comparisons  R Documentation 
Predict the outcome variable at different regressor values (e.g., college
graduates vs. others), and compare those predictions by computing a difference,
ratio, or some other function. comparisons()
can return many quantities of
interest, such as contrasts, differences, risk ratios, changes in log odds, lift,
slopes, elasticities, etc.
comparisons()
: unitlevel (conditional) estimates.
avg_comparisons()
: average (marginal) estimates.
variables
identifies the focal regressors whose "effect" we are interested in. comparison
determines how predictions with different regressor values are compared (difference, ratio, odds, etc.). The newdata
argument and the datagrid()
function control where statistics are evaluated in the predictor space: "at observed values", "at the mean", "at representative values", etc.
See the comparisons vignette and package website for worked examples and case studies:
comparisons(
model,
newdata = NULL,
variables = NULL,
comparison = "difference",
type = NULL,
vcov = TRUE,
by = FALSE,
conf_level = 0.95,
transform = NULL,
cross = FALSE,
wts = FALSE,
hypothesis = NULL,
equivalence = NULL,
p_adjust = NULL,
df = Inf,
eps = NULL,
numderiv = "fdforward",
...
)
avg_comparisons(
model,
newdata = NULL,
variables = NULL,
type = NULL,
vcov = TRUE,
by = TRUE,
conf_level = 0.95,
comparison = "difference",
transform = NULL,
cross = FALSE,
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 comparisons.

variables 
Focal variables

comparison 
How should pairs of predictions be compared? Difference, ratio, odds ratio, or userdefined functions.

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 
vcov 
Type of uncertainty estimates to report (e.g., for robust standard errors). Acceptable values:

by 
Aggregate unitlevel estimates (aka, marginalize, average over). Valid inputs:

conf_level 
numeric value between 0 and 1. Confidence level to use to build a confidence interval. 
transform 
string or function. Transformation applied to unitlevel estimates and confidence intervals just before the function returns results. Functions must accept a vector and return a vector of the same length. Support string shortcuts: "exp", "ln" 
cross 

