# Utilities and options for emmeans

## Updating an emmGrid object

Several internal settings are saved when functions like ref_grid(), emmeans(), contrast(), etc. are run. Those settings can be manipulated via the update() method for emmGrids. To illustrate, consider the pigs dataset and model yet again:

pigs.lm <- lm(log(conc) ~ source + factor(percent), data = pigs)
pigs.emm <- emmeans(pigs.lm, "source")
pigs.emm
##  source emmean     SE df lower.CL upper.CL
##  fish     3.39 0.0367 23     3.32     3.47
##  soy      3.67 0.0374 23     3.59     3.74
##  skim     3.80 0.0394 23     3.72     3.88
##
## Results are averaged over the levels of: percent
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95

We see confidence intervals but not tests, by default. This happens as a result of internal settings in pigs.emm.s that are passed to summary() when the object is displayed. If we are going to work with this object a lot, we might want to change its internal settings rather than having to rely on explicitly calling summary() with several arguments. If so, just update the internal settings to what is desired; for example:

pigs.emm.s <- update(pigs.emm, infer = c(TRUE, TRUE), null = log(35),
calc = c(n = ".wgt."))
pigs.emm.s
##  source emmean     SE df  n lower.CL upper.CL null t.ratio p.value
##  fish     3.39 0.0367 23 10     3.32     3.47 3.56  -4.385  0.0002
##  soy      3.67 0.0374 23 10     3.59     3.74 3.56   2.988  0.0066
##  skim     3.80 0.0394 23  9     3.72     3.88 3.56   6.130  <.0001
##
## Results are averaged over the levels of: percent
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95

Note that by adding of calc, we have set a default to calculate and display the sample size when the object is summarized. See help("update.emmGrid") for details on the keywords that can be changed. Mostly, they are the same as the names of arguments in the functions that construct these objects.

Of course, we can always get what we want via calls to test(), confint() or summary() with appropriate arguments. But the update() function is more useful in sophisticated manipulations of objects, or called implicitly via the ... or options argument in emmeans() and other functions. Those options are passed to update() just before the object is returned. For example, we could have done the above update within the emmeans() call as follows (results are not shown because they are the same as before):

emmeans(pigs.lm, "source", infer = c(TRUE, TRUE), null = log(35),
calc = c(n = ".wgt."))

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## Setting options

Speaking of the options argument, note that the default in emmeans() is options = get_emm_option("emmeans"). Let’s see what that is:

get_emm_option("emmeans")
## $infer ## [1] TRUE FALSE So, by default, confidence intervals, but not tests, are displayed when the result is summarized. The reverse is true for results of contrast() (and also the default for pairs() which calls contrast()): get_emm_option("contrast") ##$infer
## [1] FALSE  TRUE

There are also defaults for a newly constructed reference grid:

get_emm_option("ref_grid")
## $is.new.rg ## [1] TRUE ## ##$infer
## [1] FALSE FALSE

The default is to display neither intervals nor tests when summarizing. In addition, the flag is.new.rg is set to TRUE, and that is why one sees a str() listing rather than a summary as the default when the object is simply shown by typing its name at the console.

### Setting and viewing defaults

The user may have other preferences. She may want to see both intervals and tests whenever contrasts are produced; and perhaps she also wants to always default to the response scale when transformations or links are present. We can change the defaults by setting the corresponding options; and that is done via the emm_options() function:

emm_options(emmeans = list(type = "response"),
contrast = list(infer = c(TRUE, TRUE)))

Now, new emmeans() results and contrasts follow the new defaults:

pigs.anal.p <- emmeans(pigs.lm, consec ~ percent)
pigs.anal.p
## $emmeans ## percent response SE df lower.CL upper.CL ## 9 31.4 1.28 23 28.8 34.1 ## 12 37.5 1.44 23 34.7 40.6 ## 15 39.0 1.70 23 35.6 42.7 ## 18 42.3 2.24 23 37.9 47.2 ## ## Results are averaged over the levels of: source ## Confidence level used: 0.95 ## Intervals are back-transformed from the log scale ## ##$contrasts
##  contrast              ratio     SE df lower.CL upper.CL null t.ratio p.value
##  percent12 / percent9   1.20 0.0671 23    1.038     1.38    1   3.202  0.0112
##  percent15 / percent12  1.04 0.0604 23    0.896     1.20    1   0.650  0.8613
##  percent18 / percent15  1.09 0.0750 23    0.911     1.29    1   1.194  0.5202
##
## Results are averaged over the levels of: source
## Confidence level used: 0.95
## Conf-level adjustment: mvt method for 3 estimates
## Intervals are back-transformed from the log scale
## P value adjustment: mvt method for 3 tests
## Tests are performed on the log scale

Observe that the contrasts “inherited” the type = "response" default from the EMMs.

NOTE: Setting the above options does not change how existing emmGrid objects are displayed; it only affects ones constructed in the future.

There is one more option – summary – that overrides all other display defaults for both existing and future objects. For example, specifying emm_options(summary = list(infer = c(TRUE, TRUE))) will result in both intervals and tests being displayed, regardless of their internal defaults, unless infer is explicitly specified in a call to summary().

