Compute average marginal effects

sim_ame() is a wrapper for sim_apply() that computes average marginal effects, the average effect of changing a single variable from one value to another (i.e., from one category to another for categorical variables or a tiny change for continuous variables).

Usage

sim_ame(
  sim,
  var,
  subset = NULL,
  by = NULL,
  contrast = NULL,
  outcome = NULL,
  type = NULL,
  eps = 1e-05,
  verbose = TRUE,
  cl = NULL
)

# S3 method for clarify_ame
print(x, digits = NULL, max.ests = 6, ...)

Arguments

sim: a clarify_sim object; the output of a call to sim() or misim().
var: either the names of the variables for which marginal effects are to be computed or a named list containing the values the variables should take. See Details.
subset: optional; a vector used to subset the data used to compute the marginal effects. This will be evaluated within the original dataset used to fit the model using subset(), so nonstandard evaluation is allowed.
by: a one-sided formula or character vector containing the names of variables for which to stratify the estimates. Each quantity will be computed within each level of the complete cross of the variables specified in by.
contrast: a string containing the name of a contrast between the average marginal means when the variable named in var is categorical and takes on two values. Allowed options include "diff" for the difference in means (also "rd"), "rr" for the risk ratio (also "irr"), "log(rr): for the log risk ratio (also "log(irr)"), "sr" for the survival ratio, "log(sr): for the log survival ratio, "srr" for the switch relative risk (also "grrr"), "or" for the odds ratio, "log(or)" for the log odds ratio, and "nnt" for the number needed to treat. These options are not case sensitive, but the parentheses must be included if present.
outcome: a string containing the name of the outcome or outcome level for multivariate (multiple outcomes) or multi-category outcomes. Ignored for univariate (single outcome) and binary outcomes.
type: a string containing the type of predicted values (e.g., the link or the response). Passed to marginaleffects::get_predict() and eventually to predict() in most cases. The default and allowable option depend on the type of model supplied, but almost always corresponds to the response scale (e.g., predicted probabilities for binomial models).
eps: when the variable named in var is continuous, the value by which to change the variable values to approximate the derivative. See Details.
verbose: logical; whether to display a text progress bar indicating progress and estimated time remaining for the procedure. Default is TRUE.
cl: a cluster object created by parallel::makeCluster(), or an integer to indicate the number of child-processes (integer values are ignored on Windows) for parallel evaluations. See pbapply::pblapply() for details. If NULL, no parallelization will take place.
x: a clarify_ame object.
digits: the minimum number of significant digits to be used; passed to print.data.frame().
max.ests: the maximum number of estimates to display.
...: optional arguments passed to FUN.

Value

A clarify_ame object, which inherits from clarify_est and is similar to the output of sim_apply(), with the additional attributes "var" containing the variable values specified in var and "by" containing the names of the variables specified in by (if any). The average adjusted predictions will be named E[Y({v})], where {v} is replaced with the values the variables named in var take on. The average marginal effect for a continuous var will be named E[dY/d({x})] where {x} is replaced with var. When by is specified, the average adjusted predictions will be named E[Y({v})|{b}] and the average marginal effect E[dY/d({x})|{b}] where {b} is a comma-separated list of of values of the by variables at which the quantity is computed. See examples.

Details

sim_ame() computes average adjusted predictions or average marginal effects depending on which variables are named in var and how they are specified. Canonically, var should be specified as a named list with the value(s) each variable should be set to. For example, specifying var = list(x1 = 0:1) computes average adjusted predictions setting x1 to 0 and 1. Specifying a variable's values as NULL, e.g., list(x1 = NULL), is equivalent to requesting average adjusted predictions at each unique value of the variable when that variable is binary or a factor or character and requests the average marginal effect of that variable otherwise. Specifying an unnamed entry in the list with a string containing the value of that variable, e.g., list("x1") is equivalent to specifying list(x1 = NULL). Similarly, supplying a vector with the names of the variables is equivalent to specifying a list, e.g., var = "x1" is equivalent to var = list(x1 = NULL).

Multiple variables can be supplied to var at the same time to set the corresponding variables to those values. If all values are specified directly or the variables are categorical, e.g., list(x1 = 0:1, x2 = c(5, 10)), this computes average adjusted predictions at each combination of the supplied variables. If any one variable's values is specified as NULL and the variable is continuous, the average marginal effect of that variable will be computed with the other variables set to their corresponding combinations. For example, if x2 is a continuous variable, specifying var = list(x1 = 0:1, x2 = NULL) requests the average marginal effect of x2 computed first setting x1 to 0 and then setting x1 to 1. The average marginal effect can only be computed for one variable at a time.

