# (Pairwise) comparisons between predictions (marginal effects)

Source:`R/test_predictions.R`

`test_predictions.Rd`

Function to test differences of adjusted predictions for
statistical significance. This is usually called contrasts or (pairwise)
comparisons, or "marginal effects". `hypothesis_test()`

is an alias.

## Usage

```
test_predictions(object, ...)
hypothesis_test(object, ...)
# Default S3 method
test_predictions(
object,
terms = NULL,
by = NULL,
test = "pairwise",
equivalence = NULL,
scale = "response",
p_adjust = NULL,
df = NULL,
ci_level = 0.95,
collapse_levels = FALSE,
margin = "mean_reference",
engine = "marginaleffects",
verbose = TRUE,
...
)
# S3 method for class 'ggeffects'
test_predictions(
object,
by = NULL,
test = "pairwise",
equivalence = NULL,
scale = "response",
p_adjust = NULL,
df = NULL,
collapse_levels = FALSE,
engine = "marginaleffects",
verbose = TRUE,
...
)
```

## Arguments

- object
A fitted model object, or an object of class

`ggeffects`

. If`object`

is of class`ggeffects`

, arguments`terms`

,`margin`

and`ci_level`

are taken from the`ggeffects`

object and don't need to be specified.- ...
Arguments passed down to

`data_grid()`

when creating the reference grid and to`marginaleffects::predictions()`

resp.`marginaleffects::slopes()`

. For instance, arguments`type`

or`transform`

can be used to back-transform comparisons and contrasts to different scales.`vcov`

can be used to calculate heteroscedasticity-consistent standard errors for contrasts. See examples at the bottom of this vignette for further details.To define a heteroscedasticity-consistent variance-covariance matrix, you can either use the same arguments as for

`predict_response()`

etc., namely`vcov_fun`

,`vcov_type`

and`vcov_args`

. These are then transformed into a matrix and passed down to the`vcov`

argument in**marginaleffects**. Or you directly use the`vcov`

argument. See`?marginaleffects::slopes`

for further details.- terms
If

`object`

is an object of class`ggeffects`

, the same`terms`

argument is used as for the predictions, i.e.`terms`

can be ignored. Else, if`object`

is a model object,`terms`

must be a character vector with the names of the focal terms from`object`

, for which contrasts or comparisons should be displayed. At least one term is required, maximum length is three terms. If the first focal term is numeric, contrasts or comparisons for the*slopes*of this numeric predictor are computed (possibly grouped by the levels of further categorical focal predictors).- by
Character vector specifying the names of predictors to condition on. Hypothesis test is then carried out for focal terms by each level of

`by`

variables. This is useful especially for interaction terms, where we want to test the interaction within "groups".`by`

is only relevant for categorical predictors.- test
Hypothesis to test, defined as character string. Can be one of:

`"pairwise"`

(default), to test pairwise comparisons.`"trend"`

(or`"slope"`

) to test for the linear trend/slope of (usually) continuous predictors. These options are just aliases for setting`trend = NULL`

.`"contrast"`

to test simple contrasts (i.e. each level is tested against the average over*all*levels).`"exclude"`

to test simple contrasts (i.e. each level is tested against the average over*all other*levels, excluding the contrast that is being tested).`"interaction"`

to test interaction contrasts (difference-in-difference contrasts).`"consecutive"`

to test contrasts between consecutive levels of a predictor.`"polynomial"`

to test orthogonal polynomial contrasts, assuming equally-spaced factor levels.A character string with a custom hypothesis, e.g.

`"b2 = b1"`

. This would test if the second level of a predictor is different from the first level. Custom hypotheses are very flexible. It is also possible to test interaction contrasts (difference-in-difference contrasts) with custom hypotheses, e.g.`"(b2 - b1) = (b4 - b3)"`

. See also section*Introduction into contrasts and pairwise comparisons*.A data frame with custom contrasts. See 'Examples'.

`NULL`

, in which case simple contrasts are computed.

