This function is designed to help calculate marginal effects including average marginal effects (AMEs) from brms models. Arguments are labeled as required when it is required that the user directly specify the argument. Arguments are labeled as optional when either the argument is optional or there are sensible default values so that users do not typically need to specify the argument.

## Usage

brmsmargins(
object,
at = NULL,
wat = NULL,
newdata = model.frame(object),
CI = 0.99,
CIType = "HDI",
contrasts = NULL,
ROPE = NULL,
MID = NULL,
subset = NULL,
dpar = NULL,
seed,
verbose = FALSE,
...
)

## Arguments

object

A required argument specifying a fitted brms model object.

at

An optional argument (but note, either at or add are required) specifying an object inheriting from data frame indicating the values to hold specific variables at when calculating average predictions. This is intended for AMEs from categorical variables.

wat

An optional list with named elements including one element named, “ID” with a single character string, the name of the variable in the model frame that is the ID variable. Additionally, there should be one or more named elements, named after variables in the model (and specified in the at argument), that contain a data.table or data.frame with three variables: (1) the ID variable giving IDs, (2) the values specified for the variable in the at argument, and (3) the actual values to be substituted for each ID. wat cannot be non null unless at also is non null.

An optional argument (but note, either at or add are required) specifying an object inheriting from data frame indicating the values to add to specific variables at when calculating average predictions. This is intended for AMEs for continuous variables.

newdata

An optional argument specifying an object inheriting from data frame indicating the baseline values to use for predictions and AMEs. It uses a sensible default: the model frame from the brms model object passed on the object argument.

CI

An optional argument with a numeric value specifying the width of the credible interval. Defaults to 0.99. This default is arbitrary, but is purposefully higher than the common 0.95 to encourage science with greater acknowledgment of uncertainty or larger sample sizes (ideally).

CIType

An optional argument, a character string specifying the type of credible interval (e.g., highest density interval). It is passed down to bsummary which in turn passes it to ci. Defaults to “HDI”.

contrasts

An optional argument specifying a contrast matrix. The posterior predictions matrix is post multiplied by the contrast matrix, so they must be conformable. The posterior predictions matrix has a separate column for each row in the at or add object, so the contrast matrix should have the same number of rows. It can have multiple columns, if you desire multiple specific contrasts.

ROPE

An optional argument, that can either be left as NULL, the default, or a numeric vector of length 2, specifying the lower and upper thresholds for the Region of Practical Equivalence (ROPE).

MID

An optional argument, that can either left as NULL, the default, or a numeric vector of length 2, specifying the lower and upper thresholds for a Minimally Important Difference (MID). Unlike the ROPE, percentages for the MID are calculated as at or exceeding the bounds specified by this argument, whereas the ROPE is the percentage of the posterior at or inside the bounds specified.

subset

An optional argument, a character string that is a valid R expression used to subset the dataset passed in newdata, prior to analysis. Defaults to NULL.

dpar

An optional argument giving the parameter passed on to the dpar argument of fitted() in brms. Defaults to NULL, indicating the mean or location parameter typically.

seed

An optional argument that controls whether (and if so what) random seed to use. This does not matter when using fixed effects only. However, when using Monte Carlo integration to integrate out random effects from mixed effects models, it is critical if you are looking at a continuous marginal effect with some small offset value as otherwise the Monte Carlo error from one set of predictions to another may exceed the true predicted difference. If seed is left missing, the default, than a single, random integer between +\- 1e7 is chosen and used to set the seed before each prediction. If manually chosen (recommended for reproducibility), the seed should either be a single value, in which case this single value is used to set the seed before each prediction. Alternately, it can be a vector of seeds with either the same length as the number of rows in at or add, whichever was specified. This is probably generally not what you want, as it means that even for the same input data, you would get slightly different predictions (when integrating out random effects) due to Monte Carlo variation. Finally, rather than being missing, you can explicitly set seed = NULL, if you do not want any seed to be set. This would be fine, for instance, when only using fixed effects, or if you know what you are doing and intend that behavior when integrating out random effects.

verbose

An optional argument, a logical value whether to print more verbose messages. Defaults to FALSE which is quieter. Set to TRUE for more messages to be printed where relevant.

...

An optional argument, additional arguments passed on to prediction. In particular, the effects argument of prediction() is important for mixed effects models to control how random effects are treated in the predictions, which subsequently changes the marginal effect estimates.

## Value

A list with four elements.

• PosteriorPosterior distribution of all predictions. These predictions default to fixed effects only, but by specifying options to prediction() they can include random effects or be predictions integrating out random effects.

• SummaryA summary of the predictions.

• ContrastsPosterior distribution of all contrasts, if a contrast matrix was specified.

