Convenience functions for analyzing factorial experiments using ANOVA or mixed models. aov_ez(), aov_car(), and aov_4() allow specification of between, within (i.e., repeated-measures), or mixed (i.e., split-plot) ANOVAs for data in long format (i.e., one observation per row), automatically aggregating multiple observations per individual and cell of the design. mixed() fits mixed models using lme4::lmer() and computes p-values for all fixed effects using either Kenward-Roger or Satterthwaite approximation for degrees of freedom (LMM only), parametric bootstrap (LMMs and GLMMs), or likelihood ratio tests (LMMs and GLMMs). afex_plot() provides a high-level interface for interaction or one-way plots using ggplot2, combining raw data and model estimates. afex uses type 3 sums of squares as default (imitating commercial statistical software).

```
*************************
** afex VERSION 0.23-x **
*************************
Changes in afex Version 0.23-x
Released February 2019
Significant User Visible Changes and New Features
o Added afex_plot.default() method which works with a wide variety of
fitted objects. See new vignette:
vignette("afex_plot_supported_models", package = "afex")
o In afex_plot(), renamed 'random' argument to 'id' argument.
Bugfixes
o Corrected bug in afex_plot() vignette and examples. Correct argument
name is factor_levels.
o Removed reference to ascii package from documentation, as the package
was removed from CRAN.
*************************
** afex VERSION 0.22-x **
*************************
Changes in afex Version 0.22-x
Released September 2018
Significant User Visible Changes and New Features
o New functions for plotting results (means, error bars, and raw data)
using ggplot2, afex_plot(), generic function for afex and lme4::merMod
objects. Furthermore added two more functions:
- interaction_plot(): workhorse producing interaction plot
- oneway_plot(): workhorse producing oneway plot
Error bars can display confidence intervals (the default) or standard
errors and can be calculated using a variety of different standard
errors (e.g., model-based, within-subjects).
o Added vignette introducing afex_plot().
o Updated ANOVA vignette to use afex_plot() and the multivariate for
follow-up test.
o Package emmeans was moved to suggests and needs to be either attached
explicitly or called with ::
Option 1: emmeans::emmeans()
Option 2: library("emmeans") and then just emmeans()
o Added call slot to mixed objects holding the matched call.
Bugfixes
o Error in ANOVA examples using emmeans corrected, see:
https://stats.stackexchange.com/q/360900/442
*************************
** afex VERSION 0.21-x **
*************************
Changes in afex Version 0.21-x
Released June 2018
Significant User Visible Changes and New Features
o Smaller package footprint:
The stringr package is not imported any more, all calls to stringr
functions were replaced with calls to base R functions.
The coin package (used in compare.2.vectors) was moved from Imports to
Suggests.
Bugfixes
o ANOVA functions produce accurate emmeans even for ANCOVAs, see:
https://afex.singmann.science/forums/topic/precise-estimates-from-emmeans-across-lm-and-aov_ez
*************************
** afex VERSION 0.20-x **
*************************
Changes in afex Version 0.20-x
Released April 2018
Significant User Visible Changes and New Features
o follow-up tests with emmeans for ANOVAs (i.e., objects of class
"afex_aov") with repeated-measures factors can now be based on a
multivariate model. This provides separate standard errors for each
estimate and more adequately accounts for violations of sphericity. To
use this model either call emmeans(..., model="multivariate") or set
globally via: afex_options(emmeans_model = "multivariate")
o ANOVA functions now allow transformations of the dv (thanks to
Russell Lenth).
o better (i.e., simpler) examples for mixed (use data from MEMSS). Added
example showing how to use mixed() with effects package for plotting.
o set_data_arg argument of mixed() is now per default controlled via
afex_options("set_data_arg"). The default has also changed from TRUE to
FALSE. The reason for this change is that FALSE appears to work better
with emmeans.
o afex_aov objects have received an additional attribute,
"incomplete_cases", that contains the IDs of removed participants due to
missing values (thanks to Frederik Aust).
o afex should now work with the upcoming versions of car (3.0) and
lmerTest (3.0). The latter thanks to Rune Haubo Bojesen.
Bugfixes
o removed bug in mixed that caused a crash if check_contrasts = FALSE
and the data contained missing values in the IVs.
o removed bug that caused a crash under certain conditions if
stringsAsFactors was set to FALSE in the global options and repeated
measures factors were present (thanks to Will Hopper for the bug report
and simultaneous fix).
o set_data_arg now works for lmer_alt and mixed(..., return = "merMod").