Technical details about the packages used as back-end to calculate contrasts and pairwise comparisons are provided in the section

*Packages used as back-end to calculate contrasts and pairwise comparisons*below.- equivalence
ROPE's lower and higher bounds. Should be

`"default"`

or a vector of length two (e.g.,`c(-0.1, 0.1)`

). If`"default"`

,`bayestestR::rope_range()`

is used. Instead of using the`equivalence`

argument, it is also possible to call the`equivalence_test()`

method directly. This requires the**parameters**package to be loaded. When using`equivalence_test()`

, two more columns with information about the ROPE coverage and decision on H0 are added. Furthermore, it is possible to`plot()`

the results from`equivalence_test()`

. See`bayestestR::equivalence_test()`

resp.`parameters::equivalence_test.lm()`

for details.- scale
Character string, indicating the scale on which the contrasts or comparisons are represented. Can be one of:

`"response"`

(default), which would return contrasts on the response scale (e.g. for logistic regression, as probabilities);`"link"`

to return contrasts on scale of the linear predictors (e.g. for logistic regression, as log-odds);`"probability"`

(or`"probs"`

) returns contrasts on the probability scale, which is required for some model classes, like`MASS::polr()`

;`"oddsratios"`

to return contrasts on the odds ratio scale (only applies to logistic regression models);`"irr"`

to return contrasts on the odds ratio scale (only applies to count models);or a transformation function like

`"exp"`

or`"log"`

, to return transformed (exponentiated respectively logarithmic) contrasts; note that these transformations are applied to the*response scale*.

**Note:**If the`scale`

argument is not supported by the provided`object`

, it is automatically changed to a supported scale-type (a message is printed when`verbose = TRUE`

).- p_adjust
Character vector, if not

`NULL`

, indicates the method to adjust p-values. See`stats::p.adjust()`

or`stats::p.adjust.methods`

for details. Further possible adjustment methods are`"tukey"`

or`"sidak"`

, and for`johnson_neyman()`

,`"fdr"`

(or`"bh"`

) and`"esarey"`

(or its short-cut`"es"`

) are available options. Some caution is necessary when adjusting p-value for multiple comparisons. See also section*P-value adjustment*below.- df
Degrees of freedom that will be used to compute the p-values and confidence intervals. If

`NULL`

, degrees of freedom will be extracted from the model using`insight::get_df()`

with`type = "wald"`

.- ci_level
Numeric, the level of the confidence intervals. If

`object`

is an object of class`ggeffects`

, the same`ci_level`

argument is used as for the predictions, i.e.`ci_level`

can be ignored.- collapse_levels
Logical, if

`TRUE`

, term labels that refer to identical levels are no longer separated by "-", but instead collapsed into a unique term label (e.g.,`"level a-level a"`

becomes`"level a"`

). See 'Examples'.- margin
Character string, indicates the method how to marginalize over non-focal terms. See

`predict_response()`

for details. If`object`

is an object of class`ggeffects`

, the same`margin`

argument is used as for the predictions, i.e.`margin`

can be ignored.- engine
Character string, indicates the package to use for computing contrasts and comparisons. Usually, this argument can be ignored, unless you want to explicitly use another package than

*marginaleffects*to calculate contrasts and pairwise comparisons.`engine`

can be either`"marginaleffects"`

(default) or`"emmeans"`

. The latter is useful when the**marginaleffects**package is not available, or when the**emmeans**package is preferred. Note that using**emmeans**as back-end is currently not as feature rich as the default (**marginaleffects**) and still in development. Setting`engine = "emmeans"`

provides some additional test options:`"interaction"`

to calculate interaction contrasts,`"consecutive"`

to calculate contrasts between consecutive levels of a predictor, or a data frame with custom contrasts (see also`test`

). There is an experimental option as well,`engine = "ggeffects"`

. However, this is currently work-in-progress and offers much less options as the default engine,`"marginaleffects"`

. It can be faster in some cases, though, and works for comparing predicted random effects in mixed models, or predicted probabilities of the zero-inflation component. If the**marginaleffects**package is not installed, the**emmeans**package is used automatically. If this package is not installed as well,`engine = "ggeffects"`

is used.- verbose
Toggle messages and warnings.

## Value

A data frame containing predictions (e.g. for `test = NULL`

),
contrasts or pairwise comparisons of adjusted predictions or estimated
marginal means.

## Introduction into contrasts and pairwise comparisons

There are many ways to test contrasts or pairwise comparisons. A detailed introduction with many (visual) examples is shown in this vignette.

## Simple workflow for pairwise comparisons

A simple workflow includes calculating adjusted predictions and passing the
results directly to `test_predictions()`

, e.g.:

```
# 1. fit your model
model <- lm(mpg ~ hp + wt + am, data = mtcars)
# 2. calculate adjusted predictions
pr <- predict_response(model, "am")
pr
# 3. test pairwise comparisons
test_predictions(pr)
```

See also this vignette.

## Packages used as back-end to calculate contrasts and pairwise comparisons

The `test`

argument is used to define which kind of contrast or comparison
should be calculated. The default is to use the **marginaleffects** package.
Here are some technical details about the packages used as back-end. When
`test`

is...

