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boottest.lm is a S3 method that allows for fast wild cluster bootstrap inference for objects of class lm by implementing fast wild bootstrap algorithms as developed in Roodman et al., 2019 and MacKinnon, Nielsen & Webb (2022).


# S3 method for lm
  clustid = NULL,
  bootcluster = "max",
  conf_int = TRUE,
  R = NULL,
  r = 0,
  beta0 = NULL,
  sign_level = 0.05,
  type = "rademacher",
  impose_null = TRUE,
  bootstrap_type = "fnw11",
  p_val_type = "two-tailed",
  tol = 1e-06,
  maxiter = 10,
  sampling = "dqrng",
  nthreads = getBoottest_nthreads(),
  ssc = boot_ssc(adj = TRUE, fixef.K = "none", cluster.adj = TRUE, cluster.df =
  engine = getBoottest_engine(),
  floattype = "Float64",
  maxmatsize = FALSE,
  bootstrapc = FALSE,
  getauxweights = FALSE,



An object of class lm


A character vector or rhs formula. The name of the regression coefficient(s) for which the hypothesis is to be tested


Integer. The number of bootstrap iterations. When the number of clusters is low, increasing B adds little additional runtime.


A character vector or rhs formula containing the names of the cluster variables. If NULL, a heteroskedasticity-robust (HC1) wild bootstrap is run.


A character vector or rhs formula of length 1. Specifies the bootstrap clustering variable or variables. If more than one variable is specified, then bootstrapping is clustered by the intersections of clustering implied by the listed variables. To mimic the behavior of stata's boottest command, the default is to cluster by the intersection of all the variables specified via the clustid argument, even though that is not necessarily recommended (see the paper by Roodman et al cited below, section 4.2). Other options include "min", where bootstrapping is clustered by the cluster variable with the fewest clusters. Further, the subcluster bootstrap (MacKinnon & Webb, 2018) is supported - see the vignette("fwildclusterboot", package = "fwildclusterboot") for details.


A logical vector. If TRUE, boottest computes confidence intervals by test inversion. If FALSE, only the p-value is returned.


Hypothesis Vector giving linear combinations of coefficients. Must be either NULL or a vector of the same length as param. If NULL, a vector of ones of length param.


A numeric. Shifts the null hypothesis H0: param = r vs H1: param != r


Deprecated function argument. Replaced by function argument 'r'.


A numeric between 0 and 1 which sets the significance level of the inference procedure. E.g. sign_level = 0.05 returns 0.95% confidence intervals. By default, sign_level = 0.05.


character or function. The character string specifies the type of boostrap to use: One of "rademacher", "mammen", "norm" and "webb". Alternatively, type can be a function(n) for drawing wild bootstrap factors. "rademacher" by default. For the Rademacher distribution, if the number of replications B exceeds the number of possible draw ombinations, 2^(#number of clusters), then boottest() will use each possible combination once (enumeration).


Logical. Controls if the null hypothesis is imposed on the bootstrap dgp or not. Null imposed (WCR) by default. If FALSE, the null is not imposed (WCU)


Determines which wild cluster bootstrap type should be run. Options are "fnw11","11", "13", "31" and "33" for the wild cluster bootstrap and "11" and "31" for the heteroskedastic bootstrap. For more information, see the details section. "fnw11" is the default for the cluster bootstrap, which runs a "11" type wild cluster bootstrap via the algorithm outlined in "fast and wild" (Roodman et al (2019)). "11" is the default for the heteroskedastic bootstrap.


Character vector of length 1. Type of p-value. By default "two-tailed". Other options include "equal-tailed", ">" and "<".


Numeric vector of length 1. The desired accuracy (convergence tolerance) used in the root finding procedure to find the confidence interval. 1e-6 by default.


Integer. Maximum number of iterations used in the root finding procedure to find the confidence interval. 10 by default.


'dqrng' or 'standard'. If 'dqrng', the 'dqrng' package is used for random number generation (when available). If 'standard', functions from the 'stats' package are used when available. This argument is mostly a convenience to control random number generation in a wrapper package around fwildclusterboot, wildrwolf. I recommend to use the fast' option.


The number of threads. Can be: a) an integer lower than, or equal to, the maximum number of threads; b) 0: meaning all available threads will be used; c) a number strictly between 0 and 1 which represents the fraction of all threads to use. The default is to use 1 core.


An object of class boot_ssc.type obtained with the function boot_ssc(). Represents how the small sample adjustments are computed. The defaults are adj = TRUE, fixef.K = "none", cluster.adj = "TRUE", cluster.df = "conventional". You can find more details in the help file for boot_ssc(). The function is purposefully designed to mimic fixest's fixest::ssc() function.


Character scalar. Either "R", "R-lean" or "WildBootTests.jl". Controls if boottest() should run via its native R implementation or WildBootTests.jl. "R" is the default and implements the cluster bootstrap as in Roodman (2019). "WildBootTests.jl" executes the wild cluster bootstrap via the WildBootTests.jl package. For it to run, Julia and WildBootTests.jl need to be installed. The "R-lean" algorithm is a memory friendly, but less performant rcpp-armadillo based implementation of the wild cluster bootstrap. Note that if no cluster is provided, boottest() always defaults to the "lean" algorithm. You can set the employed algorithm globally by using the setBoottest_engine() function.


Float64 by default. Other option: Float32. Should floating point numbers in Julia be represented as 32 or 64 bit? Only relevant when 'engine= "WildBootTests.jl"'


NULL by default = no limit. Else numeric scalar to set the maximum size of auxilliary weight matrix (v), in gigabytes. Only relevant when 'engine= "WildBootTests.jl"'


Logical scalar, FALSE by default. TRUE to request bootstrap-c instead of bootstrap-t. Only relevant when 'engine = "WildBootTests.jl"'


Logical. Whether to save auxilliary weight matrix (v)


Further arguments passed to or from other methods.


