Using a fitted model object, determine a reference grid for which estimated
marginal means are defined. The resulting ref_grid object encapsulates
all the information needed to calculate EMMs and make inferences on them.
ref_grid(object, at, cov.reduce = mean,
cov.keep = get_emm_option("cov.keep"), mult.names, mult.levs,
options = get_emm_option("ref_grid"), data, df, type, regrid, nesting,
offset, sigma, counterfactuals, wt.counter, avg.counter = TRUE,
nuisance = character(0), non.nuisance, wt.nuis = "equal",
rg.limit = get_emm_option("rg.limit"), ...)An object of the S4 class "emmGrid" (see
emmGrid-class). These objects encapsulate everything needed
to do calculations and inferences for estimated marginal means, and contain
nothing that depends on the model-fitting procedure.
An object produced by a supported model-fitting function, such
as lm. Many models are supported. See
vignette("models", "emmeans").
Optional named list of levels for the corresponding variables
A function, logical value, or formula; or a named list of
these. Each covariate not specified in cov.keep or at
is reduced according to these specifications. See the section below on
“Using cov.reduce and cov.keep”.
Character vector: names of covariates that are not
to be reduced; these are treated as factors and used in weighting calculations.
cov.keep may also include integer value(s), and if so, the maximum
of these is used to set a threshold such that any covariate having no more
than that many unique values is automatically included in cov.keep.
Character value: the name(s) to give to the
pseudo-factor(s) whose levels delineate the elements of a multivariate
response. If this is provided, it overrides the default name(s) used for
class(object) when it has a multivariate response (e.g., the default
is "rep.meas" for "mlm" objects).
A named list of levels for the dimensions of a multivariate
response. If there is more than one element, the combinations of levels are
used, in expand.grid order. The (total) number of levels must
match the number of dimensions. If mult.name is specified, this
argument is ignored.
If non-NULL, a named list of arguments to pass
to update.emmGrid, just after the object is constructed.
A data.frame to use to obtain information about the
predictors (e.g. factor levels). If missing, then
recover_data is used to attempt to reconstruct the data. See
the note with recover_data for an important precaution.
Numeric value. This is equivalent to specifying options(df =
df). See update.emmGrid.
Character value. If provided, this is saved as the
"predict.type" setting. See update.emmGrid and the
section below on prediction types and transformations.
Character, logical, or list. If non-missing, the reference
grid is reconstructed via regrid with the argument
transform = regrid. See the section below on prediction types and
transformations. Note: This argument was named transform in
version 1.7.2 and earlier. For compatibility with old code, transform
is still accepted if found among ...,
as long as it doesn't match tran.
If the model has nested fixed effects, this may be specified
here via a character vector or named list specifying the nesting
structure. Specifying nesting overrides any nesting structure that
is automatically detected. See the section below on Recovering or Overriding
Model Information.
Numeric scalar value (if a vector, only the first element is
used). This may be used to add an offset, or override offsets based on the
model. A common usage would be to specify offset = 0 for a Poisson
regression model, so that predictions from the reference grid become rates
relative to the offset that had been specified in the model.
Numeric value to use for subsequent predictions or
back-transformation bias adjustments. If not specified, we use
sigma(object), if available, and NULL otherwise.
Note: This applies only when the family is "gaussian"; for other families,
sigma is set to NA and cannot be overridden.
counterfactuals specifies character
names of counterfactual factors. If this is non-missing, a reference grid
is created consisting of combinations of counterfactual levels and a constructed
factor .obs.no. having a level for each observation in the dataset.
By default, this grid is re-gridded with the response transformation
and averaged over .obs.no. (by default, with equal weights, but
a vector of weights may be specified in wt.counter; it must be
of length equal to the number of observations in the dataset).
If avg.counter is set to FALSE, this averaging is disabled.
See the section below on counterfactuals.
If nuisance is a vector of predictor names,
those predictors are omitted from the reference grid. Instead, the result
will be as if we had averaged over the levels of those factors, with either
equal or proportional weights as specified in wt.nuis (see the
weights argument in emmeans). The factors in
nuisance must not interact with other factors, not even other
nuisance factors. Specifying nuisance factors can save considerable
storage and computation time, and help avoid exceeding the maximum
reference-grid size (get_emm_option("rg.limit")).
