slopes  R Documentation 
Partial derivative of the regression equation with respect to a regressor of interest.
slopes()
: unitlevel (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 = FALSE,
hypothesis = NULL,
equivalence = NULL,
p_adjust = NULL,
df = Inf,
eps = NULL,
numderiv = "fdforward",
...
)
avg_slopes(
model,
newdata = NULL,
variables = NULL,
type = NULL,
by = TRUE,
vcov = TRUE,
conf_level = 0.95,
slope = "dydx",
wts = FALSE,
hypothesis = NULL,
equivalence = NULL,
p_adjust = NULL,
df = Inf,
eps = NULL,
numderiv = "fdforward",
...
)
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 modelspecific list of
acceptable values is returned in an error message. When 
by 
Aggregate unitlevel 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 
logical, string or numeric: weights to use when computing average predictions, 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, a string formula, or a function.

equivalence 
Numeric vector of length 2: bounds used for the twoonesided test (TOST) of equivalence, and for the noninferiority and nonsuperiority tests. See Details section below. 
p_adjust 
Adjust pvalues for multiple comparisons: "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", or "fdr". See stats::p.adjust 
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 
numderiv 
string or list of strings indicating the method to use to for the numeric differentiation used in to compute delta method standard errors.

... 
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 nonlinear 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.
p.value
: p value associated to the estimate
column. The null is determined by the hypothesis
argument (0 by default), and p values are computed before applying the transform
argument. For models of class feglm
, Gam
, glm
and negbin
, p values are computed on the link scale by default unless the type
argument is specified explicitly.
s.value
: Shannon information transforms of p values. How many consecutive "heads" tosses would provide the same amount of evidence (or "surprise") against the null hypothesis that the coin is fair? The purpose of S is to calibrate the analyst's intuition about the strength of evidence encoded in p against a wellknown physical phenomenon. See Greenland (2019) and Cole et al. (2020).
conf.low
: lower bound of the confidence interval (or equaltailed interval for bayesian models)
conf.high
: upper bound of the confidence interval (or equaltailed interval for bayesian models)
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 1e8
, or to 1e4
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 = 1e6)))
options(marginaleffects_numDeriv = list(method = "Richardson", method.args = list(eps = 1e5)))
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://marginaleffects.com/vignettes/uncertainty.html
Note that the inferences()
function can be used to compute uncertainty estimates using a bootstrap or simulationbased inference. See the vignette:
https://marginaleffects.com/vignettes/bootstrap.html
Some model types allow modelspecific arguments to modify the nature of
marginal effects, predictions, marginal means, and contrasts. Please report
other packagespecific predict()
arguments on Github so we can add them to
the table below.
https://github.com/vincentarelbundock/marginaleffects/issues
Package  Class  Argument  Documentation 
brms  brmsfit  ndraws  brms::posterior_predict 
re_formula  brms::posterior_predict  
lme4  merMod  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 equaltailed 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).
\theta
is an estimate, \sigma_\theta
its estimated standard error, and [a, b]
are the bounds of the interval supplied to the equivalence
argument.
Noninferiority:
H_0
: \theta \leq a
H_1
: \theta > a
t=(\theta  a)/\sigma_\theta
p: Uppertail probability
Nonsuperiority:
H_0
: \theta \geq b
H_1
: \theta < b
t=(\theta  b)/\sigma_\theta
p: Lowertail probability
Equivalence: Two OneSided Tests (TOST)
p: Maximum of the noninferiority and nonsuperiority p values.
Thanks to Russell V. Lenth for the excellent emmeans
package and documentation which inspired this feature.
The type
argument determines the scale of the predictions used to compute quantities of interest with functions from the marginaleffects
package. Admissible values for type
depend on the model object. When users specify an incorrect value for type
, marginaleffects
will raise an informative error with a list of valid type
values for the specific model object. The first entry in the list in that error message is the default type.
The invlink(link)
is a special type defined by marginaleffects
. It is available for some (but not all) models and functions. With this link type, we first compute predictions on the link scale, then we use the inverse link function to backtransform the predictions to the response scale. This is useful for models with nonlinear link functions as it can ensure that confidence intervals stay within desirable bounds, ex: 0 to 1 for a logit model. Note that an average of estimates with type="invlink(link)"
will not always be equivalent to the average of estimates with type="response"
.
Some of the most common type
values are:
response, link, E, Ep, average, class, conditional, count, cum.prob, cumhaz, cumprob, density, detection, disp, ev, expected, expvalue, fitted, hazard, invlink(link), latent, latent_N, linear, linear.predictor, linpred, location, lp, mean, numeric, p, ppd, pr, precision, prediction, prob, probability, probs, quantile, risk, rmst, scale, survival, unconditional, utility, variance, xb, zero, zlink, zprob
The slopes()
and comparisons()
functions can use parallelism to
speed up computation. Operations are parallelized for the computation of
standard errors, at the model coefficient level. There is always
considerable overhead when using parallel computation, mainly involved
in passing the whole dataset to the different processes. Thus, parallel
computation is most likely to be useful when the model includes many parameters
and the dataset is relatively small.
Warning: In many cases, parallel processing will not be useful at all.
To activate parallel computation, users must load the future.apply
package,
call plan()
function, and set a global option. For example:
library(future.apply) plan("multicore", workers = 4) options(marginaleffects_parallel = TRUE) slopes(model)
To disable parallelism in marginaleffects
altogether, you can set a global option:
options(marginaleffects_parallel = FALSE)
Behind the scenes, the arguments of marginaleffects
functions are evaluated in this order:
newdata
variables
comparison
and slopes
by
vcov
hypothesis
transform
Greenland S. 2019. "Valid PValues Behave Exactly as They Should: Some Misleading Criticisms of PValues and Their Resolution With SValues." The American Statistician. 73(S1): 106–114.
Cole, Stephen R, Jessie K Edwards, and Sander Greenland. 2020. "Surprise!" American Journal of Epidemiology 190 (2): 191–93. https://doi.org/10.1093/aje/kwaa136
# Unitlevel (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 UserSpecified Values
# Variables not explicitly included in `datagrid()` are held at their means
slopes(mod, newdata = datagrid(hp = c(100, 110)))
# GroupAverage Marginal Effects (GAME)
# 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 UserSpecified 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)
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