An object of class boottest


The bootstrap p-value.


The bootstrap confidence interval.


The tested parameter.


Sample size. Might differ from the regression sample size if the cluster variables contain NA values.


Number of Bootstrap Iterations.


Names of the cluster Variables.


Dimension of the cluster variables as used in boottest.


Significance level used in boottest.


Distribution of the bootstrap weights.


Whether the null was imposed on the bootstrap dgp or not.


The vector "R" in the null hypothesis of interest Rbeta = r.


The scalar "r" in the null hypothesis of interest Rbeta = r.


R'beta. A scalar: the constraints vector times the regression coefficients.


All t-statistics calculated while calculating the confidence interval.


All p-values calculated while calculating the confidence interval.


The 'original' regression test statistics.


All bootstrap t-statistics.


The regression object used in boottest.


Function call of boottest.


The employed bootstrap algorithm.


The number of threads employed.

Setting Seeds

To guarantee reproducibility, you need to set a global random seed via

  • set.seed() when using

    1. the lean algorithm (via engine = "R-lean") including the heteroskedastic wild bootstrap

    2. the wild cluster bootstrap via engine = "R" with Mammen weights or

    3. engine = "WildBootTests.jl"

  • dqrng::dqset.seed() when using engine = "R" for Rademacher, Webb or Normal weights

Via the engine function argument, it is possible to specify different variants of the wild cluster bootstrap, and if the algorithm should be run via R or WildBootTests.jl.

Confidence Intervals

boottest computes confidence intervals by inverting p-values. In practice, the following procedure is used:

  • Based on an initial guess for starting values, calculate p-values for 26 equal spaced points between the starting values.

  • Out of the 26 calculated p-values, find the two pairs of values x for which the corresponding p-values px cross the significance level sign_level.

  • Feed the two pairs of x into an numerical root finding procedure and solve for the root. boottest currently relies on stats::uniroot and sets an absolute tolerance of 1e-06 and stops the procedure after 10 iterations.

Standard Errors

boottest does not calculate standard errors.

Run boottest quietly

You can suppress all warning and error messages by setting the following global options: options(rlib_warning_verbosity = "quiet") options(rlib_message_verbosity = "quiet") Not that this will turn off all warnings (messages) produced via rlang::warn() and rlang::inform(), which might not be desirable if you use other software build on rlang, as e.g. the tidyverse.

Stata, Julia and Python Implementations

The fast wild cluster bootstrap algorithms are further implemented in the following software packages:


Roodman et al., 2019, "Fast and wild: Bootstrap inference in STATA using boottest", The STATA Journal. (

MacKinnon, James G., Morten Ørregaard Nielsen, and Matthew D. Webb. Fast and reliable jackknife and bootstrap methods for cluster-robust inference. No. 1485. 2022.

Cameron, A. Colin, Jonah B. Gelbach, and Douglas L. Miller. "Bootstrap-based improvements for inference with clustered errors." The Review of Economics and Statistics 90.3 (2008): 414-427.

Cameron, A.Colin & Douglas L. Miller. "A practitioner's guide to cluster-robust inference" Journal of Human Resources (2015) doi:10.3368/jhr.50.2.317

Davidson & MacKinnon. "Wild Bootstrap Tests for IV regression" Journal of Economics and Business Statistics (2010) doi:10.1198/jbes.2009.07221

MacKinnon, James G., and Matthew D. Webb. "The wild bootstrap for few (treated) clusters." The Econometrics Journal 21.2 (2018): 114-135.

MacKinnon, James G., and Matthew D. Webb. "Cluster-robust inference: A guide to empirical practice" Journal of Econometrics (2022) doi:10.1016/j.jeconom.2022.04.001

MacKinnon, James. "Wild cluster bootstrap confidence intervals." L'Actualite economique 91.1-2 (2015): 11-33.

Webb, Matthew D. Reworking wild bootstrap based inference for clustered errors. No. 1315. Queen's Economics Department Working Paper, 2013.


if (FALSE) {
lm_fit <- lm(proposition_vote ~ treatment + ideology1 + log_income +
data = voters
boot1 <- boottest(lm_fit,
  B = 9999,
  param = "treatment",
  clustid = "group_id1"
boot2 <- boottest(lm_fit,
  B = 9999,
  param = "treatment",
  clustid = c("group_id1", "group_id2")
boot3 <- boottest(lm_fit,
  B = 9999,
  param = "treatment",
  clustid = c("group_id1", "group_id2"),
  sign_level = 0.2,
  r = 2
# test treatment + ideology1 = 2
boot4 <- boottest(lm_fit,
  B = 9999,
  clustid = c("group_id1", "group_id2"),
  param = c("treatment", "ideology1"),
  R = c(1, 1),
  r = 2

# run different bootstrap types following MacKinnon, Nielsen & Webb (2022):

# default: the fnw algorithm
boot_fnw11 <- boottest(lm_fit,
  B = 9999,
  param = "treatment",
  clustid = "group_id1",
  bootstrap_type = "fnw11"

# WCR 31
boot_WCR31 <- boottest(lm_fit,
  B = 9999,
  param = "treatment",
  clustid = "group_id1",
  bootstrap_type = "31"

# WCU33
boot_WCR31 <- boottest(lm_fit,
  B = 9999,
  param = "treatment",
  clustid = "group_id1",
  bootstrap_type = "33",
  impose_null = FALSE