# Adjusted predictions from regression models

Source:`R/data_frame_methods.R`

, `R/ggaverage.R`

, `R/ggeffect.R`

, and 2 more
`ggpredict.Rd`

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()`

(testing
results for statistically significant differences) and `plot()`

(communicate
results).

By default, adjusted predictions or marginal means are by 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 consistent 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()`

. 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 do this now.

## Usage

```
# S3 method for class 'ggeffects'
as.data.frame(
x,
row.names = NULL,
optional = FALSE,
...,
stringsAsFactors = FALSE,
terms_to_colnames = FALSE
)
ggaverage(
model,
terms,
ci_level = 0.95,
type = "fixed",
typical = "mean",
condition = NULL,
back_transform = TRUE,
vcov_fun = NULL,
vcov_type = NULL,
vcov_args = NULL,
weights = NULL,
verbose = TRUE,
...
)
ggeffect(model, terms, ci_level = 0.95, verbose = TRUE, ci.lvl = ci_level, ...)
ggemmeans(
model,
terms,
ci_level = 0.95,
type = "fixed",
typical = "mean",
condition = NULL,
back_transform = TRUE,
vcov_fun = NULL,
vcov_type = NULL,
vcov_args = NULL,
interval = "confidence",
verbose = TRUE,
ci.lvl = ci_level,
back.transform = back_transform,
...
)
ggpredict(
model,
terms,
ci_level = 0.95,
type = "fixed",
typical = "mean",
condition = NULL,
back_transform = TRUE,
vcov_fun = NULL,
vcov_type = NULL,
vcov_args = NULL,
interval,
verbose = TRUE,
ci.lvl = ci_level,
back.transform = back_transform,
vcov.fun = vcov_fun,
vcov.type = vcov_type,
vcov.args = vcov_args,
...
)
```

## Arguments

- x
An object of class

`ggeffects`

, as returned by`predict_response()`

,`ggpredict()`

,`ggeffect()`

,`ggaverage()`

or`ggemmeans()`

.- row.names
`NULL`

or a character vector giving the row names for the data frame. Missing values are not allowed.- optional
logical. If

`TRUE`

, setting row names and converting column names (to syntactic names: see`make.names`

) is optional. Note that all of R's base package`as.data.frame()`

methods use`optional`

only for column names treatment, basically with the meaning of`data.frame(*, check.names = !optional)`

. See also the`make.names`

argument of the`matrix`

method.- ...
Arguments are passed down to

`ggpredict()`

(further down to`predict()`

) or`ggemmeans()`

(and thereby to`emmeans::emmeans()`

), 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()`

.- stringsAsFactors
logical: should the character vector be converted to a factor?

- terms_to_colnames
Logical, if

`TRUE`

, standardized column names (like`"x"`

,`"group"`

or`"facet"`

) are replaced by the variable names of the focal predictors specified in`terms`

.- model
A model object, or a list of model objects.

- terms
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()`

.- ci_level
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.- type
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.- typical
Character vector, naming the function to be applied to the covariates (non-focal terms) over which the effect is "averaged". The default is

`"mean"`

. Can be`"mean"`

, "`weighted.mean`

",`"median"`

,`"mode"`

or`"zero"`

, which call the corresponding R functions (except`"mode"`

, which calls an internal function to compute the most common value);`"zero"`

simply returns 0. By default, if the covariate is a factor, only`"mode"`

is applicable; for all other values (including the default,`"mean"`

) the reference level is returned. For character vectors, only the mode is returned. You can use a named vector to apply different functions to integer, numeric and categorical covariates, e.g.`typical = c(numeric = "median", factor = "mode")`

. If`typical`

is`"weighted.mean"`

, weights from the model are used. If no weights are available, the function falls back to`"mean"`

.**Note**that this argument is ignored for`predict_response()`

, because the`margin`

argument takes care of this.- condition
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'.- back_transform
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.- vcov_fun
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.

- vcov_type
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.- vcov_args
List of named vectors, used as additional arguments that are passed down to

`vcov_fun`

.- weights
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.

- verbose
Toggle messages or warnings.

- ci.lvl, vcov.fun, vcov.type, vcov.args, back.transform
Deprecated arguments. Please use

`ci_level`

,`vcov_fun`

,`vcov_type`

,`vcov_args`

and`back_transform`

instead.- interval
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.

## Value

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.

## Details

Please see `?predict_response`

for details and examples.