To temporarily revert to factory defaults in a single call to emmeans() or contrast() or pairs(), specify options = NULL in the call. To reset everything to factory defaults (which we do presently), null-out all of the emmeans package options:

options(emmeans = NULL)

### Optimal digits to display

When an emmGrid object is summarized and displayed, the factory default is to display it with just enough digits as is justified by the standard errors or HPD intervals of the estimates displayed. You may use the "opt.digits" option to change this. If it is TRUE (the default), we display only enough digits as is justified (but at least 3). If it is set to FALSE, the number of digits is set using the R system’s default, getOption("digits"); this is often much more precision than is justified. To illustrate, here is the summary of pigs.emm displayed without optimizing digits. Compare it with the first summary in this vignette.

emm_options(opt.digits = FALSE)
pigs.emm
##  source   emmean         SE df lower.CL upper.CL
##  fish   3.394492 0.03668122 23 3.318612 3.470373
##  soy    3.667260 0.03744798 23 3.589793 3.744727
##  skim   3.796770 0.03938283 23 3.715300 3.878240
##
## Results are averaged over the levels of: percent
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95
emm_options(opt.digits = TRUE)  # revert to optimal digits

By the way, setting this option does not round the calculated values computed by summary.emmGrid() or saved in a summary)emm object; it simply controls the precision displayed by print.summary_emm().

### Startup options

The options accessed by emm_options() and get_emm_option() are stored in a list named emmeans within R’s options environment. Therefore, if you desire options other than the defaults provided on a regular basis, this can be easily arranged by specifying them in your startup script for R. For example, if you want to default to Satterthwaite degrees of freedom for lmer models, and display confidence intervals rather than tests for contrasts, your .Rprofile file could contain the line

options(emmeans = list(lmer.df = "satterthwaite",
contrast = list(infer = c(TRUE, FALSE))))

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## Combining and subsetting emmGrid objects

Two or more emmGrid objects may be combined using the rbind() or + methods. The most common reason (or perhaps the only good reason) to do this is to combine EMMs or contrasts into one family for purposes of applying a multiplicity adjustment to tests or intervals. A user may want to combine the three pairwise comparisons of sources with the three comparisons above of consecutive percents into a single family of six tests with a suitable multiplicity adjustment. This is done quite simply:

rbind(pairs(pigs.emm.s), pigs.anal.p[[2]])
##  contrast              estimate     SE df t.ratio p.value
##  fish - soy             -0.2728 0.0529 23  -5.153  0.0002
##  fish - skim            -0.4023 0.0542 23  -7.428  <.0001
##  soy - skim             -0.1295 0.0530 23  -2.442  0.1364
##  percent12 - percent9    0.1796 0.0561 23   3.202  0.0238
##  percent15 - percent12   0.0378 0.0582 23   0.650  1.0000
##  percent18 - percent15   0.0825 0.0691 23   1.194  1.0000
##
## Results are averaged over some or all of the levels of: percent, source
## Results are given on the log (not the response) scale.
## P value adjustment: bonferroni method for 6 tests

The default adjustment is "bonferroni"; we could have specified something different via the adjust argument. An equivalent way to combine emmGrids is via the addition operator. Any options may be provided by update(). Below, we combine the same results into a family but ask for the “exact” multiplicity adjustment.

update(pigs.anal.p[[2]] + pairs(pigs.emm.s), adjust = "mvt")
##  contrast              ratio     SE df lower.CL upper.CL null t.ratio p.value
##  percent12 / percent9  1.197 0.0671 23    1.022    1.402    1   3.202  0.0214
##  percent15 / percent12 1.039 0.0604 23    0.881    1.224    1   0.650  0.9681
##  percent18 / percent15 1.086 0.0750 23    0.894    1.320    1   1.194  0.7305
##  fish / soy            0.761 0.0403 23    0.656    0.884    1  -5.153  0.0002
##  fish / skim           0.669 0.0362 23    0.574    0.779    1  -7.428  <.0001
##  soy / skim            0.879 0.0466 23    0.756    1.020    1  -2.442  0.1109
##
## Results are averaged over some or all of the levels of: source, percent
## Confidence level used: 0.95
## Conf-level adjustment: mvt method for 6 estimates
## Intervals are back-transformed from the log scale
## P value adjustment: mvt method for 6 tests
## Tests are performed on the log scale

Also evident in comparing these results is that settings are obtained from the first object combined. So in the second output, where they are combined in reverse order, we get both confidence intervals and tests, and transformation to the response scale.

To subset an emmGrid object, just use the subscripting operator []. For instance,

pigs.emm[2:3]
##  source emmean     SE df lower.CL upper.CL
##  soy      3.67 0.0374 23     3.59     3.74
##  skim     3.80 0.0394 23     3.72     3.88
##
## Results are averaged over the levels of: percent
## Results are given on the log (not the response) scale.
## Confidence level used: 0.95

## Accessing results to use elsewhere

Sometimes, users want to use the results of an analysis (say, an emmeans() call) in other computations. The summary() method creates a summary_emm object that inherits from the data.frame class; so one may use the variables therein just as those in a data frame.

