rrtest: Generic residual randomization test
In RRI: Residual Randomization Inference for Regression Models

Description Usage Arguments Details Value Note See Also Examples

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

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

`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.

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.

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.

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

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

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

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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")