from
the clubSandwich package.
A string which indicates the name of the vcov*()-function from the
sandwich or clubSandwich packages, e.g. vcov_fun = "vcovCL",
which is used to compute (cluster) robust standard errors for predictions.
If NULL, standard errors (and confidence intervals) for predictions are
based on the standard errors as returned by the predict()-function.
Note that probably not all model objects that work with predict_response()
are also supported by the sandwich or clubSandwich packages.
See details in this vignette.
Character vector, specifying the estimation type for the
robust covariance matrix estimation (see ?sandwich::vcovHC
or ?clubSandwich::vcovCR for details). Only used when vcov_fun is a
character string indicating one of the functions from those packages.
When vcov_fun is a function, a possible type argument must be provided
via the vcov_args argument.
List of named vectors, used as additional arguments that
are passed down to vcov_fun.
This argument is used in two different ways, depending on the
margin argument.
When margin = "empirical", weights can either be a character vector,
naming the weigthing variable in the data, or a vector of weights (of same
length as the number of observations in the data). This variable will be
used to weight adjusted predictions.
When margin = "marginalmeans", weights must be a character vector and
is passed to emmeans::emmeans(), specifying weights to use in averaging
non-focal categorical predictors. See https://rvlenth.github.io/emmeans/reference/emmeans.html
for details.
Type of interval calculation, can either be "confidence"
(default) or "prediction". May be abbreviated. Unlike confidence intervals,
prediction intervals include the residual variance (sigma^2) to account for
the uncertainty of predicted values. For mixed models, interval = "prediction"
is the default for type = "random". When type = "fixed", the default is
interval = "confidence". Note that prediction intervals are not available
for all models, but only for models that work with insight::get_sigma().
For Bayesian models, when interval = "confidence", predictions are based on
posterior draws of the linear predictor rstantools::posterior_epred().
If interval = "prediction", rstantools::posterior_predict() is called.
Logical, if TRUE, adjusts for bias-correction when
back-transforming the predicted values (to the response scale) for
non-Gaussian mixed models. Back-transforming the the population-level
predictions ignores the effect of the variation around the population mean,
so the result on the original data scale is biased due to Jensen's
inequality. To apply bias-correction, a valid value of sigma is required,
which is extracted by default using insight::get_variance_residual().
Optionally, to provide own estimates of uncertainty, use the sigma
argument. Note that bias_correction currently only applies to mixed models,
where there are additive random components involved and where that
bias-adjustment can be appropriate. If ggemmeans() is called,
bias-correction can also be applied to GEE-models.
Toggle messages or warnings.
If margin is set to "mean_reference" or "mean_mode", arguments
are passed down to ggpredict() (further down to predict()); for
margin = "marginalmeans", further arguments passed down to ggemmeans() and
thereby to emmeans::emmeans(); if margin = "empirical", further arguments are
passed down to marginaleffects::avg_predictions(). If type = "simulate",
... may also be used to set the number of simulation, e.g. nsim = 500.
When calling ggeffect(), further arguments passed down to effects::Effect().
A list of supported models can be found at the package website.
Support for models varies by marginalization method (the margin argument),
i.e. although predict_response() supports most models, some models are only
supported exclusively by one of the four downstream functions (ggpredict(),
ggemmeans(), ggeffect() or ggaverage()). This means that not all models
work for every margin option of predict_response().
predict_response() is a wrapper around ggpredict(), ggemmeans() and
ggaverage(). Depending on the value of the margin argument,
predict_response() calls one of those functions. The margin argument
indicates how to marginalize over the non-focal predictors, i.e. those
variables that are not specified in terms. Possible values are:
"mean_reference" and "mean_mode": For "mean_reference", non-focal
predictors are set to their mean (numeric variables), reference level
(factors), or "most common" value (mode) in case of character vectors.
For "mean_mode", non-focal predictors are set to their mean (numeric
variables) or mode (factors, or "most common" value in case of character
vectors).