This allows to use those objects with e.g., the effects package.
o afex should now work with car version 3.0.
*************************
** afex VERSION 0.19-x **
*************************
Changes in afex Version 0.19-0
Released January 2018
Significant User Visible Changes and New Features
o afex now works with emmeans (successor of lsmeans pckage).
Bugfixes
o lsmeans did not work with mixed objects if type=2 and method used nested
model comparions (e.g., LRT or PB).
o removed warning 'Error() model is singular' when units of observations
have missing values for ANOVAs.
*************************
** afex VERSION 0.18-x **
*************************
Changes in afex Version 0.18-0
Released May 2017
Bugfixes
o aov_ez did not work with more than one covariate
(https://github.com/singmann/afex/issues/29).
*************************
** afex VERSION 0.17-x **
*************************
Changes in afex Version 0.17-x
Released April 2017
Significant User Visible Changes and New Features
o Added Satterthwaite approximation (method="S") to mixed(), which is
implemented via lmerTest. Satterthwaite approximates the degrees-of-
freedom of an F-test, similar to the default Kenward-Roger method, but
requires less RAM.
o mixed() methods "KR" and "S" are now obtained via tests on the full
model directly. No restricted models are calculated for these methods.
The former KR method is still available: method="nested-KR"
o mixed() now per default exports and uses lmerTest::lmer and not
lme4::lmer(). This can be changed via calling
afex_options(lmer_function = "lme4")
o afex does not depend on reshape2 any more. It is only imported.
o All arguments with "." in the name have been renamed to use "_". The old
names have been deprecated (i.e., still work, but should not be used).
check.contrasts = check_contrasts, test.intercept = test_intercept,
args.test = args_test, ...
o Names of slots of mixed model objects with "." have been renamed to have
a "_" instead: full.model = full_model and restricted.models =
restricted_models
o afex_options() now uses the global R options accessible via options()
(with prefix afex.) and allows to reset all options via list (i.e.,:
aop <- afex_options(); ...; afex_options(aov); works).
o renamed allFit() to all_fit() and argument meth.tab to meth_tab.
Added method dfoptim::nmkb() to all_fit(). To use nmkb, dfoptim needs to
be loaded explicitly via library (see examples).
o Added argument all_fit to mixed(). If TRUE, each model is fitted with
all available optimizers and the best fit in each case selected.
o mixed objects have an additional slot, "data", that contains the data
used for fitting.
o Added vignette with extensive mixed model example.
o Created forum for providing afex support: http://afex.singmann.science/
Bugfixes
o Sphericity correction now correctly displayed as none if all within-
factors have only two levels (bug removed by Frederik Aust).
o removed bug when calling nice() on afex_aov objects created with
explicit effect size.
o aov_...(): anova_table = list(intercept = TRUE) now correctly suppresses
the intercept (bug removed by Frederik Aust).
o aov_...(): return = "nice" did not work (bug removed by Frederik Aust).
o aov_...() now supports column names with spaces (using backticks), see:
https://github.com/singmann/afex/issues/22 Thx to Jonathan Love for fix.
o changed license to GPL >=2 (as it call some function from GPL >=2
packages).
o removed bug that mixed() object with type=2 could not be printed.
o removed bug that model names for anova.mixed with multiple models were
incorrect.
o all_fit() now uses a data argument correctly and passes it update().
This again allows to use it for data with suppressed correlations.
all_fit(... verbose = TRUE) now correctly signals if a fit failed.
*************************
** afex VERSION 0.16-x **
*************************
Changes in afex Version 0.16-x
Released April 2016
Significant User Visible Changes and New Features
o added "correction" and "observed" attributes to the anova_table slot of
afex_aov objects, which is used per default by nice(). This ensures
that nice(object) and object always return the same data.frame.
Also added "nice_table" class to data.frame returned by nice which
print the value of the slots for information.
Both contributed by Frederik Aust (who was also promoted to author).
o added return="data" for mixed. This allows to obtain the data set used
for fitting a model. Can be useful in combination with expand.re=TRUE
and allFit() or for obtaining predictions. See ?allFit for a simple
example.
Bugfixes
o increased required version of R (>= 3.1.0) and the following packages
to ensure afex runs with older versions of R: lme4 (>= 1.1-8),
pbkrtest (>= 0.4-1), and Matrix (>= 1.1.1).
