rrtest {RRI}

Generic residual randomization test

Description

This function tests the specified linear hypothesis in model assuming the errors are distributionally invariant with respect to stochastic function g_invar.

Usage

rrtest(model, g_invar, num_R = 999, alpha = 0.05, val_type = "decision")

Arguments

model

Regression model and hypothesis. See example_model for details.

g_invar

Stochastic function that transforms residuals. Accepts n-vector and returns n-vector.

num_R

Number of test statistic values to calculate in the randomization test.

alpha

Nominal test level (between 0 to 1).

val_type

The type of return value.

Details

For the regression y = X * beta + e, this function is testing the following linear null hypothesis:

H0: lam' beta = lam[1] * beta[1] + ... + lam[p] * beta[p] = lam0,

where y, X, lam, lam0 are specified in model. The assumption is that the errors, e, have some form of cluster invariance. Specifically:

(e_1, e_2, ..., e_n) ~ g_invar(e_1, e_2, ..., e_n),

where ~ denotes equality in distribution, and g_invar is the supplied invariance function.

Value

If val_type = "decision" (default) we get the test binary decision (1=REJECT H0).

If val_type = "pval" we get the test p-value.

If val_type = "full" we get the full test output, i.e., a List with elements tobs, tvals, the observed and randomization values of the test statistic, respectively.

Note

There is no guarantee that an arbitrary g_invar will produce valid tests. The rrtest_clust function has such guarantees under mild assumptions.

See Also

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

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

Examples

model = example_model(n = 100)  # test H0: beta2 = 0 (here, H0 is true)
g_invar = function(e) sample(e)   # Assume errors are exchangeable.
rrtest(model, g_invar) # same as rrtest_clust(model, "perm")