These predictons represent a rather "theoretical" view on your data, which does not necessarily exactly reflect the characteristics of your sample. It helps answer the question, "What is the predicted (or: expected) value of the response at meaningful values or levels of my focal terms for a 'typical' observation in my data?", where 'typical' refers to certain characteristics of the remaining predictors.
"marginalmeans": non-focal predictors are set to their mean (numeric
variables) or averaged over the levels or "values" for factors and
character vectors. Averaging over the factor levels of non-focal terms
computes a kind of "weighted average" for the values at which these terms
are hold constant. Thus, non-focal categorical terms are conditioned on
"weighted averages" of their levels. There are different weighting
options that can be altered using the weights argument.
These predictions come closer to the sample, because all possible values and levels of the non-focal predictors are taken into account. It would answer the question, "What is the predicted (or: expected) value of the response at meaningful values or levels of my focal terms for an 'average' observation in my data?". It refers to randomly picking a subject of your sample and the result you get on average.
"empirical" (or "counterfactual"): non-focal predictors are averaged
over the observations in the sample. The response is predicted for each
subject in the data and predicted values are then averaged across all
subjects, aggregated/grouped by the focal terms. In particular, averaging
is applied to counterfactual predictions (Dickerman and Hernan 2020).
There is a more detailed description in
this vignette.
Counterfactual predictions are useful, insofar as the results can also be transferred to other contexts. It answers the question, "What is the predicted (or: expected) value of the response at meaningful values or levels of my focal terms for the 'average' observation in the population?". It does not only refer to the actual data in your sample, but also "what would be if" we had more data, or if we had data from a different population. This is where "counterfactual" refers to.
You can set a default-option for the margin argument via options(), e.g.
options(ggeffects_margin = "empirical"), so you don't have to specify your
"default" marginalization method each time you call predict_response().
Use options(ggeffects_margin = NULL) to remove that setting.
The condition argument can be used to fix non-focal terms to specific
values.
Meaningful values of focal terms can be specified via the terms argument.
Specifying meaningful or representative values as string pattern is the
preferred way in the ggeffects package. However, it is also possible to
use a list() for the focal terms if prefer the "classical" R way. terms
can also be a data (or reference) grid provided as data frame. All options
are described in this vignette.
Indicating levels in square brackets allows for selecting only certain
groups or values resp. value ranges. The term name and the start of the
levels in brackets must be separated by a whitespace character, e.g.
terms = c("age", "education [1,3]"). Numeric ranges, separated with colon,
are also allowed: terms = c("education", "age [30:60]"). The stepsize for
ranges can be adjusted using by, e.g. terms = "age [30:60 by=5]".
The terms argument also supports the same shortcuts as the values argument
in values_at(). So terms = "age [meansd]" would return predictions for
the values one standard deviation below the mean age, the mean age and one SD
above the mean age. terms = "age [quart2]" would calculate predictions at
the value of the lower, median and upper quartile of age.
Furthermore, it is possible to specify a function name. Values for predictions
will then be transformed, e.g. terms = "income [exp]". This is useful when
model predictors were transformed for fitting the model and should be
back-transformed to the original scale for predictions. It is also possible
to define own functions (see
this vignette).
Instead of a function, it is also possible to define the name of a variable
with specific values, e.g. to define a vector v = c(1000, 2000, 3000) and
then use terms = "income [v]".
You can take a random sample of any size with sample=n, e.g
terms = "income [sample=8]", which will sample eight values from
all possible values of the variable income. This option is especially
useful for plotting predictions at certain levels of random effects
group levels, where the group factor has too many levels to be completely
plotted. For more details, see
this vignette.