*************************
** afex VERSION 0.15-x **
*************************
Changes in afex Version 0.15-x
Released October 2015
Significant User Visible Changes and New Features
o added p.adjust.method argument for ANOVA functions (anova and nice
methods). Can be used to control for multiple comparisons in
exploratory ANOVAs (see Cramer, et al., 2015; PB&R). Functionality
contributed by Frederik Aust (https://github.com/singmann/afex/pull/3).
Bugfixes
o ANOVA functions work with dplyr data.frames now (data is transformed
via as.data.frame). See: https://github.com/singmann/afex/issues/6
o formulas for mixed can now be of a maximum length of 500 characters
(was 60 chars previously): https://github.com/singmann/afex/issues/5
o aov_car et al. did not work with within-subject factors that were also
included outside the Error term. This was caused by the use of regular
expressions not appropriate for the new stringi backend of stringr.
Thanks to Tom Wenseleers for reporting this bug.
*************************
** afex VERSION 0.14-x **
*************************
Changes in afex Version 0.14-x
Released August 2015
Significant User Visible Changes and New Features
o new default return argument for ANOVA functions, afex_aov,
an S3 object containing the following:
(1) ANOVA table of class "anova"
(2) ANOVA fitted with base R's aov (can be passed to lsmeans
for post-hoc tests)
(3) output from car::Anova (for tests of effects),
ANOVA table (1) is based on this model
(4) lm object passed to car::Anova
(5) data used for estimating (2) and (4)
o added support for lsmeans: objects of class afex_aov can be
passed to lsmeans directly. afex now depends on lsmeans.
o added afex_options() functionality for setting options globally.
o added expand_re argument to mixed which, if TRUE, correctly interprets
the || notation in random effects with factors (i.e., suppresses
estimation of correlation among random effects). lmer_alt is a wrapper
for mixed which uses expand_re = TRUE, returns an object of class
merMod (i.e., does not calculate p-values), and otherwise behaves
like g/lmer (i.e., does not enforce certain contrasts)
o added three new data sets (Singmann & Klauer, 2011; Klauer &
Singmann, 2013) and a vignette showing how to calculate
contrasts after ANOVA.
o ANOVA functions renamed to aov_car, aov_ez, and aov_4. Old
functions are now deprecated.
o first element in mixed object renamed to anova_table.
o nice.anova renamed to nice. nice() can be called for afex_aov
and mixed objects and returns a nicely formatted (numbers
converted to characters) results table (which is also the
default print method for both objects).
o anova() can be called for afex_aov and mixed objects and returns
the numeric anova table (i.e., the first element of each object).
There also exists print methods for those data.frames.
o summary method for mixed objects now calls summary.merMod on
full model.
o afex does not depend on car package anymore, it is only imported.
o afex is now hosted on github: https://github.com/singmann/afex
Bugfixes
o ANOVA: for "aov"-objects, contrasts are only set for factors.
o compare.2.vector failed when the two means were exactly equal
(due to an issue with median_test). This only throws a warning
now.
o compare.2.vector documentation updated for coin 1-1.0.
*************************
** afex VERSION 0.13-x **
*************************
Changes in afex Version 0.13-x
Released January 2015
Significant User Visible Changes and New Features
o added ems() function for deriving the expected values of the
mean squares for factorial designs (contributed by Jake
Westfall).
Bugfixes
o aov.car et al. stop with error message if a factor has only one
level.
o aov.car transforms id variable to factor which ensures that
return = "aov" provides equivalent results.
o changed regex for detecting "observed" variables to work with
the new version of stringr which uses stringi.
*************************
** afex VERSION 0.12-x **
*************************
Changes in afex Version 0.12-x
Released November 2014
Significant User Visible Changes and New Features
o ANOVA functions give informative error if some parameters are
not estimable (most likely due to structural missings, i.e.
empty cells).
Bugfixes
o mixed(..., method = "PB") does not fail anymore when only
having a single fixed effect (thanks to Kiyoshi Sasaki for
reporting it).
o aov.car() failed when a within-subject factor had empty levels.
Unused factor levels are now dropped. This bug was probably
introduced in Rev 126 as part of an attempt to solve a bug.
(thanks to Will Bowditch for reporting it).
