Comparisons Between Predictions Made With Different Regressor Values
Source:R/comparisons.R
comparisons.Rd
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,
slopes, elasticities, etc.
comparisons()
: unit-level (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:
Usage
comparisons(
model,
newdata = NULL,
variables = NULL,
comparison = "difference",
type = NULL,
vcov = TRUE,
by = FALSE,
conf_level = 0.95,
transform = NULL,
cross = FALSE,
wts = NULL,
hypothesis = NULL,
equivalence = NULL,
p_adjust = NULL,
df = Inf,
eps = NULL,
...
)
avg_comparisons(
model,
newdata = NULL,
variables = NULL,
type = NULL,
vcov = TRUE,
by = TRUE,
conf_level = 0.95,
comparison = "difference",
transform = NULL,
cross = FALSE,
wts = NULL,
hypothesis = NULL,
equivalence = NULL,
p_adjust = NULL,
df = Inf,
eps = NULL,
...
)
Arguments
- model
Model object
- newdata
Grid of predictor values at which we evaluate the comparisons.
NULL
(default): Unit-level contrasts for each observed value in the original dataset (empirical distribution). Seeinsight::get_data()
data frame: Unit-level contrasts for each row of the
newdata
data frame.string:
"mean": Contrasts at the Mean. Contrasts when each predictor is held at its mean or mode.
"median": Contrasts at the Median. Contrasts when each predictor is held at its median or mode.
"marginalmeans": Contrasts at Marginal Means.
"tukey": Contrasts at Tukey's 5 numbers.
"grid": Contrasts on a grid of representative numbers (Tukey's 5 numbers and unique values of categorical predictors).
datagrid()
call to specify a custom grid of regressors. For example:newdata = datagrid(cyl = c(4, 6))
:cyl
variable equal to 4 and 6 and other regressors fixed at their means or modes.newdata = datagrid(mpg = fivenum)
:mpg
variable held at Tukey's five numbers (using thefivenum
function), and other regressors fixed at their means or modes.See the Examples section and the datagrid documentation.
- variables
Focal variables
NULL
: compute comparisons for all the variables in the model object (can be slow).Character vector: subset of variables (usually faster).
Named list: names identify the subset of variables of interest, and values define the type of contrast to compute. Acceptable values depend on the variable type:
Factor or character variables:
"reference": Each factor level is compared to the factor reference (base) level
"all": All combinations of observed levels
"sequential": Each factor level is compared to the previous factor level
"pairwise": Each factor level is compared to all other levels
"minmax": The highest and lowest levels of a factor.
Vector of length 2 with the two values to compare.
Logical variables:
NULL: contrast between TRUE and FALSE
Numeric variables:
Numeric of length 1: Contrast for a gap of
x
, computed at the observed value plus and minusx / 2
. For example, estimating a+1
contrast compares adjusted predictions when the regressor is equal to its observed value minus 0.5 and its observed value plus 0.5.Numeric vector of length 2: Contrast between the 2nd element and the 1st element of the
x
vector.Data frame with the same number of rows as
newdata
, with two columns of "low" and "high" values to compare.Function which accepts a numeric vector and returns a data frame with two columns of "low" and "high" values to compare. See examples below.
"iqr": Contrast across the interquartile range of the regressor.
"sd": Contrast across one standard deviation around the regressor mean.
"2sd": Contrast across two standard deviations around the regressor mean.
"minmax": Contrast between the maximum and the minimum values of the regressor.
Examples:
variables = list(gear = "pairwise", hp = 10)
variables = list(gear = "sequential", hp = c(100, 120))
See the Examples section below for more.
- comparison
How should pairs of predictions be compared? Difference, ratio, odds ratio, or user-defined functions.
string: shortcuts to common contrast functions.
Supported shortcuts strings: difference, differenceavg, differenceavgwts, dydx, eyex, eydx, dyex, dydxavg, eyexavg, eydxavg, dyexavg, dydxavgwts, eyexavgwts, eydxavgwts, dyexavgwts, ratio, ratioavg, ratioavgwts, lnratio, lnratioavg, lnratioavgwts, lnor, lnoravg, lnoravgwts, expdydx, expdydxavg, expdydxavgwts
See the Comparisons section below for definitions of each transformation.
function: accept two equal-length numeric vectors of adjusted predictions (
hi
andlo
) and returns a vector of contrasts of the same length, or a unique numeric value.See the Transformations section below for examples of valid 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 model-specific list of acceptable values is returned in an error message. When
type
isNULL
, the default value is used. This default is the first model-related row in themarginaleffects:::type_dictionary
dataframe.- vcov
Type of uncertainty estimates to report (e.g., for robust standard errors). Acceptable values:
FALSE: Do not compute standard errors. This can speed up computation considerably.
TRUE: Unit-level standard errors using the default
vcov(model)
variance-covariance matrix.String which indicates the kind of uncertainty estimates to return.
Heteroskedasticity-consistent:
"HC"
,"HC0"
,"HC1"
,"HC2"
,"HC3"
,"HC4"
,"HC4m"
,"HC5"
. See?sandwich::vcovHC
Heteroskedasticity and autocorrelation consistent:
"HAC"
Mixed-Models degrees of freedom: "satterthwaite", "kenward-roger"
Other:
"NeweyWest"
,"KernHAC"
,"OPG"
. See thesandwich
package documentation.
