This package provides methods for obtaining estimated marginal means (EMMs, also known as least-squares means) for factor combinations in a variety of models. Supported models include [generalized linear] models, models for counts, multivariate, multinomial and ordinal responses, survival models, GEEs, and Bayesian models. For the latter, posterior samples of EMMs are provided. The package can compute contrasts or linear combinations of these marginal means with various multiplicity adjustments. One can also estimate and contrast slopes of trend lines. Some graphical displays of these results are provided.
A number of vignettes are provided to help the user get acquainted with the emmeans package and see some examples. See the vignette index.
Estimated marginal means (see Searle et al. 1980 are popular for summarizing linear models that include factors. For balanced experimental designs, they are just the marginal means. For unbalanced data, they in essence estimate the marginal means you would have observed that the data arisen from a balanced experiment. Earlier developments regarding these techniques were developed in a least-squares context and are sometimes referred to as “least-squares means”. Since its early development, the concept has expanded far beyond least-squares settings.
The implementation in emmeans relies on our own
concept of a reference grid, which is an array of factor and predictor
levels. Predictions are made on this grid, and estimated marginal means (or
EMMs) are defined as averages of these predictions over zero or more
dimensions of the grid. The function ref_grid explicitly
creates a reference grid that can subsequently be used to obtain
least-squares means. The object returned by ref_grid is of class
"emmGrid", the same class as is used for estimated marginal means (see
below).
Our reference-grid framework expands slightly upon Searle et al.'s definitions of EMMs, in that it is possible to include multiple levels of covariates in the grid.
As is mentioned in the package description, many types of models are supported by the package. See vignette("models", "emmeans") for full details. Some models may require other packages be installed in order to access all of the available features.
The emmeans function computes EMMs given a fitted model (or a
previously constructed emmGrid object), using a specification indicating
what factors to include. The emtrends function creates the same
sort of results for estimating and comparing slopes of fitted lines. Both
return an emmGrid object.
The summary.emmGrid method may be used to display an emmGrid
object. Special-purpose summaries are available via confint.emmGrid and
test.emmGrid, the latter of which can also do a joint test of several
estimates. The user may specify by variables, multiplicity-adjustment
methods, confidence levels, etc., and if a transformation or link function is
involved, may reverse-transform the results to the response scale.
The contrast method for emmGrid objects is used to obtain
contrasts among the estimates; several standard contrast families are
available such as deviations from the mean, polynomial contrasts, and
comparisons with one or more controls. Another emmGrid object is returned,
which can be summarized or further analyzed. For convenience, a pairs.emmGrid
method is provided for the case of pairwise comparisons. Related to this is
the CLD.emmGrid method, which provides a compact letter display for
grouping pairs of means that are not significantly different. CLD
requires the multcompView package.
The plot.emmGrid method will display
side-by-side confidence intervals for the estimates, and/or
“comparison arrows” whereby the significance of pairwise differences
can be judged by how much they overlap. The emmip function
displays estimates like an interaction plot, multi-paneled if there are by
variables. These graphics capabilities require the lattice package be
installed.
When a model is fitted using MCMC methods, the posterior chains(s) of parameter estimates are retained and converted into posterior samples of EMMs or contrasts thereof. These may then be summarized or plotted like any other MCMC results, using tools in, say coda or bayesplot.
The as.glht function and
glht method for emmGrids provide an interface to the
glht function in the multcomp package, thus
providing for more exacting simultaneous estimation or testing. The package
also provides an emm function that works as an alternative to
mcp in a call to glht.