• ContrastSummaryA summary of the posterior distribution of all contrasts, if specified

## Details

The main parts required for the function are a fitted model object, (via the object argument) a dataset to be used for prediction, (via the newdata argument which defaults to the model frame), and a dataset passed to either at or add. The steps are as follows:

1. Check that the function inputs (model object, data, etc.) are valid.

2. Take the dataset from the newdata argument and either add the values from the first row of add or replace the values using the first row of at. Only variables specified in at or add are modified. Other variables are left as is.

3. Use the fitted() function to generate predictions based on this modified dataset. If effects is set to “fixedonly” (meaning only generate predictions using fixed effects) or to “includeRE” (meaning generate predictions using fixed and random effects), then predictions are generated entirely using the fitted() function and are, typically back transformed to the response scale. For mixed effects models with fixed and random effects where effects is set to “integrateoutRE”, then fitted() is only used to generate predictions using the fixed effects on the linear scale. For each prediction generated, the random effects are integrated out by drawing k random samples from the model assumed random effect(s) distribution. These are added to the fixed effects predictions, back transformed, and then averaged over all k random samples to perform numerical Monte Carlo integration.

4. All the predictions for each posterior draw, after any back transformation has been applied, are averaged, resulting in one, marginal value for each posterior draw. These are marginal predictions. They are average marginal predictions if averaging over the sample dataset, or may be marginal predictions at the means, if the initial input dataset used mean values, etc.

5. Steps two to four are repeated for each row of at or add. Results are combined into a matrix where the columns are different rows from at or add and the rows are different posterior draws.

6. If contrasts were specified, using a contrast matrix, the marginal prediction matrix is post multiplied by the contrast matrix. Depending on the choice(s) of add or at and the values in the contrast matrix, these can then be average marginal effects (AMEs) by using numerical integration (add with 0 and a very close to 0 value) or discrete difference (at with say 0 and 1 as values) for a given predictor(s).

7. The marginal predictions and the contrasts, if specified are summarized.

Although brmsmargins() is focused on helping to calculate marginal effects, it can also be used to generate marginal predictions, and indeed these marginal predictions are the foundation of any marginal effect estimates. Through manipulating the input data, at or add and the contrast matrix, other types of estimates averaged or weighting results in specific ways are also possible.

## References

Pavlou, M., Ambler, G., Seaman, S., & Omar, R. Z. (2015) doi:10.1186/s12874-015-0046-6 “A note on obtaining correct marginal predictions from a random intercepts model for binary outcomes” and Skrondal, A., & Rabe-Hesketh, S. (2009) doi:10.1111/j.1467-985X.2009.00587.x “Prediction in multilevel generalized linear models” and Norton EC, Dowd BE, Maciejewski ML. (2019) doi:10.1001/jama.2019.1954 “Marginal Effects—Quantifying the Effect of Changes in Risk Factors in Logistic Regression Models”

## Examples

if (FALSE) {
#### Testing ####
## sample data and logistic model with brms
set.seed(1234)
Tx <- rep(0:1, each = 50)
ybin <- c(rep(0:1, c(40,10)), rep(0:1, c(10,40)))
logitd <- data.frame(Tx = Tx, ybin = ybin)
logitd$x <- rnorm(100, mean = logitd$ybin, sd = 2)

mbin <- brms::brm(ybin ~ Tx + x, data = logitd, family = brms::bernoulli())

summary(mbin)

## now check AME for Tx
tmp <- brmsmargins(
object = mbin,
at = data.table::data.table(Tx = 0:1),
contrasts = matrix(c(-1, 1), nrow = 2),
ROPE = c(-.05, +.05),
MID = c(-.10, +.10))

tmp$Summary tmp$ContrastSummary ## Tx AME

## now check AME for Tx with bootstrapping the AME population
tmpalt <- brmsmargins(
object = mbin,
at = data.table::data.table(Tx = 0:1),
contrasts = matrix(c(-1, 1), nrow = 2),
ROPE = c(-.05, +.05),
MID = c(-.10, +.10),
resample = 100L)

tmpalt$Summary tmpalt$ContrastSummary ## Tx AME

## now check AME for continuous predictor, x
## use .01 as an approximation for first derivative
## 1 / .01 in the contrast matrix to get back to a one unit change metric
tmp2 <- brmsmargins(
object = mbin,
add = data.table::data.table(x = c(0, .01)),
contrasts = matrix(c(-1/.01, 1/.01), nrow = 2),
ROPE = c(-.05, +.05),
MID = c(-.10, +.10))

tmp2$ContrastSummary ## x AME if (FALSE) { library(lme4) data(sleepstudy) fit <- brms::brm(Reaction ~ 1 + Days + (1 + Days | Subject), data = sleepstudy, cores = 4) summary(fit, prob = 0.99) tmp <- brmsmargins( object = fit, at = data.table::data.table(Days = 0:1), contrasts = matrix(c(-1, 1), nrow = 2), ROPE = c(-.05, +.05), MID = c(-.10, +.10), CIType = "ETI", effects = "integrateoutRE", k = 5L) tmp$Summary
tmp\$ContrastSummary
}
}