One-sided formula which indicates the name of cluster variables (e.g.,
~unit_id
). This formula is passed to thecluster
argument of thesandwich::vcovCL
function.Square covariance matrix
Function which returns a covariance matrix (e.g.,
stats::vcov(model)
)
- by
Aggregate unit-level estimates (aka, marginalize, average over). Valid inputs:
FALSE
: return the original unit-level estimates.TRUE
: aggregate estimates for each term.Character vector of column names in
newdata
or in the data frame produced by calling the function without theby
argument.Data frame with a
by
column of group labels, and merging columns shared bynewdata
or the data frame produced by calling the same function without theby
argument.See examples below.
- conf_level
numeric value between 0 and 1. Confidence level to use to build a confidence interval.
- transform
string or function. Transformation applied to unit-level 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
FALSE
: Contrasts represent the change in adjusted predictions when one predictor changes and all other variables are held constant.TRUE
: Contrasts represent the changes in adjusted predictions when all the predictors specified in thevariables
argument are manipulated simultaneously (a "cross-contrast").
- wts
string or numeric: weights to use when computing average contrasts or slopes. These weights only affect the averaging in
avg_*()
or with theby
argument, and not the unit-level estimates themselves.string: column name of the weights variable in
newdata
. When supplying a column name towts
, it is recommended to supply the original data (including the weights variable) explicitly tonewdata
.numeric: vector of length equal to the number of rows in the original data or in
newdata
(if supplied).
- hypothesis
specify a hypothesis test or custom contrast using a numeric value, vector, or matrix, a string, or a string formula.
Numeric:
Single value: the null hypothesis used in the computation of Z and p (before applying
transform
).Vector: Weights to compute a linear combination of (custom contrast between) estimates. Length equal to the number of rows generated by the same function call, but without the
hypothesis
argument.Matrix: Each column is a vector of weights, as describe above, used to compute a distinct linear combination of (contrast between) estimates. The column names of the matrix are used as labels in the output.
String formula to specify linear or non-linear hypothesis tests. If the
term
column uniquely identifies rows, terms can be used in the formula. Otherwise, useb1
,b2
, etc. to identify the position of each parameter. Examples:hp = drat
hp + drat = 12
b1 + b2 + b3 = 0
String:
"pairwise": pairwise differences between estimates in each row.
"reference": differences between the estimates in each row and the estimate in the first row.
"sequential": difference between an estimate and the estimate in the next row.
"revpairwise", "revreference", "revsequential": inverse of the corresponding hypotheses, as described above.
See the Examples section below and the vignette: https://vincentarelbundock.github.io/marginaleffects/articles/hypothesis.html
- equivalence
Numeric vector of length 2: bounds used for the two-one-sided test (TOST) of equivalence, and for the non-inferiority and non-superiority tests. See Details section below.
- p_adjust
Adjust p-values 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
Inf
. Whendf
isInf
, the normal distribution is used. Whendf
is finite, thet
distribution is used. See insight::get_df for a convenient function to extract degrees of freedom. Ex:slopes(model, df = insight::get_df(model))
- eps
NULL or numeric value which determines the step size to use when calculating numerical derivatives: (f(x+eps)-f(x))/eps. When
eps
isNULL
, the step size is 0.0001 multiplied by the difference between the maximum and minimum values of the variable with respect to which we are taking the derivative. Changingeps
may be necessary to avoid numerical problems in certain models.- ...
Additional arguments are passed to the
predict()
method supplied by the modeling package.These arguments are particularly useful for mixed-effects or bayesian models (see the online vignettes on themarginaleffects
website). Available arguments can vary from model to model, depending on the range of supported arguments by each modeling package. See the "Model-Specific Arguments" section of the?marginaleffects
documentation for a non-exhaustive list of available arguments.
Value
A data.frame
with one row per observation (per term/group) and several columns:
rowid
: row number of thenewdata
data frametype
: prediction type, as defined by thetype
argumentgroup
: (optional) value of the grouped outcome (e.g., categorical outcome models)term
: the variable whose marginal effect is computeddydx
: slope of the outcome with respect to the term, for a given combination of predictor valuesstd.error
: standard errors computed by via the delta method.p.value
: p value associated to theestimate
column. The null is determined by thehypothesis
argument (0 by default), and p values are computed before applying thetransform
argument.
See ?print.marginaleffects
for printing options.
Standard errors using the delta method
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
Model-Specific Arguments
Some model types allow model-specific arguments to modify the nature of
marginal effects, predictions, marginal means, and contrasts. Please report
other package-specific 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 |
comparison argument functions
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) - mean(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)))) |
expdydx | \(hi, lo, eps) ((exp(hi) - exp(lo))/exp(eps))/eps |
expdydxavg | \(hi, lo, eps) mean(((exp(hi) - exp(lo))/exp(eps))/eps) |
Bayesian posterior summaries
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).
Equivalence, Inferiority, Superiority
\(\theta\) is an estimate, \(\sigma_\theta\) its estimated standard error, and \([a, b]\) are the bounds of the interval supplied to the equivalence
argument.
Non-inferiority:
\(H_0\): \(\theta \leq a\)
\(H_1\): \(\theta > a\)
\(t=(\theta - a)/\sigma_\theta\)
p: Upper-tail probability
Non-superiority:
\(H_0\): \(\theta \geq b\)
\(H_1\): \(\theta < b\)
\(t=(\theta - b)/\sigma_\theta\)
p: Lower-tail probability
Equivalence: Two One-Sided Tests (TOST)
p: Maximum of the non-inferiority and non-superiority p values.
Thanks to Russell V. Lenth for the excellent emmeans
package and documentation which inspired this feature.
Examples
if (FALSE) {
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 user-specified 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)
# variable-specific 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)
# `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)
}