Finally, numeric vectors for which no specific values are given, a "pretty range"
is calculated (see pretty_range()), to avoid memory allocation problems
for vectors with many unique values. If a numeric vector is specified as
second or third term (i.e. if this focal term is used for "stratification"),
representative values (see values_at()) are chosen (unless other values
are specified), which are typically the mean value, as well as one standard
deviation below and above the mean. If all values for a numeric vector should
be used to compute predictions, you may use e.g. terms = "age [all]". See
also package vignettes.
To create a pretty range that should be smaller or larger than the default
range (i.e. if no specific values would be given), use the n tag, e.g.
terms="age [n=5]" or terms="age [n=12]". Larger values for n return a
larger range of predicted values.
predict_response() also works with Stan-models from the rstanarm or
brms-packages. The predicted values are the median value of all drawn
posterior samples. Standard errors are the median absolute deviation of the
posterior samples. The confidence intervals for Stan-models are Bayesian
predictive intervals. By default, the predictions are based on
rstantools::posterior_epred() and hence have the limitations that the
uncertainty of the error term (residual variance) is not taken into account.
The recommendation is to use the posterior predictive distribution
(rstantools::posterior_predict()), i.e. setting interval = "prediction".
Models of class brmsfit always condition on the zero-inflation component,
if the model has such a component. Hence, there is no type = "zero_inflated"
nor type = "zi_random" for brmsfit-models, because predictions are based
on draws of the posterior distribution, which already account for the
zero-inflation part of the model.
Zero-Inflated and Zero-Inflated Mixed Models with glmmTMB
If model is of class glmmTMB, hurdle, zeroinfl or zerotrunc, and
margin is not set to "empirical, simulations from a multivariate
normal distribution (see ?MASS::mvrnorm) are drawn to calculate mu*(1-p).
Confidence intervals are then based on quantiles of these results.
For type = "zi_random", prediction intervals also take the uncertainty in
the random-effect paramters into account (see also Brooks et al. 2017,
pp.391-392 for details).
An alternative for models fitted with glmmTMB that take all model
uncertainties into account are simulations based on simulate(), which
is used when type = "simulate" (see Brooks et al. 2017, pp.392-393 for
details).
Finally, if margin = "empirical", the returned predictions are already
conditioned on the zero-inflation part (and possible random effects) of the
model, thus these are most comparable to the type = "simulate" option. In
other words, if all model components should be taken into account for
predictions, you should consider using margin = "empirical".
Predicted values for the fixed effects component (type = "fixed" or
type = "zero_inflated") are based on predict(..., type = "mean_subject"),
while predicted values for random effects components (type = "random" or
type = "zi_random") are calculated with predict(..., type = "subject_specific")
(see ?GLMMadaptive::predict.MixMod for details). The latter option
requires the response variable to be defined in the newdata-argument
of predict(), which will be set to its typical value (see
values_at()).
polr, clm models, or more generally speaking, models with ordinal or
multinominal outcomes, have an additional column response.level, which
indicates with which level of the response variable the predicted values are
associated.
For averaged model predictions, i.e. when the input model is an object of
class "averaging" (MuMIn::model.avg()), predictions are made with the
full averaged coefficients.
Brooks ME, Kristensen K, Benthem KJ van, Magnusson A, Berg CW, Nielsen A, et al. glmmTMB Balances Speed and Flexibility Among Packages for Zero-inflated Generalized Linear Mixed Modeling. The R Journal. 2017;9: 378-400.
Johnson PC. 2014. Extension of Nakagawa & Schielzeth's R2GLMM to random slopes models. Methods Ecol Evol, 5: 944-946.
