slopes {marginaleffects} | R Documentation |
Partial derivative of the regression equation with respect to a regressor of interest.
slopes()
: unit-level (conditional) estimates.
avg_slopes()
: average (marginal) estimates.
The newdata
argument and the datagrid()
function can be used to control where statistics are evaluated in the predictor space: "at observed values", "at the mean", "at representative values", etc.
See the slopes vignette and package website for worked examples and case studies:
slopes(
model,
newdata = NULL,
variables = NULL,
type = NULL,
by = FALSE,
vcov = TRUE,
conf_level = 0.95,
slope = "dydx",
wts = NULL,
hypothesis = NULL,
df = Inf,
eps = NULL,
...
)
avg_slopes(
model,
newdata = NULL,
variables = NULL,
type = NULL,
by = TRUE,
vcov = TRUE,
conf_level = 0.95,
slope = "dydx",
wts = NULL,
hypothesis = NULL,
df = Inf,
eps = NULL,
...
)
model |
Model object |
newdata |
Grid of predictor values at which we evaluate the slopes.
|
variables |
Focal variables
|
type |
string indicates the type (scale) of the predictions used to
compute contrasts or slopes. This can differ based on the model
type, but will typically be a string such as: "response", "link", "probs",
or "zero". When an unsupported string is entered, the model-specific list of
acceptable values is returned in an error message. When |
by |
Aggregate unit-level estimates (aka, marginalize, average over). Valid inputs:
|
vcov |
Type of uncertainty estimates to report (e.g., for robust standard errors). Acceptable values:
|
conf_level |
numeric value between 0 and 1. Confidence level to use to build a confidence interval. |
slope |
string indicates the type of slope or (semi-)elasticity to compute:
|
wts |
string or numeric: weights to use when computing average
contrasts or slopes. These weights only affect the averaging in
|
hypothesis |
specify a hypothesis test or custom contrast using a numeric value, vector, or matrix, a string, or a string formula.
|
df |
Degrees of freedom used to compute p values and confidence intervals. A single numeric value between 1 and |
eps |
NULL or numeric value which determines the step size to use when
calculating numerical derivatives: (f(x+eps)-f(x))/eps. When |
... |
Additional arguments are passed to the |
A "slope" or "marginal effect" is the partial derivative of the regression equation with respect to a variable in the model. This function uses automatic differentiation to compute slopes for a vast array of models, including non-linear models with transformations (e.g., polynomials). Uncertainty estimates are computed using the delta method.
Numerical derivatives for the slopes
function are calculated
using a simple epsilon difference approach: \partial Y / \partial X = (f(X + \varepsilon/2) - f(X+\varepsilon/2)) / \varepsilon
,
where f is the predict()
method associated with the model class, and
\varepsilon
is determined by the eps
argument.
A data.frame
with one row per observation (per term/group) and several columns:
rowid
: row number of the newdata
data frame
type
: prediction type, as defined by the type
argument
group
: (optional) value of the grouped outcome (e.g., categorical outcome models)
term
: the variable whose marginal effect is computed
dydx
: slope of the outcome with respect to the term, for a given combination of predictor values
std.error
: standard errors computed by via the delta method.
See ?print.marginaleffects
for printing options.
avg_slopes()
: Average slopes
Standard errors for all quantities estimated by marginaleffects
can be obtained via the delta method. This requires differentiating a function with respect to the coefficients in the model using a finite difference approach. In some models, the delta method standard errors can be sensitive to various aspects of the numeric differentiation strategy, including the step size. By default, the step size is set to 1e-8
, or to 1e-4
times the smallest absolute model coefficient, whichever is largest.
marginaleffects
can delegate numeric differentiation to the numDeriv
package, which allows more flexibility. To do this, users can pass arguments to the numDeriv::jacobian
function through a global option. For example:
options(marginaleffects_numDeriv = list(method = "simple", method.args = list(eps = 1e-6)))
options(marginaleffects_numDeriv = list(method = "Richardson", method.args = list(eps = 1e-5)))
options(marginaleffects_numDeriv = NULL)
See the "Standard Errors and Confidence Intervals" vignette on the marginaleffects
website for more details on the computation of standard errors:
https://vincentarelbundock.github.io/marginaleffects/articles/uncertainty.html
Note that the inferences()
function can be used to compute uncertainty estimates using a bootstrap or simulation-based inference. See the vignette:
https://vincentarelbundock.github.io/marginaleffects/articles/bootstrap.html
Some model types allow model-specific arguments to modify the nature of marginal effects, predictions, marginal means, and contrasts.