Integer limit on the number of reference-grid rows to allow (checked before any multivariate responses are included).
Optional arguments passed to summary.emmGrid,
emm_basis, and
recover_data, such as params, vcov. (see
Covariance matrix below), or options such as mode for
specific model types (see vignette("models",
"emmeans")).
The cov.keep argument was not available in emmeans versions
1.4.1 and earlier. Any covariates named in this list are treated as if they
are factors: all the unique levels are kept in the reference grid. The user
may also specify an integer value, in which case any covariate having no more
than that number of unique values is implicitly included in cov.keep.
The default for cov.keep is set and retrieved via the
emm_options framework, and the system default is "2",
meaning that covariates having only two unique values are automatically
treated as two-level factors. See also the Note below on backward compatibility.
There is a subtle distinction between including a covariate in cov.keep
and specifying its values manually in at: Covariates included in
cov.keep are treated as factors for purposes of weighting, while
specifying levels in at will not include the covariate in weighting.
See the mtcars.lm example below for an illustration.
cov.reduce may be a function,
logical value, formula, or a named list of these.
If a single function, it is applied to each covariate.
If logical and TRUE, mean is used. If logical and
FALSE, it is equivalent to including all covariates in
cov.keep. Use of cov.reduce = FALSE is inadvisable because it
can result in a huge reference grid; it is far better to use
cov.keep.
If a formula (which must be two-sided), then a model is fitted to that
formula using lm; then in the reference grid, its response
variable is set to the results of predict for that model,
with the reference grid as newdata. (This is done after the
reference grid is determined.) A formula is appropriate here when you think
experimental conditions affect the covariate as well as the response.
To allow for situations where a simple lm() call as described above won't
be adequate, a formula of the form ext ~ fcnname is also supported,
where the left-hand side may be ext, extern, or
external (and must not be a predictor name) and the
right-hand side is the name of an existing function. The function is called
with one argument, a data frame with columns for each variable in the
reference grid. The function is expected to use that frame as new data to
be used to obtain predictions for one or more models; and it should return
a named list or data frame with replacement values for one or more of the
covariates.
If cov.reduce is a named list, then the above criteria are used to
determine what to do with covariates named in the list. (However, formula
elements do not need to be named, as those names are determined from the
formulas' left-hand sides.) Any unresolved covariates are reduced using
"mean".
Any cov.reduce of cov.keep specification for a covariate
also named in at is ignored.
Care must be taken when covariate values
depend on one another. For example, when a polynomial model was fitted
using predictors x, x2 (equal to x^2), and x3
(equal to x^3), the reference grid will by default set x2 and
x3 to their means, which is inconsistent. The user should instead
use the at argument to set these to the square and cube of
mean(x). Better yet, fit the model using a formula involving
poly(x, 3) or I(x^2) and I(x^3); then there is only
x appearing as a covariate; it will be set to its mean, and the
model matrix will have the correct corresponding quadratic and cubic terms.
Support for covariates that appear in the dataset
as matrices is very limited. If the matrix has but one column, it is
treated like an ordinary covariate. Otherwise, with more than one column,
each column is reduced to a single reference value -- the result of
applying cov.reduce to each column (averaged together if that
produces more than one value); you may not specify values in at; and
they are not treated as variables in the reference grid, except for
purposes of obtaining predictions.
Ability to support a
particular class of object depends on the existence of
recover_data and emm_basis methods -- see
extending-emmeans for details. The call
methods("recover_data") will help identify these.
Data. In certain models, (e.g., results of
glmer.nb), it is not possible to identify the original
dataset. In such cases, we can work around this by setting data
equal to the dataset used in fitting the model, or a suitable subset. Only
the complete cases in data are used, so it may be necessary to
exclude some unused variables. Using data can also help save
computing, especially when the dataset is large. In any case, data
must represent all factor levels used in fitting the model. It
cannot be used as an alternative to at. (Note: If there is a
pattern of NAs that caused one or more factor levels to be excluded
when fitting the model, then data should also exclude those levels.)
