A suite of functions for conducting and interpreting analysis
of statistical interaction in regression models that was formerly part of the
'jtools' package. Functionality includes visualization of two- and three-way
interactions among continuous and/or categorical variables as well as
calculation of "simple slopes" and Johnson-Neyman intervals (see e.g.,
Bauer & Curran, 2005
This package consists of a number of tools that pertain to the analysis
and exploration of statistical interactions in the context of
regression. Some of these features, especially those that pertain to
visualization, are not exactly impossible to do oneself but are tedious
and error-prone when done “by hand.” Most things in
once part of the
jtools package and
have been spun off to this package for clarity and simplicity.
Quick rundown of features:
All of these are implemented in a consistent interface designed to be as
simple as possible with tweaks and guts available to advanced users.
GLMs, models from the
survey package, and multilevel models from
lme4 are fully supported as is visualization for Bayesian models from
For the moment, the package has just been submitted to CRAN and may not yet be available as you read this. If that is the case, please install from Github.
Unless you have a really keen eye and good familiarity with both the underlying mathematics and the scale of your variables, it can be very difficult to look at the output of regression model that includes an interaction and actually understand what the model is telling you.
This package contains several means of aiding understanding and doing statistical inference with interactions.
The “classic” way of probing an interaction effect is to calculate the slope of the focal predictor at different values of the moderator. When the moderator is binary, this is especially informative—e.g., what is the slope for men vs. women? But you can also arbitrarily choose points for continuous moderators.
With that said, the more statistically rigorous way to explore these effects is to find the Johnson-Neyman interval, which tells you the range of values of the moderator in which the slope of the predictor is significant vs. nonsignificant at a specified alpha level.
sim_slopes function will by default find the Johnson-Neyman
interval and tell you the predictor’s slope at specified values of the
moderator; by default either both values of binary predictors or the
mean and the mean +/- one standard deviation for continuous moderators.
library(interactions)fiti <- lm(mpg ~ hp * wt, data = mtcars)sim_slopes(fiti, pred = hp, modx = wt, jnplot = TRUE)
#> JOHNSON-NEYMAN INTERVAL #> #> When wt is OUTSIDE the interval [3.69, 5.90], the slope of hp is p < #> .05. #> #> Note: The range of observed values of wt is [1.51, 5.42]
#> SIMPLE SLOPES ANALYSIS #> #> Slope of hp when wt = 4.20 (+ 1 SD): #> #> Est. S.E. t val. p #> ------ ----- ------- ----- #> -0.00 0.01 -0.31 0.76 #> #> Slope of hp when wt = 3.22 (Mean): #> #> Est. S.E. t val. p #> ------ ----- ------- ----- #> -0.03 0.01 -4.07 0.00 #> #> Slope of hp when wt = 2.24 (- 1 SD): #> #> Est. S.E. t val. p #> ------ ----- ------- ----- #> -0.06 0.01 -5.66 0.00
The Johnson-Neyman plot can really help you get a handle on what the
interval is telling you, too. Note that you can look at the
Johnson-Neyman interval directly with the
The above all generalize to three-way interactions, too.
This function plots two- and three-way interactions using
a similar interface to the aforementioned
sim_slopes function. Users
can customize the appearance with familiar
ggplot2 commands. It
supports several customizations, like confidence intervals.
interact_plot(fiti, pred = hp, modx = wt, interval = TRUE)
You can also plot the observed data for comparison:
interact_plot(fiti, pred = hp, modx = wt, plot.points = TRUE)
The function also supports categorical moderators—plotting observed data in these cases can reveal striking patterns.
fitiris <- lm(Petal.Length ~ Petal.Width * Species, data = iris)interact_plot(fitiris, pred = Petal.Width, modx = Species, plot.points = TRUE)
You may also combine the plotting and simple slopes functions by using
probe_interaction, which calls both functions simultaneously.
Categorical by categorical interactions can be investigated using the
I’m happy to receive bug reports, suggestions, questions, and (most of all) contributions to fix problems and add features. I prefer you use the Github issues system over trying to reach out to me in other ways. Pull requests for contributions are encouraged.
Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.
The source code of this package is licensed under the MIT License.