`"pairwise"`

(default), pairwise comparisons are based on the**marginaleffects**package.`"trend"`

or`"slope"`

also uses the**marginaleffects**package.`"contrast"`

uses the**emmeans**package, i.e.`emmeans::contrast(method = "eff")`

is called.`"exclude"`

relies on the**emmeans**package, i.e.`emmeans::contrast(method = "del.eff")`

is called.`"polynomial"`

relies on the**emmeans**package, i.e.`emmeans::contrast(method = "poly")`

is called.`"interaction"`

uses the**emmeans**package, i.e.`emmeans::contrast(interaction = ...)`

is called.`"consecutive"`

also relies on the**emmeans**package, i.e.`emmeans::contrast(method = "consec")`

is called.a character string with a custom hypothesis, the

**marginaleffects**package is used.a data frame with custom contrasts,

**emmeans**is used again.`NULL`

calls functions from the**marginaleffects**package with`hypothesis = NULL`

.If all focal terms are only present as random effects in a mixed model, or if predicted probabilities for the zero-inflation component of a model should be tested, functions from the

**ggeffects**package are used. There is an example for pairwise comparisons of random effects in this vignette.

## P-value adjustment for multiple comparisons

Note that p-value adjustment for methods supported by `p.adjust()`

(see also
`p.adjust.methods`

), each row is considered as one set of comparisons, no
matter which `test`

was specified. That is, for instance, when `test_predictions()`

returns eight rows of predictions (when `test = NULL`

), and `p_adjust = "bonferroni"`

,
the p-values are adjusted in the same way as if we had a test of pairwise
comparisons (`test = "pairwise"`

) where eight rows of comparisons are
returned. For methods `"tukey"`

or `"sidak"`

, a rank adjustment is done
based on the number of combinations of levels from the focal predictors
in `terms`

. Thus, the latter two methods may be useful for certain tests
only, in particular pairwise comparisons.

For `johnson_neyman()`

, the only available adjustment methods are `"fdr"`

(or `"bh"`

) (*Benjamini & Hochberg (1995)*) and `"esarey"`

(or `"es"`

)
(*Esarey and Sumner 2017*). These usually return similar results. The major
difference is that `"fdr"`

can be slightly faster and more stable in edge
cases, however, confidence intervals are not updated. Only the p-values are
adjusted. `"esarey"`

is slower, but confidence intervals are updated as well.

## Global options to choose package for calculating comparisons

`ggeffects_test_engine`

can be used as option to either use the **marginaleffects**
package for computing contrasts and comparisons (default), or the **emmeans**
package (e.g. `options(ggeffects_test_engine = "emmeans")`

). The latter is
useful when the **marginaleffects** package is not available, or when the
**emmeans** package is preferred. You can also provide the engine directly, e.g.
`test_predictions(..., engine = "emmeans")`

. Note that using **emmeans** as
backend is currently not as feature rich as the default (**marginaleffects**)
and still in development.

If `engine = "emmeans"`

, the `test`

argument can also be `"interaction"`

to calculate interaction contrasts (difference-in-difference contrasts),
`"consecutive"`

to calculate contrasts between consecutive levels of a predictor,
or a data frame with custom contrasts. If `test`

is one of the latter options,
and `engine`

is not specified, the `engine`

is automatically set to `"emmeans"`

.

If the **marginaleffects** package is not installed, the **emmeans** package is
used automatically. If this package is not installed as well,
`engine = "ggeffects"`

is used.

## Global Options to Customize Tables when Printing

The `verbose`

argument can be used to display or silence messages and
warnings. Furthermore, `options()`

can be used to set defaults for the
`print()`

and `print_html()`

method. The following options are available,
which can simply be run in the console:

`ggeffects_ci_brackets`

: Define a character vector of length two, indicating the opening and closing parentheses that encompass the confidence intervals values, e.g.`options(ggeffects_ci_brackets = c("[", "]"))`

.`ggeffects_collapse_ci`

: Logical, if`TRUE`

, the columns with predicted values (or contrasts) and confidence intervals are collapsed into one column, e.g.`options(ggeffects_collapse_ci = TRUE)`

.`ggeffects_collapse_p`

: Logical, if`TRUE`

, the columns with predicted values (or contrasts) and p-values are collapsed into one column, e.g.`options(ggeffects_collapse_p = TRUE)`

. Note that p-values are replaced by asterisk-symbols (stars) or empty strings when`ggeffects_collapse_p = TRUE`

