(EXPERIMENTAL) Bootstrap, Conformal, and Simulation-Based Inference


Warning: This function is experimental. It may be renamed, the user interface may change, or the functionality may migrate to arguments in other marginaleffects functions.

Apply this function to a marginaleffects object to change the inferential method used to compute uncertainty estimates.


  R = 1000,
  conf_type = "perc",
  conformal_test = NULL,
  conformal_calibration = NULL,
  conformal_score = "residual_abs",


x Object produced by one of the core marginaleffects functions.


  • "delta": delta method standard errors

  • "boot" package

  • "fwb": fractional weighted bootstrap

  • "rsample" package

  • "simulation" from a multivariate normal distribution (Krinsky & Robb, 1986)

  • "mi" multiple imputation for missing data

  • "conformal_split": prediction intervals using split conformal prediction (see Angelopoulos & Bates, 2022)

  • "conformal_cv+": prediction intervals using cross-validation+ conformal prediction (see Barber et al., 2020)

R Number of resamples, simulations, or cross-validation folds.

String: type of bootstrap interval to construct.

  • boot: "perc", "norm", "basic", or "bca"

  • fwb: "perc", "norm", "basic", "bc", or "bca"

  • rsample: "perc" or "bca"

  • simulation: argument ignored.

conformal_test Data frame of test data for conformal prediction.
conformal_calibration Data frame of calibration data for split conformal prediction (method=“conformal_split).

String. Warning: The type argument in predictions() must generate predictions which are on the same scale as the outcome variable. Typically, this means that type must be "response" or "probs".

  • "residual_abs" or "residual_sq" for regression tasks (numeric outcome)

  • "softmax" for classification tasks (when predictions() returns a group columns, such as multinomial or ordinal logit models.

  • If method=“boot”, additional arguments are passed to boot::boot().

  • If method=“fwb”, additional arguments are passed to fwb::fwb().

  • If method=“rsample”, additional arguments are passed to rsample::bootstraps().

  • Additional arguments are ignored for all other methods.


When method=“simulation”, we conduct simulation-based inference following the method discussed in Krinsky & Robb (1986):

  1. Draw R sets of simulated coefficients from a multivariate normal distribution with mean equal to the original model’s estimated coefficients and variance equal to the model’s variance-covariance matrix (classical, "HC3", or other).

  2. Use the R sets of coefficients to compute R sets of estimands: predictions, comparisons, slopes, or hypotheses.

  3. Take quantiles of the resulting distribution of estimands to obtain a confidence interval and the standard deviation of simulated estimates to estimate the standard error.

When method=“fwb”, drawn weights are supplied to the model fitting function’s weights argument; if the model doesn’t accept non-integer weights, this method should not be used. If weights were included in the original model fit, they are extracted by weights() and multiplied by the drawn weights. These weights are supplied to the wts argument of the estimation function (e.g., comparisons()).


A marginaleffects object with simulation or bootstrap resamples and objects attached.


Krinsky, I., and A. L. Robb. 1986. “On Approximating the Statistical Properties of Elasticities.” Review of Economics and Statistics 68 (4): 715–9.

King, Gary, Michael Tomz, and Jason Wittenberg. "Making the most of statistical analyses: Improving interpretation and presentation." American journal of political science (2000): 347-361

Dowd, Bryan E., William H. Greene, and Edward C. Norton. "Computation of standard errors." Health services research 49.2 (2014): 731-750.

Angelopoulos, Anastasios N., and Stephen Bates. 2022. "A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification." arXiv. https://doi.org/10.48550/arXiv.2107.07511.

Barber, Rina Foygel, Emmanuel J. Candes, Aaditya Ramdas, and Ryan J. Tibshirani. 2020. “Predictive Inference with the Jackknife+.” arXiv. http://arxiv.org/abs/1905.02928.



mod <- lm(Sepal.Length ~ Sepal.Width * Species, data = iris)

# bootstrap
avg_predictions(mod, by = "Species") %>%
  inferences(method = "boot")

avg_predictions(mod, by = "Species") %>%
  inferences(method = "rsample")

# Fractional (bayesian) bootstrap
avg_slopes(mod, by = "Species") %>%
  inferences(method = "fwb") %>%
  posterior_draws("rvar") %>%

# Simulation-based inference
slopes(mod) %>%
  inferences(method = "simulation") %>%