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 equation; string; a 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 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.
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_comparisons()
: Average comparisons
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 
gam  exclude  mgcv::predict.gam  
robustlmm  rlmerMod  re.form  robustlmm::predict.rlmerMod 
allow.new.levels  robustlmm::predict.rlmerMod  
MCMCglmm  MCMCglmm  ndraws  
sampleSelection  selection  part  sampleSelection::predict.selection 
The following transformations can be applied by supplying one of the shortcut strings to the
comparison
argument.
hi
is a vector of adjusted predictions for the "high" side of the
contrast. lo
is a vector of adjusted predictions for the "low" side of the
contrast. y
is a vector of adjusted predictions for the original data. x
is the predictor in the original data. eps
is the step size to use to
compute derivatives and elasticities.
Shortcut  Function 
difference  \(hi, lo) hi  lo 
differenceavg  \(hi, lo) mean(hi  lo) 
dydx  \(hi, lo, eps) (hi  lo)/eps 
eyex  \(hi, lo, eps, y, x) (hi  lo)/eps * (x/y) 
eydx  \(hi, lo, eps, y, x) ((hi  lo)/eps)/y 
dyex  \(hi, lo, eps, x) ((hi  lo)/eps) * x 
dydxavg  \(hi, lo, eps) mean((hi  lo)/eps) 
eyexavg  \(hi, lo, eps, y, x) mean((hi  lo)/eps * (x/y)) 
eydxavg  \(hi, lo, eps, y, x) mean(((hi  lo)/eps)/y) 
dyexavg  \(hi, lo, eps, x) mean(((hi  lo)/eps) * x) 
ratio  \(hi, lo) hi/lo 
ratioavg  \(hi, lo) mean(hi)/mean(lo) 
lnratio  \(hi, lo) log(hi/lo) 
lnratioavg  \(hi, lo) log(mean(hi)/mean(lo)) 
lnor  \(hi, lo) log((hi/(1  hi))/(lo/(1  lo))) 
lnoravg  \(hi, lo) log((mean(hi)/(1  mean(hi)))/(mean(lo)/(1  mean(lo)))) 
lift  \(hi, lo) (hi  lo)/lo 
liftavg  \(hi, lo) (mean(hi  lo))/mean(lo) 
expdydx  \(hi, lo, eps) ((exp(hi)  exp(lo))/exp(eps))/eps 
expdydxavg  \(hi, lo, eps) mean(((exp(hi)  exp(lo))/exp(eps))/eps) 
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 only for the predictions()
function. 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"
. This type is default when calling predictions()
. It is available—but not default—when calling avg_predictions()
or predictions()
with the by
argument.
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
Behind the scenes, the arguments of marginaleffects
functions are evaluated in this order:
newdata
variables
comparison
and slopes
by
vcov
hypothesis
transform
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)
The behavior of marginaleffects
functions can be modified by setting global options.
Disable some safety checks:
options(marginaleffects_safe = FALSE)
Omit some columns from the printed output:
options(marginaleffects_print_omit = c("p.value", "s.value"))`
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
library(marginaleffects)
# Linear model
tmp < mtcars
tmp$am < as.logical(tmp$am)
mod < lm(mpg ~ am + factor(cyl), tmp)
avg_comparisons(mod, variables = list(cyl = "reference"))
avg_comparisons(mod, variables = list(cyl = "sequential"))
avg_comparisons(mod, variables = list(cyl = "pairwise"))
# GLM with different scale types
mod < glm(am ~ factor(gear), data = mtcars)
avg_comparisons(mod, type = "response")
avg_comparisons(mod, type = "link")
# Contrasts at the mean
comparisons(mod, newdata = "mean")
# Contrasts between marginal means
comparisons(mod, newdata = "marginalmeans")
# Contrasts at userspecified values
comparisons(mod, newdata = datagrid(am = 0, gear = tmp$gear))
comparisons(mod, newdata = datagrid(am = unique, gear = max))
m < lm(mpg ~ hp + drat + factor(cyl) + factor(am), data = mtcars)
comparisons(m, variables = "hp", newdata = datagrid(FUN_factor = unique, FUN_numeric = median))
# Numeric contrasts
mod < lm(mpg ~ hp, data = mtcars)
avg_comparisons(mod, variables = list(hp = 1))
avg_comparisons(mod, variables = list(hp = 5))
avg_comparisons(mod, variables = list(hp = c(90, 100)))
avg_comparisons(mod, variables = list(hp = "iqr"))
avg_comparisons(mod, variables = list(hp = "sd"))
avg_comparisons(mod, variables = list(hp = "minmax"))
# using a function to specify a custom difference in one regressor
dat < mtcars
dat$new_hp < 49 * (dat$hp  min(dat$hp)) / (max(dat$hp)  min(dat$hp)) + 1
modlog < lm(mpg ~ log(new_hp) + factor(cyl), data = dat)
fdiff < \(x) data.frame(x, x + 10)
avg_comparisons(modlog, variables = list(new_hp = fdiff))
# Adjusted Risk Ratio: see the contrasts vignette
mod < glm(vs ~ mpg, data = mtcars, family = binomial)
avg_comparisons(mod, comparison = "lnratioavg", transform = exp)
# Adjusted Risk Ratio: Manual specification of the `comparison`
avg_comparisons(
mod,
comparison = function(hi, lo) log(mean(hi) / mean(lo)),
transform = exp)
# cross contrasts
mod < lm(mpg ~ factor(cyl) * factor(gear) + hp, data = mtcars)
avg_comparisons(mod, variables = c("cyl", "gear"), cross = TRUE)
# variablespecific contrasts
avg_comparisons(mod, variables = list(gear = "sequential", hp = 10))
# hypothesis test: is the `hp` marginal effect at the mean equal to the `drat` marginal effect
mod < lm(mpg ~ wt + drat, data = mtcars)
comparisons(
mod,
newdata = "mean",
hypothesis = "wt = drat")
# same hypothesis test using row indices
comparisons(
mod,
newdata = "mean",
hypothesis = "b1  b2 = 0")
# same hypothesis test using numeric vector of weights
comparisons(
mod,
newdata = "mean",
hypothesis = c(1, 1))
# two custom contrasts using a matrix of weights
lc < matrix(c(
1, 1,
2, 3),
ncol = 2)
comparisons(
mod,
newdata = "mean",
hypothesis = lc)
# Effect of a 1 groupwise standard deviation change
# First we calculate the SD in each group of `cyl`
# Second, we use that SD as the treatment size in the `variables` argument
library(dplyr)
mod < lm(mpg ~ hp + factor(cyl), mtcars)
tmp < mtcars %>%
group_by(cyl) %>%
mutate(hp_sd = sd(hp))
avg_comparisons(mod,
variables = list(hp = function(x) data.frame(x, x + tmp$hp_sd)),
by = "cyl")
# `by` argument
mod < lm(mpg ~ hp * am * vs, data = mtcars)
comparisons(mod, by = TRUE)
mod < lm(mpg ~ hp * am * vs, data = mtcars)
avg_comparisons(mod, variables = "hp", by = c("vs", "am"))
library(nnet)
mod < multinom(factor(gear) ~ mpg + am * vs, data = mtcars, trace = FALSE)
by < data.frame(
group = c("3", "4", "5"),
by = c("3,4", "3,4", "5"))
comparisons(mod, type = "probs", by = by)
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