Covariance matrix. By default, the variance-covariance matrix for
the fixed effects is obtained from object, usually via its
vcov method. However, the user may override this via a
vcov. argument, specifying a matrix or a function. If a matrix, it
must be square and of the same dimension and parameter order of the fixed
effects. If a function, must return a suitable matrix when it is called
with arguments (object, ...). Be careful with possible
unintended conflicts with arguments in ...; for example,
sandwich::vcovHAC() has optional arguments adjust and weights
that may be intended for emmeans() but will also be passed to vcov.().
Nested factors. Having a nesting structure affects marginal
averaging in emmeans in that it is done separately for each level
(or combination thereof) of the grouping factors. ref_grid tries to
discern which factors are nested in other factors, but it is not always
obvious, and if it misses some, the user must specify this structure via
nesting; or later using update.emmGrid. The
nesting argument may be a character vector, a named list,
or NULL.
If a list, each name should be the name of a single factor in the
grid, and its entry a character vector of the name(s) of its grouping
factor(s). nested may also be a character value of the form
"factor1 %in% (factor2*factor3)" (the parentheses are optional).
If there is more than one such specification, they may be appended
separated by commas, or as separate elements of a character vector. For
example, these specifications are equivalent: nesting = list(state =
"country", city = c("state", "country"), nesting = "state %in%
country, city %in% (state*country)", and nesting = c("state %in%
country", "city %in% state*country").
When the fitted
model contains subscripts or explicit references to data sets, the
reference grid may optionally be post-processed to simplify the variable
names, depending on the simplify.names option (see
emm_options), which by default is TRUE. For example,
if the model formula is data1$resp ~ data1$trt + data2[[3]] +
data2[["cov"]], the simplified predictor names (for use, e.g., in the
specs for emmeans) will be trt,
data2[[3]], and cov. Numerical subscripts are not simplified;
nor are variables having simplified names that coincide, such as if
data2$trt were also in the model.
Please note that this simplification is performed after the
reference grid is constructed. Thus, non-simplified names must be used in
the at argument (e.g., at = list(`data2["cov"]` = 2:4).
If you don't want names simplified, use emm_options(simplify.names =
FALSE).
Transformations can exist because of a link function in a generalized linear model,
or as a response transformation, or even both. In many cases, they are auto-detected,
for example a model formula of the form sqrt(y) ~ .... Even transformations
containing multiplicative or additive constants, such as 2*sqrt(y + pi) ~ ...,
are auto-detected. A response transformation of y + 1 ~ ... is not
auto-detected, but I(y + 1) ~ ... is interpreted as identity(y + 1) ~ ....
A warning is issued if it gets too complicated.
Complex transformations like the Box-Cox transformation are not auto-detected; but see
the help page for make.tran for information on some advanced methods.
There is a subtle difference
between specifying type = "response" and regrid =
"response". While the summary statistics for the grid itself are the same,
subsequent use in emmeans will yield different results if
there is a response transformation or link function. With type =
"response", EMMs are computed by averaging together predictions on the
linear-predictor scale and then back-transforming to the response
scale; while with regrid = "response", the predictions are
already on the response scale so that the EMMs will be the arithmetic means
of those response-scale predictions. To add further to the possibilities,
geometric means of the response-scale predictions are obtainable via
regrid = "log", type = "response". See also the help page for
regrid.
Order-of-processing issues:
The regrid argument, if present, is acted on immediately after the reference
grid is constructed, while some of the ... arguments may be used to
update the object at the very end. Thus, code like
ref_grid(mod, tran = "sqrt", regrid = "response") will not work correctly
if the intention was to specify the response transformation, because the re-grid
is done before it processes tran = "sqrt". To get the intended
result, do
regrid(ref_grid(mod, tran = "sqrt"), transform = "response").
If counterfactuals is specified, the rows of the entire dataset
become a factor in the reference grid, and the other reference levels are
confined to those named in counterfactuals. In this type of analysis
(called G-computation), we substitute each combination of counterfactual
levels into the entire dataset. Thus, predictions from this grid are those
of each observation under each of the counterfactual levels. For this to
make sense, we require an assumption of exchangeability of these levels.
By default, this grid is converted to the response scale (unless otherwise
specified in regrid and averaged over the observations in the dataset.
Averaging can be disabled by setting avg.counter = FALSE, but
be warned that the resulting reference grid is potentially huge -- the
number of observations in the dataset times the number of counterfactual
combinations, times the number of multivariate levels.