Package | Class | Argument | Documentation |
brms | brmsfit | ndraws | brms::posterior_predict |
re_formula | |||
lme4 | merMod | include_random | insight::get_predicted |
re.form | lme4::predict.merMod | ||
allow.new.levels | lme4::predict.merMod | ||
glmmTMB | glmmTMB | re.form | glmmTMB::predict.glmmTMB |
allow.new.levels | glmmTMB::predict.glmmTMB | ||
zitype | glmmTMB::predict.glmmTMB | ||
mgcv | bam | exclude | mgcv::predict.bam |
robustlmm | rlmerMod | re.form | robustlmm::predict.rlmerMod |
allow.new.levels | robustlmm::predict.rlmerMod | ||
MCMCglmm | MCMCglmm | ndraws | |
By default, credible intervals in bayesian models are built as equal-tailed intervals. This can be changed to a highest density interval by setting a global option:
options("marginaleffects_posterior_interval" = "eti")
options("marginaleffects_posterior_interval" = "hdi")
By default, the center of the posterior distribution in bayesian models is identified by the median. Users can use a different summary function by setting a global option:
options("marginaleffects_posterior_center" = "mean")
options("marginaleffects_posterior_center" = "median")
When estimates are averaged using the by
argument, the tidy()
function, or
the summary()
function, the posterior distribution is marginalized twice over.
First, we take the average across units but within each iteration of the
MCMC chain, according to what the user requested in by
argument or
tidy()/summary()
functions. Then, we identify the center of the resulting
posterior using the function supplied to the
"marginaleffects_posterior_center"
option (the median by default).
# Unit-level (conditional) Marginal Effects
mod <- glm(am ~ hp * wt, data = mtcars, family = binomial)
mfx <- slopes(mod)
head(mfx)
# Average Marginal Effect (AME)
avg_slopes(mod, by = TRUE)
# Marginal Effect at the Mean (MEM)
slopes(mod, newdata = datagrid())
# Marginal Effect at User-Specified Values
# Variables not explicitly included in `datagrid()` are held at their means
slopes(mod, newdata = datagrid(hp = c(100, 110)))
# Group-Average Marginal Effects (G-AME)
# Calculate marginal effects for each observation, and then take the average
# marginal effect within each subset of observations with different observed
# values for the `cyl` variable:
mod2 <- lm(mpg ~ hp * cyl, data = mtcars)
avg_slopes(mod2, variables = "hp", by = "cyl")
# Marginal Effects at User-Specified Values (counterfactual)
# Variables not explicitly included in `datagrid()` are held at their
# original values, and the whole dataset is duplicated once for each
# combination of the values in `datagrid()`
mfx <- slopes(mod,
newdata = datagrid(hp = c(100, 110),
grid_type = "counterfactual"))
head(mfx)
# Heteroskedasticity robust standard errors
mfx <- slopes(mod, vcov = sandwich::vcovHC(mod))
head(mfx)
# hypothesis test: is the `hp` marginal effect at the mean equal to the `drat` marginal effect
mod <- lm(mpg ~ wt + drat, data = mtcars)
slopes(
mod,
newdata = "mean",
hypothesis = "wt = drat")
# same hypothesis test using row indices
slopes(
mod,
newdata = "mean",
hypothesis = "b1 - b2 = 0")
# same hypothesis test using numeric vector of weights
slopes(
mod,
newdata = "mean",
hypothesis = c(1, -1))
# two custom contrasts using a matrix of weights
lc <- matrix(c(
1, -1,
2, 3),
ncol = 2)
colnames(lc) <- c("Contrast A", "Contrast B")
slopes(
mod,
newdata = "mean",
hypothesis = lc)