*************************
** afex VERSION 0.11-x **
*************************
Changes in afex Version 0.11-x
Released October 2014
Significant User Visible Changes and New Features
o added allFit() function (written by Ben Bolker).
o mixed() gives warning if nested model provides worse fit
(logLik) than full model (when fitted with ML).
o print, summary, and anova method for mixed objects are now
identical.
o description of returned object from mixed() extended (Thanks
to Ben Bolker, see http://stackoverflow.com/a/25612960/289572)
o added return = "aov" to aov.car which returns the ANOVA
fitted with aov (with correct Error strata) so that it can be
passed to lsmeans for post-hoc tests or plotting (lsmip).
Bugfixes
o all required functions are now correctly imported avoiding
CRAN warnings and better functioning.
o data argument to lmer calls in mixed set correctly. Note that
still contrasts added to the data in mixed may prohibit use of
predict.merMod() or similar functions. It is recommended to
set the contrasts globally to "contr.sum", e.g.,
via set_sum_contrasts(), for correct functioning
(disable via set.data.arg argument for mixed).
************************
** afex VERSION 0.10-x **
************************
Changes in afex Version 0.10-x
Released August 2014
Significant User Visible Changes and New Features
o afex does not change the global contrasts anymore when loading
the package (due to popular demand).
o new functions to globally set contrasts: set_sum_contrasts &
set_treatment_contrasts (and some more wrappers).
o Added more mixed model examples from Maxwell & Delaney, Chapter
15 ("Multilevel Models for within subjects designs"), see ?mixed
and ?md_15.1. Thanks to Ulf Mertens.
Bugfixes
o removed bug when factor levels of within-subject factors
contained "+" or "-" and were not converted correctly. Added
tests for known bugs in aov.car.
************************
** afex VERSION 0.9-x **
************************
Changes in afex Version 0.9-x
Released April 2014
Significant User Visible Changes and New Features
o added function aov4: another wrapper of car::Anova for ANOVA
models specified via lme4::lmer syntax.
o added return="marginal" to aov.car which returns the marginal
means of all effects (i.e., grand mean and mean of main
effects and interactions). Is also returned if return="full".
o testing the intercept in mixed models in now only optional.
The default is that the new argument test.intercept = FALSE.
o removed return="lme4" from aov.car.
o added argument intercept to nice.anova (default FALSE) which
allows to selective display the intercept in an ANOVA table.
o added method = "F" to mixed() which only returns the F-value
but no ddf (and hence no p-value). Experimental, not documented.
o renamed colname "stat" to "F" when method = "KR" (mixed).
o added tests (currently mainly for mixed()) via pkg testthat,
see tests/testthat.
Bugfixes
o increased requirement of R version and lme4 version.
o print.mixed should now propagate all warnings from lme4 (i.e.,
also the new convergence warnings).
o lme4 is now loaded at worker nodes for mixed (default,
turn of via check.contrasts)
************************
** afex VERSION 0.8-x **
************************
Changes in afex Version 0.8-x
Released February 2014
Significant User Visible Changes and New Features
o removed renaming of within subject factor levels to names
with length 1 (which was introduced in 0.6).
o helper function round_ps which nicely rounds p-values
is now exported.
o warning about numerical non-centered variables in mixed
is now a message only.
o added examples data sets from Maxwell & Delaney (2004) for
within-subjects ANOVA and mixed models.
o reshape2 is now again in depends but coin only imported.
Bugfixes
o the default effect size (ges: generalized eta-squared) was
calculated wrong (the error term for the intercept was not
included). Sorry. This is now corrected (with new examples).
o removed bug that aov.car didn't work when running some ANCOVAs
(thanks to Gang Chen for reporting this).
************************
** afex VERSION 0.7-x **
************************
Changes in afex Version 0.7-x
Released December 2013
Significant User Visible Changes and New Features
o nicer output of print.mixed
Bugfixes
o mixed() correctly converts all non-formula arguments to
formula correctly to a formula (gave error if formula
was a different object and not-available on cluster nodes).
Prints message if formula is converted to a formula.
o Using multicore for fitting the models prodcued erroneous
results (did not use correct contrasts at nodes). Now the
current contrasts are also set at the nodes.
o mixed() sets REML = FALSE if method = "LRT" and no
family argument is present (i.e., for LMMs) as LRTs
for models fitted with REML are not recommended.
o on the cluster nodes now only the lme4 namespace is
loaded (instead of using library) to avoid a CRAN note.