Below are some examples of specifications and what they request, assuming x1 is a binary variable taking on values of 0 and 1 and x2 is a continuous variable:

list(x1 = 0:1), list(x1 = NULL), list("x1"), "x1" -- the average adjusted predictions setting x1 to 0 and to 1
list(x2 = NULL), list("x2"), "x2" -- the average marginal effect of x2
list(x2 = c(5, 10)) -- the average adjusted predictions setting x2 to 5 and to 10
list(x1 = 0:1, x2 = c(5, 10)), list("x1", x2 = c(5, 10)) -- the average adjusted predictions setting x1 and x2 in a full cross of 0, 1 and 5, 10, respectively (e.g., (0, 5), (0, 10), (1, 5), and (1, 10))
list(x1 = 0:1, "x2"), list("x1", "x2"), c("x1", "x2") -- the average marginal effects of x2 setting x1 to 0 and to 1

The average adjusted prediction is the average predicted outcome value after setting all units' value of a variable to a specified level. (This quantity has several names, including the average potential outcome, average marginal mean, and standardized mean). When exactly two average adjusted predictions are requested, a contrast between them can be requested by supplying an argument to contrast (see Effect Measures section below). Contrasts can be manually computed using transform() afterward as well; this is required when multiple average adjusted predictions are requested (i.e., because a single variable was supplied to var with more than two levels or a combination of multiple variables was supplied).

A marginal effect is the instantaneous rate of change corresponding to changing a unit's observed value of a variable by a tiny amount and considering to what degree the predicted outcome changes. The ratio of the change in the predicted outcome to the change in the value of the variable is the marginal effect; these are averaged across the sample to arrive at an average marginal effect. The "tiny amount" used is eps times the standard deviation of the focal variable.

The difference between using by or subset vs. var is that by and subset subset the data when computing the requested quantity, whereas var sets the corresponding variable to given a value for all units. For example, using by = ~v computes the quantity of interest separately for each subset of the data defined by v, whereas setting var = list(., "v") computes the quantity of interest for all units setting their value of v to its unique values. The resulting quantities have different interpretations. Both by and var can be used simultaneously.

Effect measures

The effect measures specified in contrast are defined below. Typically only "diff" is appropriate for continuous outcomes and "diff" or "irr" are appropriate for count outcomes; the rest are appropriate for binary outcomes. For a focal variable with two levels, 0 and 1, and an outcome Y, the average marginal means will be denoted in the below formulas as E[Y(0)] and E[Y(1)], respectively.

`contrast`	Description	Formula
`"diff"`/`"rd"`	Mean/risk difference	`E[Y(1)] - E[Y(0)]`
`"rr"`/`"irr"`	Risk ratio/incidence rate ratio	`E[Y(1)] / E[Y(0)]`
`"sr"`	Survival ratio	`(1 - E[Y(1)]) / (1 - E[Y(0)])`
`"srr"`/`"grrr"`	Switch risk ratio	`1 - sr` if `E[Y(1)] > E[Y(0)]`
		`rr - 1` if `E[Y(1)] < E[Y(0)]`
		`0` otherwise
`"or"`	Odds ratio	`O[Y(1)] / O[Y(0)]`
		where `O[Y(.)]` = `E[Y(.)] / (1 - E[Y(.)])`
`"nnt"`	Number needed to treat	`1 / rd`

The log(.) versions are defined by taking the log() (natural log) of the corresponding effect measure.

Examples

data("lalonde", package = "MatchIt")

# Fit the model
fit <- glm(I(re78 > 0) ~ treat + age + race +
             married + re74,
           data = lalonde, family = binomial)

# Simulate coefficients
set.seed(123)
s <- sim(fit, n = 100)

# Average marginal effect of `age`
est <- sim_ame(s, var = "age", verbose = FALSE)
summary(est)
#>              Estimate    2.5 %   97.5 %
#> E[dY/d(age)] -0.00695 -0.01027 -0.00427

# Contrast between average adjusted predictions
# for `treat`
est <- sim_ame(s, var = "treat", contrast = "rr",
               verbose = FALSE)
summary(est)
#>         Estimate 2.5 % 97.5 %
#> E[Y(0)]    0.743 0.700  0.783
#> E[Y(1)]    0.810 0.755  0.860
#> RR         1.090 0.996  1.186

# Average adjusted predictions for `race`; need to follow up
# with contrasts for specific levels
est <- sim_ame(s, var = "race", verbose = FALSE)

est <- transform(est,
                 `RR(h,b)` = `E[Y(hispan)]` / `E[Y(black)]`)

summary(est)
#>              Estimate 2.5 % 97.5 %
#> E[Y(black)]     0.706 0.640  0.760
#> E[Y(hispan)]    0.832 0.739  0.903
#> E[Y(white)]     0.800 0.746  0.850
#> RR(h,b)         1.178 1.026  1.356

