emtrends: Estimated marginal means of linear trends

View source: R/emtrends.R

emtrendsR Documentation

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, ...)



A supported model object (not a reference grid)


Specifications for what marginal trends are desired – as in emmeans. If specs is missing or NULL, emmeans is not run and the reference grid for specified trends is returned.


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, var should be a numeric predictor that interacts with at least one factor in specs. Then instead of computing EMMs, we compute and compare the slopes of the var trend over levels of the specified other predictor(s). As in EMMs, marginal averages are computed for the predictors in specs and by. See also the “Generalizations” section below.


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 var over the dataset.


Integer value. The maximum degree of trends to compute (this is capped at 5). If greater than 1, an additional factor degree is added to the grid, with corresponding numerical derivatives of orders 1, 2, ..., max.degree as the estimates.


Additional arguments passed to ref_grid or emmeans as appropriate. See Details.


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.

See Also

emmeans, ref_grid


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

# 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 documentation

emmeans documentation built on Oct. 18, 2023, 1:13 a.m.