rrinf_clust: Residual randomization inference based on cluster invariances
In RRI: Residual Randomization Inference for Regression Models

Description Usage Arguments Details Value Note See Also Examples

This function is a wrapper over rrtest_clust and gives confidence intervals for all parameters assuming a particular cluster invariance on the errors.

rrinf_clust(
  y,
  X,
  type,
  clustering = NULL,
  cover = 0.95,
  num_R = 999,
  control = list(num_se = 6, num_breaks = 60)
)

`y`	Vector of outcomes (length n)
`X`	Covariate matrix (n x p). First column should be ones to include intercept.
`type`	A string, either "perm", "sign" or "double".
`clustering`	A `List` that specifies a clustering of datapoint indexes 1, ..., n. See example_clustering for details.
`cover`	Number from [0, 1] that denotes the confidence interval coverage (e.g., 0.95 denotes 95%)
`num_R`	Number of test statistic values to calculate in the randomization test (similar to no. of bootstrap samples).
`control`	A `List` that controls the scope of the test inversion.

This function has similar funtionality as standard confint. It generates confidence intervals by testing plausible values for each parameter. The plausible values are generated as follows. For some parameter beta_i we test successively

H0: beta_i = hat_beta_i - num_se * se_i

...up to...

H0: beta_i = hat_beta_i + num_se * se_i

broken in num_breaks intervals. Here, hat_beta_i is the OLS estimate of beta_i and se_i is the standard error. We then report the minimum and maximum values in this search space which we cannot reject at level alpha. This forms the desired confidence interval.

Matrix that includes the OLS estimate, and confidence interval endpoints.

If the confidence interval appears to be a point or is empty, then this means that the nulls we consider are implausible. We can try to improve the search through control.tinv. For example, we can both increase num_se to increase the width of search, and increase num_breaks to make the search space finer.

See rrtest_clust for a description of type and clustering.

Life after bootstrap: residual randomization inference in regression models (Toulis, 2019)

https://www.ptoulis.com/residual-randomization

# Heterogeneous example
set.seed(123)
n = 200
X = cbind(rep(1, n), 1:n/n)
beta = c(-1, 0.2)
ind = c(rep(0, 0.9*n), rep(1, .1*n))  # cluster indicator
y = X %*% beta + rnorm(n, sd= (1-ind) * 0.1 + ind * 5) # heteroskedastic
confint(lm(y ~ X + 0))  # normal OLS CI is imprecise

cl = list(which(ind==0), which(ind==1))  #  define the clustering
rrinf_clust(y, X, "perm", cl)  # improved CI through clustered errors