# Average adjusted predictions for `treat` within levels of
# `married`, first using `subset` and then using `by`
est0 <- sim_ame(s, var = "treat", subset = married == 0,
                contrast = "rd", verbose = FALSE)
names(est0) <- paste0(names(est0), "|married=0")
est1 <- sim_ame(s, var = "treat", subset = married == 1,
                contrast = "rd", verbose = FALSE)
names(est1) <- paste0(names(est1), "|married=1")

summary(cbind(est0, est1))
#>                   Estimate    2.5 %   97.5 %
#> E[Y(0)]|married=0  0.72406  0.65502  0.77967
#> E[Y(1)]|married=0  0.79519  0.73823  0.84874
#> RD|married=0       0.07113 -0.00361  0.14954
#> E[Y(0)]|married=1  0.76974  0.71670  0.82070
#> E[Y(1)]|married=1  0.83078  0.75193  0.89550
#> RD|married=1       0.06104 -0.00330  0.11733

est <- sim_ame(s, var = "treat", by = ~married,
               contrast = "rd", verbose = FALSE)

est
#> A `clarify_est` object (from `sim_ame()`)
#>  - Average adjusted predictions for `treat`
#>    - within levels of `married`
#>  - 100 simulated values
#>  - 6 quantities estimated:                     
#>  E[Y(0)|0] 0.72405662
#>  E[Y(1)|0] 0.79518774
#>  RD[0]     0.07113112
#>  E[Y(0)|1] 0.76974375
#>  E[Y(1)|1] 0.83078255
#>  RD[1]     0.06103880
summary(est)
#>           Estimate    2.5 %   97.5 %
#> E[Y(0)|0]  0.72406  0.65502  0.77967
#> E[Y(1)|0]  0.79519  0.73823  0.84874
#> RD[0]      0.07113 -0.00361  0.14954
#> E[Y(0)|1]  0.76974  0.71670  0.82070
#> E[Y(1)|1]  0.83078  0.75193  0.89550
#> RD[1]      0.06104 -0.00330  0.11733

# Average marginal effect of `age` within levels of
# married*race
est <- sim_ame(s, var = "age", by = ~married + race,
               verbose = FALSE)
est
#> A `clarify_est` object (from `sim_ame()`)
#>  - Average marginal effect of `age`
#>    - within levels of `married` and `race`
#>  - 100 simulated values
#>  - 6 quantities estimated:                                   
#>  E[dY/d(age)|0,black]  -0.007950175
#>  E[dY/d(age)|0,hispan] -0.005599656
#>  E[dY/d(age)|0,white]  -0.006626402
#>  E[dY/d(age)|1,black]  -0.008058486
#>  E[dY/d(age)|1,hispan] -0.005497813
#>  E[dY/d(age)|1,white]  -0.006303652
summary(est, null = 0)
#>                       Estimate    2.5 %   97.5 % P-value    
#> E[dY/d(age)|0,black]  -0.00795 -0.01182 -0.00523  <2e-16 ***
#> E[dY/d(age)|0,hispan] -0.00560 -0.01022 -0.00272  <2e-16 ***
#> E[dY/d(age)|0,white]  -0.00663 -0.00965 -0.00391  <2e-16 ***
#> E[dY/d(age)|1,black]  -0.00806 -0.01210 -0.00495  <2e-16 ***
#> E[dY/d(age)|1,hispan] -0.00550 -0.00944 -0.00282  <2e-16 ***
#> E[dY/d(age)|1,white]  -0.00630 -0.00944 -0.00370  <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

# Comparing AMEs between married and unmarried for
# each level of `race`
est_diff <- est[4:6] - est[1:3]
names(est_diff) <- paste0("AME_diff|", levels(lalonde$race))
summary(est_diff)
#>                  Estimate     2.5 %    97.5 %
#> AME_diff|black  -0.000108 -0.001314  0.001106
#> AME_diff|hispan  0.000102 -0.001415  0.001477
#> AME_diff|white   0.000323 -0.001428  0.001627

# Average adjusted predictions at a combination of `treat`
# and `married`
est <- sim_ame(s, var = c("treat", "married"),
               verbose = FALSE)
est
#> A `clarify_est` object (from `sim_ame()`)
#>  - Average adjusted predictions for `treat` and `married`
#>  - 100 simulated values
#>  - 4 quantities estimated:                    
#>  E[Y(0,0)] 0.7374364
#>  E[Y(1,0)] 0.8054577
#>  E[Y(0,1)] 0.7517871
#>  E[Y(1,1)] 0.8171229

# Average marginal effect of `age` setting `married` to 1
est <- sim_ame(s, var = list("age", married = 1),
               verbose = FALSE)