The emmeans package provides a variety of post hoc analyses such as obtaining estimated marginal means (EMMs) and comparisons thereof, displaying these results in a graph, and a number of related tasks.

This vignette illustrates basic uses of emmeans with lm_robust objects. For more details, refer to the emmeans package itself and its vignettes.

### A factorial experiment

The warpbreaks dataset provided in base R has the results of a two-factor experiment. We start by fitting a model

library(estimatr)

warp.rlm <- lm_robust(log(breaks) ~ wool * tension, data = warpbreaks)

Typical use of emmeans() is to obtain predictions, or marginal means thereof, via a formula of the form ~ primary.variables | by.variables:

library(emmeans)

emm <- emmeans(warp.rlm, ~ tension | wool)
class(emm)
str(emm)
emm

These results may be plotted as side-by-side intervals or as an interaction-style plot:

plot(emm)
emmip(emm, wool ~ tension, CIs = TRUE)

This particular example has a response transformation. That transformation is detected and we may back-transform to the original scale:

confint(emm, type = "response")

We may do comparisons and other contrasts:

pairs(emm) # pairwise comparisons
contrast(emm, "trt.vs.ctrl", ref = "L", type = "response", adjust = "mvt")

Note that with a log transformations, it is possible to back-transform comparisons, and they become ratios. With other transformations, back-transforming is not possible.

### Rank-deficient models

Let’s create a variation on this example where one cell is omitted:

warpi.rlm <- update(warp.rlm, subset = -(37:48))
(rgi <- ref_grid(warpi.rlm))
summary(rgi)

Note that the empty cell is detected and flagged as non-estimable.

Some additional explanation here. EMMs are based on a reference grid, defined as the grid created by all possible combinations of factor levels, together with the mean of each numerical predictor. The reference grid here (rgi) is also an "emmGrid" object just like the previous emm. The grid itself is available as a data frame via the grid member, and you can verify that the above results match those of the predict function for the model:

predict(warpi.rlm, newdata = rgi@grid, se.fit = TRUE)

There is one exception for the empty cell. I will leave it as a user exercise to demonstrate that if we were to use different contrasts when fitting warpi.rlm, the predictions will be the same except for the empty cell.

### Multivariate models

If there is a multivariate response, it is treated as another factor that is crossed with the other factors in the model. To illustrate, consider the dataset MOats, provided in emmeans:

MOats.rlm <- lm_robust(yield ~ Block + Variety, data = MOats)
ref_grid(MOats.rlm)

By default, the pseudo-factor is named rep.meas, but we can change it if we like:

emmeans(MOats.rlm, pairwise ~ nitro, mult.name = "nitro")

This illustrates an additional feature of emmeans that we can put a contrast method in the left side of a formula.

### Afterword

There are numerous capabilities of emmeans not illustrated here. See that package’s help files and vignettes. Using vignette("basics", "emmeans") is a good starting point.