The counterfactuals code is still fairly rudimentary and we can't guarantee
it will always work, such as in cases of nested models. Sometimes, an error
can be averted by specifying avg.counter = FALSE.
If the save.ref_grid option is set to
TRUE (see emm_options),
The most recent result of ref_grid, whether
called directly or indirectly via emmeans,
emtrends, or some other function that calls one of these, is
saved in the user's environment as .Last.ref_grid. This facilitates
checking what reference grid was used, or reusing the same reference grid
for further calculations. This automatic saving is disabled by default, but
may be enabled via emm_options(save.ref_grid = TRUE).
To users, the ref_grid function itself is important because most of
its arguments are in effect arguments of emmeans and related
functions, in that those functions pass their ... arguments to
ref_grid.
The reference grid consists of combinations of independent variables over
which predictions are made. Estimated marginal means are defined as these
predictions, or marginal averages thereof. The grid is determined by first
reconstructing the data used in fitting the model (see
recover_data), or by using the data.frame provided in
data. The default reference grid is determined by the observed levels
of any factors, the ordered unique values of character-valued predictors, and
the results of cov.reduce for numeric predictors. These may be
overridden using at. See also the section below on
recovering/overriding model information.
Reference grids are of class emmGrid,
and several methods exist for them -- for example
summary.emmGrid. Reference grids are fundamental to
emmeans. Supported models are detailed in
vignette("models", "emmeans").
See update.emmGrid for details of arguments that can be in
options (or in ...).
fiber.lm <- lm(strength ~ machine*diameter, data = fiber)
ref_grid(fiber.lm)
ref_grid(fiber.lm, at = list(diameter = c(15, 25)))
if (FALSE) {
# We could substitute the sandwich estimator vcovHAC(fiber.lm)
# as follows:
summary(ref_grid(fiber.lm, vcov. = sandwich::vcovHAC))
}
# If we thought that the machines affect the diameters
# (admittedly not plausible in this example), then we should use:
ref_grid(fiber.lm, cov.reduce = diameter ~ machine)
### Model with indicator variables as predictors:
mtcars.lm <- lm(mpg ~ disp + wt + vs * am, data = mtcars)
(rg.default <- ref_grid(mtcars.lm))
(rg.nokeep <- ref_grid(mtcars.lm, cov.keep = character(0)))
(rg.at <- ref_grid(mtcars.lm, at = list(vs = 0:1, am = 0:1)))
# Two of these have the same grid but different weights:
rg.default@grid
rg.at@grid
### Using cov.reduce formulas...
# Above suggests we can vary disp indep. of other factors - unrealistic
rg.alt <- ref_grid(mtcars.lm, at = list(wt = c(2.5, 3, 3.5)),
cov.reduce = disp ~ vs * wt)
rg.alt@grid
# Alternative to above where we model sqrt(disp)
disp.mod <- lm(sqrt(disp) ~ vs * wt, data = mtcars)
disp.fun <- function(dat)
list(disp = predict(disp.mod, newdata = dat)^2)
rg.alt2 <- ref_grid(mtcars.lm, at = list(wt = c(2.5, 3, 3.5)),
cov.reduce = external ~ disp.fun)
rg.alt2@grid
# Multivariate example
MOats.lm = lm(yield ~ Block + Variety, data = MOats)
ref_grid(MOats.lm, mult.names = "nitro")
# Silly illustration of how to use 'mult.levs' to make comb's of two factors
ref_grid(MOats.lm, mult.levs = list(T=LETTERS[1:2], U=letters[1:2]))
# Comparing estimates with and without counterfactuals
neuralgia.glm <- glm(Pain ~ Treatment + Sex + Age + Duration,
family = binomial(), data = neuralgia)
emmeans(neuralgia.glm, "Treatment", type = "response")
emmeans(neuralgia.glm, "Treatment", counterfactuals = "Treatment")
# Using 'params'
require("splines")
my.knots = c(2.5, 3, 3.5)
mod = lm(Sepal.Length ~ Species * ns(Sepal.Width, knots = my.knots), data = iris)
## my.knots is not a predictor, so need to name it in 'params'
ref_grid(mod, params = "my.knots")
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