Compute estimated marginal means (EMMs) for specified factors or factor combinations in a linear model; and optionally, comparisons or contrasts among them. EMMs are also known as least-squares means.
emmeans(object, specs, by = NULL, fac.reduce = function(coefs) apply(coefs,
2, mean), contr, options = get_emm_option("emmeans"), weights, offset, ...,
tran)When specs is a character vector or one-sided formula,
an object of class "emmGrid". A number of methods
are provided for further analysis, including
summary.emmGrid, confint.emmGrid,
test.emmGrid, contrast.emmGrid,
and pairs.emmGrid.
When specs is a list or a formula having a left-hand
side, the return value is an emm_list object, which is simply a
list of emmGrid objects.
An object of class emmGrid; or a fitted model object
that is supported, such as the result of a call to lm or
lmer. Many fitted-model objects are supported; see
vignette("models", "emmeans") for details.
A character vector specifying the names of the predictors
over which EMMs are desired. specs may also be a formula
or a list (optionally named) of valid specs. Use of formulas
is described in the Overview section below.
Note: We recommend against using two-sided formulas; see the
note below for contr.
A character vector specifying the names of predictors to condition on.
A function that combines the rows of a matrix into a single
vector. This implements the ``marginal averaging'' aspect of EMMs.
The default is the mean of the rows. Typically if it is overridden,
it would be some kind of weighted mean of the rows. If fac.reduce is
nonlinear, bizarre results are likely, and EMMs will not be
interpretable. NOTE: If the weights argument is non-missing,
fac.reduce is ignored.
A character value or list specifying contrasts to be
added. See contrast. Note: contr is ignored when
specs is a formula. Note 2:: We recommend against using this
argument; obtaining means and obtaining contrasts are two different things,
and it is best to do them in separate steps, using the contrast
function for the contrasts.
If non-NULL, a named list of arguments to pass
to update.emmGrid, just after the object is constructed.
(Options may also be included in ...; see the ‘options’
section below.)
Character value, numeric vector, or numeric matrix specifying
weights to use in averaging predictions. See “Weights” section below.
Also, if object is not already a reference grid, weights
(if it is character) is passed to ref_grid as wt.nuis in case
nuisance factors are specified. We can override this by specifying
wt.nuis explicitly.
This more-or-less makes the weighting of nuisance factors consistent with
that of primary factors.
Numeric vector or scalar. If specified, this adds an offset to the predictions, or overrides any offset in the model or its reference grid. If a vector of length differing from the number of rows in the result, it is subsetted or cyclically recycled.
When object is not already a "emmGrid"
object, these arguments are passed to ref_grid. Common
examples are at, cov.reduce, data, type,
regrid, df, nesting, and vcov..
Model-type-specific options (see
vignette("models", "emmeans")), commonly
mode, may be used here as well. In addition, if the model formula
contains references to variables that are not predictors, you must provide
a params argument with a list of their names.
These arguments may also be used in lieu of options. See the
‘Options’ section below.
Placeholder to prevent it from being included in ....
If non-missing, it is added to `options`. See the ‘Options’
section.
Estimated marginal means or EMMs (sometimes called least-squares means) are
predictions from a linear model over a reference grid; or marginal
averages thereof. The ref_grid function identifies/creates the
reference grid upon which emmeans is based.
For those who prefer the terms “least-squares means” or
“predicted marginal means”, functions lsmeans and
pmmeans are provided as wrappers. See wrappers.
If specs is a formula, it should be of the form ~ specs,
~ specs | by, contr ~ specs, or contr ~ specs | by. The
formula is parsed and the variables therein are used as the arguments
specs, by, and contr as indicated. The left-hand side is
optional (and we don't recommend it), but if specified it should be the
name of a contrast family (e.g., pairwise). Operators like
* or : are needed in the formula to delineate names, but
otherwise are ignored.
In the special case where the mean (or weighted mean) of all the predictions
is desired, specify specs as ~ 1 or "1".
A number of standard contrast families are provided. They can be identified
as functions having names ending in .emmc -- see the documentation
for emmc-functions for details -- including how to write your
own .emmc function for custom contrasts.
If weights is a vector, its length must equal
the number of predictions to be averaged to obtain each EMM.
If a matrix, each row of the matrix is used in turn, wrapping back to the
first row as needed. When in doubt about what is being averaged (or how
many), first call emmeans with weights = "show.levels".
If weights is a string, it should partially match one of the following:
"equal"Use an equally weighted average.
"proportional"Weight in proportion to the frequencies (in the original data) of the factor combinations that are averaged over.
"outer"Weight in proportion to each individual factor's marginal frequencies. Thus, the weights for a combination of factors are the outer product of the one-factor margins
"cells"Weight according to the frequencies of the cells being averaged.
"flat"Give equal weight to all cells with data, and ignore empty cells.
"show.levels"This is a convenience feature for understanding what is being averaged over. Instead of a table of EMMs, this causes the function to return a table showing the levels that are averaged over, in the order that they appear.
Outer weights are like the 'expected' counts in a chi-square test of
independence, and will yield the same results as those obtained by
proportional averaging with one factor at a time. All except "cells"
uses the same set of weights for each mean. In a model where the predicted
values are the cell means, cell weights will yield the raw averages of the
data for the factors involved. Using "flat" is similar to
"cells", except nonempty cells are weighted equally and empty cells
are ignored.
Unlike in ref_grid, an offset need not be scalar. If not enough values
are supplied, they are cyclically recycled. For a vector of offsets, it is
important to understand that the ordering of results goes with the first
name in specs varying fastest. If there are any by factors,
those vary slower than all the primary ones, but the first by variable
varies the fastest within that hierarchy. See the examples.
Arguments that could go in options may instead be included in ...,
typically, arguments such as type, infer, etc. that in essence
are passed to summary.emmGrid. Arguments in both places are
overridden by the ones in ....
There is a danger that ... arguments could partially match those used
by both ref_grid and update.emmGrid, creating a conflict.
If these occur, usually they can be resolved by providing complete (or at least
longer) argument names; or by isolating non-ref_grid arguments in
options; or by calling ref_grid separately and passing the
result as object. See a not-run example below.
Also, when specs is a two-sided formula, or contr is specified,
there is potential confusion concerning which ... arguments
apply to the means, and which to the contrasts. When such confusion is possible,
we suggest doing things separately
(a call to emmeans with no contrasts, followed by a call to
contrast). We treat
adjust as a special case: it is applied to the emmeans results
only if there are
no contrasts specified, otherwise it is passed only to contrast.
Users should also consult the documentation for ref_grid,
because many important options for EMMs are implemented there, via the
... argument.
ref_grid, contrast,
vignette("models", "emmeans")
warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks)
emmeans (warp.lm, ~ wool | tension)
# or equivalently emmeans(warp.lm, "wool", by = "tension")
# 'adjust' argument ignored in emmeans, passed to contrast part...
emmeans (warp.lm, poly ~ tension | wool, adjust = "sidak")
# 'adjust' argument NOT ignored ...
emmeans (warp.lm, ~ tension | wool, adjust = "sidak")
if (FALSE) {
### Offsets: Consider a silly example:
emmeans(warp.lm, ~ tension | wool, offset = c(17, 23, 47)) @ grid
# note that offsets are recycled so that each level of tension receives
# the same offset for each wool.
# But using the same offsets with ~ wool | tension will probably not
# be what you want because the ordering of combinations is different.
}
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