, depending on the significance level.`ggeffects_collapse_tables`

: Logical, if`TRUE`

, multiple tables for subgroups are combined into one table. Only works when there is more than one focal term, e.g.`options(ggeffects_collapse_tables = TRUE)`

.`ggeffects_output_format`

: String, either`"text"`

,`"markdown"`

or`"html"`

. Defines the default output format from`predict_response()`

. If`"html"`

, a formatted HTML table is created and printed to the view pane.`"markdown"`

creates a markdown-formatted table inside Rmarkdown documents, and prints a text-format table to the console when used interactively. If`"text"`

or`NULL`

, a formatted table is printed to the console, e.g.`options(ggeffects_output_format = "html")`

.`ggeffects_html_engine`

: String, either`"tt"`

or`"gt"`

. Defines the default engine to use for printing HTML tables. If`"tt"`

, the*tinytable*package is used, if`"gt"`

, the*gt*package is used, e.g.`options(ggeffects_html_engine = "gt")`

.

Use `options(<option_name> = NULL)`

to remove the option.

## References

Esarey, J., & Sumner, J. L. (2017). Marginal effects in interaction models: Determining and controlling the false positive rate. Comparative Political Studies, 1–33. Advance online publication. doi: 10.1177/0010414017730080

## See also

There is also an `equivalence_test()`

method in the **parameters**
package (`parameters::equivalence_test.lm()`

), which can be used to
test contrasts or comparisons for practical equivalence. This method also
has a `plot()`

method, hence it is possible to do something like:

## Examples

```
if (FALSE) { # requireNamespace("marginaleffects") && requireNamespace("parameters") && interactive()
# \donttest{
data(efc)
efc$c172code <- as.factor(efc$c172code)
efc$c161sex <- as.factor(efc$c161sex)
levels(efc$c161sex) <- c("male", "female")
m <- lm(barthtot ~ c12hour + neg_c_7 + c161sex + c172code, data = efc)
# direct computation of comparisons
test_predictions(m, "c172code")
# passing a `ggeffects` object
pred <- predict_response(m, "c172code")
test_predictions(pred)
# test for slope
test_predictions(m, "c12hour")
# interaction - contrasts by groups
m <- lm(barthtot ~ c12hour + c161sex * c172code + neg_c_7, data = efc)
test_predictions(m, c("c161sex", "c172code"), test = NULL)
# interaction - pairwise comparisons by groups
test_predictions(m, c("c161sex", "c172code"))
# equivalence testing
test_predictions(m, c("c161sex", "c172code"), equivalence = c(-2.96, 2.96))
# equivalence testing, using the parameters package
pr <- predict_response(m, c("c161sex", "c172code"))
parameters::equivalence_test(pr)
# interaction - collapse unique levels
test_predictions(m, c("c161sex", "c172code"), collapse_levels = TRUE)
# p-value adjustment
test_predictions(m, c("c161sex", "c172code"), p_adjust = "tukey")
# not all comparisons, only by specific group levels
test_predictions(m, "c172code", by = "c161sex")
# specific comparisons
test_predictions(m, c("c161sex", "c172code"), test = "b2 = b1")
# interaction - slope by groups
m <- lm(barthtot ~ c12hour + neg_c_7 * c172code + c161sex, data = efc)
test_predictions(m, c("neg_c_7", "c172code"))
# Interaction and consecutive contrasts -----------------
# -------------------------------------------------------
data(coffee_data, package = "ggeffects")
m <- lm(alertness ~ time * coffee + sex, data = coffee_data)
# consecutive contrasts
test_predictions(m, "time", by = "coffee", test = "consecutive")
# interaction contrasts - difference-in-difference comparisons
pr <- predict_response(m, c("time", "coffee"), margin = "marginalmeans")
test_predictions(pr, test = "interaction")
# Custom contrasts --------------------------------------
# -------------------------------------------------------
wakeup_time <- data.frame(
"wakeup vs later" = c(-2, 1, 1) / 2, # make sure each "side" sums to (+/-)1!
"start vs end of day" = c(-1, 0, 1)
)
test_predictions(m, "time", by = "coffee", test = wakeup_time)
# Example: marginal effects -----------------------------
# -------------------------------------------------------
data(iris)
m <- lm(Petal.Width ~ Petal.Length + Species, data = iris)
# we now want the marginal effects for "Species". We can calculate
# the marginal effect using the "marginaleffects" package
marginaleffects::avg_slopes(m, variables = "Species")
# finally, test_predictions() returns the same. while the previous results
# report the marginal effect compared to the reference level "setosa",
# test_predictions() returns the marginal effects for all pairwise comparisons
test_predictions(m, "Species")
# }
}
```