This is, as the name suggests, related to
sim_slopes(). However, instead of
slopes, what is being estimated are
In the case of OLS linear regression, this is basically the same thing. The
slope in OLS is the expected change in the outcome for each 1-unit increase in
the predictor. For other models, however, the actual change in the outcome
when there's a 1-unit increase in a variable depends on the level of other
covariates and the initial value of the predictor. In a logit model,
for instance, the change in probability will be different if the initial
probability was 50% (could go quite a bit up or down) than if it was 99.9%
(can't go up).
sim_margins() uses the
package under the hood to estimate marginal effects. Unlike
in which by default all covariates not involved in the interaction are
sim_margins() these covariates are always left at their
observed values because they influence the level of the marginal effect.
Instead, the marginal effect is calculated with the covariates and focal
pred) at their observed values and the moderator(s) held at the
specified values (e.g., the mean and 1 standard deviation above/below the mean).
I advise using
sim_margins() rather than
sim_slopes() when analyzing models
other than OLS regression.
cat_plot()now respect the user's selection of
outcome.scale; in 1.0.0, it always plotted on the response scale. (#12)
modx.valuesargument is now better documented to explain that you may use it to specify the exact values you want. Thanks to Jakub Lysek for asking the question that prompted this. (#8)
"mean-plus-minus"as a manual specification of the default auto-calculated values for continuous moderators.
NULLstill defaults to this, but you can now make this explicit in your code if desired for clarity or to guard against future changes in the default behavior.
mod2.valuesinclude values outside the observed range of the
mod2are not all involved in an interaction with each other in the provided model. (#10)
mod2.valuesarguments but now works properly. (#17)
sim_slopes()now handles non-syntactic variable names better.
interactionsnow requires you to have a relatively new version of
rlang. Users with older versions were experiencing cryptic errors. (#15)
cat_plot()now have an
atargument for more granular control over the values of covariates.
sim_slopes()now allows for custom specification of robust standard error estimators via providing a function to
v.covand arguments to
This is the first release, but a look at the NEWS for
jtools prior to its version 2.0.0 will
give you an idea of the history of the functions in this package.
What follows is an accounting of changes to functions in this package since
they were last in
interactionsnow have a new theme, which you can use yourself, called
jtoolspackage). The previous default,
theme_apa(), is still available but I don't like it as a default since I don't think the APA has defined the nicest-looking design guidelines for general use.
interact_plot()now has appropriate coloring for observed data when the moderator is numeric (#1). In previous versions I had to use a workaround that involved tweaking the alpha of the observed data points.
cat_plot()now use tidy evaluation for the
mod2arguments. This means you can pass a variable that contains the name of
mod2, which is most useful if you are creating a function, for loop, etc. If using a variable, put a
rlangpackage before it (e.g.,
pred = !! variable). For most users, these changes will not affect their usage.
sim_slopes()no longer prints coefficient tables as data frames because this caused RStudio notebook users issues with the output not being printed to the console and having the notebook format them in less-than-ideal ways. The tables now have a markdown format that might remind you of Stata's coefficient tables. Thanks to Kim Henry for contacting me about this.
One negative when visualizing predictions alongside original data
interact_plot() or similar
tools is that the observed data may be too spread out to pick up on any
patterns. However, sometimes your model is controlling for the causes of this
scattering, especially with multilevel models that have random intercepts.
Partial residuals include the effects of all the controlled-for variables
and let you see how well your model performs with all of those things accounted
You can plot partial residuals instead of the observed data in
cat_plot() via the argument
partial.residuals = TRUE.
make_predictions()and removal of
jtools 1.0.0 release, I introduced
make_predictions() as a lower-level
way to emulate the functionality of
cat_plot(). This would return a list object with predicted data, the original
data, and a bunch of attributes containing information about how to plot it.
One could then take this object, with class
predictions, and use it as the
main argument to
plot_predictions(), which was another new function that
creates the plots you would see in
effect_plot() et al.
I have simplified
make_predictions() to be less specific to those plotting
functions and eliminated
plot_predictions(), which was ultimately too complex
to maintain and caused problems for separating the interaction tools into a
make_predictions() by default simply creates a new data frame
of predicted values along a
pred variable. It no longer accepts
mod2 arguments. Instead, it accepts an argument called
at where a user can
specify any number of variables and values to generate predictions at. This
syntax is designed to be similar to the
margins packages. See
jtools documentation for more info on this revised syntax.