Dickerman BA, Hernan, MA. Counterfactual prediction is not only for causal inference. Eur J Epidemiol 35, 615–617 (2020).
if (FALSE) { # requireNamespace("sjlabelled") && requireNamespace("ggplot2")
library(sjlabelled)
data(efc)
fit <- lm(barthtot ~ c12hour + neg_c_7 + c161sex + c172code, data = efc)
predict_response(fit, terms = "c12hour")
predict_response(fit, terms = c("c12hour", "c172code"))
# more compact table layout for printing
out <- predict_response(fit, terms = c("c12hour", "c172code", "c161sex"))
print(out, collapse_table = TRUE)
# specified as formula
predict_response(fit, terms = ~ c12hour + c172code + c161sex)
# only range of 40 to 60 for variable 'c12hour'
predict_response(fit, terms = "c12hour [40:60]")
# terms as named list
predict_response(fit, terms = list(c12hour = 40:60))
# covariate "neg_c_7" is held constant at a value of 11.84 (its mean value).
# To use a different value, use "condition"
predict_response(fit, terms = "c12hour [40:60]", condition = c(neg_c_7 = 20))
# to plot ggeffects-objects, you can use the 'plot()'-function.
# the following examples show how to build your ggplot by hand.
# \donttest{
# plot predicted values, remaining covariates held constant
library(ggplot2)
mydf <- predict_response(fit, terms = "c12hour")
ggplot(mydf, aes(x, predicted)) +
geom_line() +
geom_ribbon(aes(ymin = conf.low, ymax = conf.high), alpha = 0.1)
# three variables, so we can use facets and groups
mydf <- predict_response(fit, terms = c("c12hour", "c161sex", "c172code"))
ggplot(mydf, aes(x = x, y = predicted, colour = group)) +
stat_smooth(method = "lm", se = FALSE) +
facet_wrap(~facet, ncol = 2)
# select specific levels for grouping terms
mydf <- predict_response(fit, terms = c("c12hour", "c172code [1,3]", "c161sex"))
ggplot(mydf, aes(x = x, y = predicted, colour = group)) +
stat_smooth(method = "lm", se = FALSE) +
facet_wrap(~facet) +
labs(
y = get_y_title(mydf),
x = get_x_title(mydf),
colour = get_legend_title(mydf)
)
# level indication also works for factors with non-numeric levels
# and in combination with numeric levels for other variables
data(efc)
efc$c172code <- sjlabelled::as_label(efc$c172code)
fit <- lm(barthtot ~ c12hour + neg_c_7 + c161sex + c172code, data = efc)
predict_response(fit, terms = c(
"c12hour",
"c172code [low level of education, high level of education]",
"c161sex [1]"
))
# when "terms" is a named list
predict_response(fit, terms = list(
c12hour = seq(0, 170, 30),
c172code = c("low level of education", "high level of education"),
c161sex = 1
))
# use categorical value on x-axis, use axis-labels, add error bars
dat <- predict_response(fit, terms = c("c172code", "c161sex"))
ggplot(dat, aes(x, predicted, colour = group)) +
geom_point(position = position_dodge(0.1)) +
geom_errorbar(
aes(ymin = conf.low, ymax = conf.high),
position = position_dodge(0.1)
) +
scale_x_discrete(breaks = 1:3, labels = get_x_labels(dat))
# 3-way-interaction with 2 continuous variables
data(efc)
# make categorical
efc$c161sex <- as_factor(efc$c161sex)
fit <- lm(neg_c_7 ~ c12hour * barthtot * c161sex, data = efc)
# select only levels 30, 50 and 70 from continuous variable Barthel-Index
dat <- predict_response(fit, terms = c("c12hour", "barthtot [30,50,70]", "c161sex"))
ggplot(dat, aes(x = x, y = predicted, colour = group)) +
stat_smooth(method = "lm", se = FALSE, fullrange = TRUE) +
facet_wrap(~facet) +
labs(
colour = get_legend_title(dat),
x = get_x_title(dat),
y = get_y_title(dat),
title = get_title(dat)
)
# or with ggeffects' plot-method
plot(dat, show_ci = FALSE)
# }
# predictions for polynomial terms
data(efc)
fit <- glm(
tot_sc_e ~ c12hour + e42dep + e17age + I(e17age^2) + I(e17age^3),
data = efc,
family = poisson()
)
predict_response(fit, terms = "e17age")
}
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