Estimated marginal means (Least-squares means)

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.

Usage

emmeans(object, specs, by = NULL, fac.reduce = function(coefs) apply(coefs,
  2, mean), contr, options = get_emm_option("emmeans"), weights, offset, ...,
  tran)

Arguments

object: 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.
specs: 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.
by: A character vector specifying the names of predictors to condition on.
fac.reduce: 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.
contr: 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.
options: 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.)
weights: 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.
offset: 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.
tran: Placeholder to prevent it from being included in .... If non-missing, it is added to `options`. See the ‘Options’ section.

Value

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.

Details

Users should also consult the documentation for ref_grid, because many important options for EMMs are implemented there, via the ... argument.

Overview

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.

Weights

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.

Offsets

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.

Options and `...`

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.

Examples

warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks)
emmeans (warp.lm,  ~ wool | tension)
#> tension = L:
#>  wool emmean   SE df lower.CL upper.CL
#>  A      44.6 3.65 48     37.2     51.9
#>  B      28.2 3.65 48     20.9     35.6
#> 
#> tension = M:
#>  wool emmean   SE df lower.CL upper.CL
#>  A      24.0 3.65 48     16.7     31.3
#>  B      28.8 3.65 48     21.4     36.1
#> 
#> tension = H:
#>  wool emmean   SE df lower.CL upper.CL
#>  A      24.6 3.65 48     17.2     31.9
#>  B      18.8 3.65 48     11.4     26.1
#> 
#> Confidence level used: 0.95 
# 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")
#> $emmeans
#> wool = A:
#>  tension emmean   SE df lower.CL upper.CL
#>  L         44.6 3.65 48     37.2     51.9
#>  M         24.0 3.65 48     16.7     31.3
#>  H         24.6 3.65 48     17.2     31.9
#> 
#> wool = B:
#>  tension emmean   SE df lower.CL upper.CL
#>  L         28.2 3.65 48     20.9     35.6
#>  M         28.8 3.65 48     21.4     36.1
#>  H         18.8 3.65 48     11.4     26.1
#> 
#> Confidence level used: 0.95 
#> 
#> $contrasts
#> wool = A:
#>  contrast  estimate   SE df t.ratio p.value
#>  linear      -20.00 5.16 48  -3.878  0.0006
#>  quadratic    21.11 8.93 48   2.363  0.0439
#> 
#> wool = B:
#>  contrast  estimate   SE df t.ratio p.value
#>  linear       -9.44 5.16 48  -1.831  0.1412
#>  quadratic   -10.56 8.93 48  -1.182  0.4272
#> 
#> P value adjustment: sidak method for 2 tests 
#> 

# 'adjust' argument NOT ignored ...
emmeans (warp.lm, ~ tension | wool, adjust = "sidak")
#> wool = A:
#>  tension emmean   SE df lower.CL upper.CL
#>  L         44.6 3.65 48    35.53     53.6
#>  M         24.0 3.65 48    14.98     33.0
#>  H         24.6 3.65 48    15.53     33.6
#> 
#> wool = B:
#>  tension emmean   SE df lower.CL upper.CL
#>  L         28.2 3.65 48    19.20     37.2
#>  M         28.8 3.65 48    19.76     37.8
#>  H         18.8 3.65 48     9.76     27.8
#> 
#> Confidence level used: 0.95 
#> Conf-level adjustment: sidak method for 3 estimates 


if (FALSE) { # \dontrun{
  ### 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.
} # }