Estimated marginal means of linear trends
The emtrends function is useful when a fitted model involves a
numerical predictor x interacting with another predictor a
(typically a factor). Such models specify that x has a different trend
depending on a; thus, it may be of interest to estimate and compare
those trends. Analogous to the emmeans setting, we construct a
reference grid of these predicted trends, and then possibly average them over
some of the predictors in the grid.
emtrends(object, specs, var, delta.var = 0.001 * rng, max.degree = 1, ...)
object |
A supported model object (not a reference grid) |
specs |
Specifications for what marginal trends are desired – as in
|
var |
Character value giving the name of a variable with respect to
which a difference quotient of the linear predictors is computed. In order
for this to be useful, |
delta.var |
The value of h to use in forming the difference
quotient (f(x+h) - f(x))/h. Changing it (especially changing its
sign) may be necessary to avoid numerical problems such as logs of negative
numbers. The default value is 1/1000 of the range of |
max.degree |
Integer value. The maximum degree of trends to compute (this
is capped at 5). If greater than 1, an additional factor |
... |
Additional arguments passed to |
The function works by constructing reference grids for object with
various values of var, and then calculating difference quotients of predictions
from those reference grids. Finally, emmeans is called with
the given specs, thus computing marginal averages as needed of
the difference quotients. Any ... arguments are passed to the
ref_grid and emmeans; examples of such optional
arguments include optional arguments (often mode) that apply to
specific models; ref_grid options such as data, at,
cov.reduce, mult.names, nesting, or transform;
and emmeans options such as weights (but please avoid
trend or offset.
An emmGrid or emm_list object, according to specs.
See emmeans for more details on when a list is returned.
Instead of a single predictor, the user may specify some monotone function of
one variable, e.g., var = "log(dose)". If so, the chain rule is
applied. Note that, in this example, if object contains
log(dose) as a predictor, we will be comparing the slopes estimated by
that model, whereas specifying var = "dose" would perform a
transformation of those slopes, making the predicted trends vary depending on
dose.
In earlier versions of emtrends, the first argument was named
model rather than object. (The name was changed because of
potential mis-matching with a mode argument, which is an option for
several types of models.) For backward compatibility, model still works
provided all arguments are named.
It is important to understand that trends computed by emtrends are
not equivalent to polynomial contrasts in a parallel model where
var is regarded as a factor. That is because the model object
here is assumed to fit a smooth function of var, and the estimated
trends reflect local behavior at particular value(s) of var;
whereas when var is modeled as a factor and polynomial contrasts are
computed, those contrasts represent the global pattern of changes over
all levels of var.
See the pigs.poly and pigs.fact examples below for an
illustration. The linear and quadratic trends depend on the value of
percent, but the cubic trend is constant (because that is true of
a cubic polynomial, which is the underlying model). The cubic contrast
in the factorial model has the same P value as for the cubic trend,
again because the cubic trend is the same everywhere.
fiber.lm <- lm(strength ~ diameter*machine, data=fiber)
# Obtain slopes for each machine ...
( fiber.emt <- emtrends(fiber.lm, "machine", var = "diameter") )
# ... and pairwise comparisons thereof
pairs(fiber.emt)
# Suppose we want trends relative to sqrt(diameter)...
emtrends(fiber.lm, ~ machine | diameter, var = "sqrt(diameter)",
at = list(diameter = c(20, 30)))
# Obtaining a reference grid
mtcars.lm <- lm(mpg ~ poly(disp, degree = 2) * (factor(cyl) + factor(am)), data = mtcars)
# Center trends at mean disp for each no. of cylinders
mtcTrends.rg <- emtrends(mtcars.lm, var = "disp",
cov.reduce = disp ~ factor(cyl))
summary(mtcTrends.rg) # estimated trends at grid nodes
emmeans(mtcTrends.rg, "am", weights = "prop")
### Higher-degree trends ...
pigs.poly <- lm(conc ~ poly(percent, degree = 3), data = pigs)
emt <- emtrends(pigs.poly, ~ degree | percent, "percent", max.degree = 3,
at = list(percent = c(9, 13.5, 18)))
# note: 'degree' is an extra factor created by 'emtrends'
summary(emt, infer = c(TRUE, TRUE))
# Compare above results with poly contrasts when 'percent' is modeled as a factor ...
pigs.fact <- lm(conc ~ factor(percent), data = pigs)
emm <- emmeans(pigs.fact, "percent")
contrast(emm, "poly")
# Some P values are comparable, some aren't! See Note in documentationPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.