Another way is to use the as.data.frame() method for emmGrid objects. This is provided to implement the standard way to coerce an object to a data frame. For illustration, let’s compute the widths of the confidence intervals in our example.

transform(pigs.emm, CI.width = upper.CL - lower.CL)
##   source   emmean         SE df lower.CL upper.CL  CI.width
## 1   fish 3.394492 0.03668122 23 3.318612 3.470373 0.1517618
## 2    soy 3.667260 0.03744798 23 3.589793 3.744727 0.1549341
## 3   skim 3.796770 0.03938283 23 3.715300 3.878240 0.1629392

This implicitly converted pigs.emm to a data frame by passing it to the as.data.frame() method, then performed the required computation. But sometimes you have to explicitly call as.data.frame(). [Note that the opt.digits option is ignored here, because this is a regular data frame, not the summary of an emmGrid.]

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Sometimes, users want to group levels of a factor into a smaller number of groups. Those groups may then be, say, averaged separately and compared, or used as a by factor. The add_grouping() function serves this purpose. The function takes four arguments: the object, the name of the grouping factor to be created, the name of the reference factor that is being grouped, and a vector of level names of the grouping factor corresponding to levels of the reference factor. Suppose for example that we want to distinguish animal and non-animal sources of protein in the pigs example:

c("animal", "vegetable", "animal"))
str(pigs.emm.ss)
## 'emmGrid' object with variables:
##     source = fish, soy, skim
##     type = animal, vegetable
## Nesting structure:  source %in% type
## Transformation: "log"

Note that the new object has a nesting structure (see more about this in the “messy-data” vignette), with the reference factor nested in the new grouping factor. Now we can obtain means and comparisons for each group

emmeans(pigs.emm.ss, pairwise ~ type)
## $emmeans ## type emmean SE df n lower.CL upper.CL ## animal 3.60 0.0267 23 19 3.54 3.65 ## vegetable 3.67 0.0374 23 10 3.59 3.74 ## ## Results are averaged over the levels of: percent, source ## Results are given on the log (not the response) scale. ## Confidence level used: 0.95 ## ##$contrasts
##  contrast           estimate     SE df t.ratio p.value
##  animal - vegetable  -0.0716 0.0455 23  -1.573  0.1295
##
## Results are averaged over the levels of: percent, source
## Results are given on the log (not the response) scale.

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## Re-labeling or re-leveling an emmGrid

Sometimes it is desirable to re-label the rows of an emmGrid, or cast it in terms of other factor(s). This can be done via the levels argument in update().

As an example, sometimes a fitted model has a treatment factor that comprises combinations of other factors. In subsequent analysis, we may well want to break it down into the individual factors’ contributions. Consider, for example, the warpbreaks data provided with R. We will define a single factor and fit a non homogeneous-variance model:

warp <- transform(warpbreaks, treat = interaction(wool, tension))
library(nlme)
warp.gls <- gls(breaks ~ treat, weights = varIdent(form = ~ 1|treat), data = warp)
( warp.emm <- emmeans(warp.gls, "treat") )
##  treat emmean   SE   df lower.CL upper.CL
##  A.L     44.6 6.03 8.01     30.6     58.5
##  B.L     28.2 3.29 8.00     20.6     35.8
##  A.M     24.0 2.89 8.00     17.3     30.7
##  B.M     28.8 3.14 8.00     21.5     36.0
##  A.H     24.6 3.42 8.00     16.7     32.5
##  B.H     18.8 1.63 8.00     15.0     22.5
##
## Degrees-of-freedom method: satterthwaite
## Confidence level used: 0.95

But now we want to re-cast this emmGrid into one that has separate factors for wool and tension. We can do this as follows:

warp.fac <- update(warp.emm, levels = list(
wool = c("A", "B"), tension = c("L", "M", "H")))
str(warp.fac)
## 'emmGrid' object with variables:
##     wool = A, B
##     tension = L, M, H

So now we can do various contrasts involving the separate factors:

contrast(warp.fac, "consec", by = "wool")
## wool = A:
##  contrast estimate   SE   df t.ratio p.value
##  M - L     -20.556 6.69 11.5  -3.074  0.0203
##  H - M       0.556 4.48 15.6   0.124  0.9899
##
## wool = B:
##  contrast estimate   SE   df t.ratio p.value
##  M - L       0.556 4.55 16.0   0.122  0.9881
##  H - M     -10.000 3.54 12.0  -2.824  0.0269
##
## Degrees-of-freedom method: satterthwaite
## P value adjustment: mvt method for 2 tests

Note: When re-leveling to more than one factor, you have to be careful to anticipate that the levels will be expanded using expand.grid(): the first factor in the list varies the fastest and the last varies the slowest. That was the case in our example, but in others, it may not be. Had the levels of treat been ordered as A.L, A.M, A.H, B.L, B.M, B.H, then we would have had to specify the levels of tension first and the levels of wool second.

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