************************
** afex VERSION 0.6-x **
************************
Changes in afex Version 0.6-x
Released September 2013
Significant User Visible Changes and New Features
o added LRT tests to mixed() which should replicate
the recommended test by Barr et al. (2013, JML).
o multicore estimation of (g)lmer models now available
through package parallel (argument cl) for mixed().
o added experimental "lme4" return method for
aov.car and ez.glm (which fits the data using lmer).
o reshape2 and stringr are not any more loaded when
loading afex (are now only imported via Imports)
Bugfixes
o Type 2 tests of mixed() were implemented incorrectly (i.e.,
they did not give what they should have given according
to the description in the help file).
o aov.car() and ez.glm() now convert factor levels of within
subjects factors to be of length one so that long levels
do not lead to problems when constructing the call to lm.
Thanks to Isaac Schwabacher for noticing this, see also:
https://bugs.r-project.org/bugzilla3/show_bug.cgi?id=15377
o mixed should now work with missing values as it construes
a new data object if the model.matrix from which the
different versions are fitted has nrow different to
nrow(data) (with warning). Thanks to Daniel Bunker
for reporting this.
o mixed should work with the newest version of lme4 (>= 1.0.4)
and the newst version of pbkrtest (>= 0.3-5.1), but not
with older versions (due to CRAN policy to disallow :::).
************************
** afex VERSION 0.5-x **
************************
Changes in afex Version 0.5-x
Released May 2013
Significant User Visible Changes and New Features
o added argument factorize (default: TRUE) to aov.car and ez.glm:
all variables are now factorized per default. (now it is
necessary to set factorize=FALSE for ANCOVAs!)
o added argument per.parameter to mixed() which allows to specify
variables for which each parameter is tested (not only the
overall effect). Can be useful to test for ordered factors.
(only implemented for "Type 3" tests)
o added more informative startup message (thanks to Robert Volcic
and Lars Konieczny)
o mixed, ez.glm and aov.car now check for correct contrasts and set
factors to contr.sum if other contrasts are found (can be tunred
off via check.contrasts argument). Resetting the default contrast
to contr.treatment should therefore not interfere with afex.
(this is not intensly tested, so please report anything)
o mixed checks numeric variables if they are centered on 0 (and
gives warning if not).
Bugfixes
o checks if observed variable is in the data and throws
an error if not (nice.anova)
************************
** afex VERSION 0.4-x **
************************
Changes in afex Version 0.4-x
Released February 2013
Significant User Visible Changes and New Features
o added generalized and partial eta-squared effect
sizes to nice.anova (this also included adding
observed arguments to aov.car, ez.glm, nice.anova)
o added new return arguments to aov.car and ez.glm
(nice, lm, data).
o changed default return value of aov.car and ez.glm
to "nice" which now returns a nice ANOVA table
(nice.anova)
o mixed has method = "PB" for obtaining parametric
bootstrapped p-values (e.g., for GLMMs)
o added alternative argument to compare.2.vectors.
o aov.car (and ez.glm) now give a warning if
observations are missing on within-subject factors.
(As before, cases with missing values are simply
excluded from the analysis)
o had to disable saving of the previous contrasts and
resetting those after detaching afex due to
CRAN policies (no assignment in global environment).
Bugfixes
o Bug when running mixed() inside a function and
handing the data.frame over as an argument fixed
(thanks, again, to Florent Duyme). See
bugs/eval.scoping.bug.R
o nice.anova did not work with a model with only one
within-subjects factor.
************************
** afex VERSION 0.3-x **
************************
Changes in afex Version 0.3-x
Released August/September 2012
Significant User Visible Changes and New Features
o added function compare.2.vectors().
o Name of function univariate() changed to univ(), as
a function with this name is part of package multcomp.
This may leed to problems. Thanks to Florent Duyme for
spotting this.
o added return argument to aov.car() and ez.glm().
o added rather dubious Type 2 tests to mixed().
o aov.car checks if each id is only present in one
cell of the between subjects design.
Bugfixes
o aov.car now uses do.call when calling lm() to avoid local
variables in the call to lm() which could led to problems when
working with the lm model.
o mixed() now passes ... (further arguments to lmer) correctly.
(Now mixed uses match.call and eval on the call instead of
invoking lmer directly.)
o corrected bug that was introduced by pbkrtest v3.2 when
invoking the print method to an object of class mixed
(again thanks to Florent Duyme for spotting this).
o removed bug when factor levels of within-subject factors
were non-legal names (solution uses make.names).
```