Scale on which to specify the equivalence margin. Default
"plm" corresponds to the partially linear model parameter
described in the details. "cov" corresponds to the conditional
covariance and "cor" to conditional correlation which lies in
\([-1, 1]\).
...
Further arguments passed to gcm
Details
The partially linear model postulates $$Y = X \theta + g(Z) + \epsilon,$$
and the target of inference is theta. The target is closely related to
the conditional covariance between Y and X given Z:
$$\theta = E[cov(X, Y | Z)] / E[Var(X | Z)].$$ The equivalence test (based
on the GCM test) tests \(H_0: \theta \not\in [{\tt from}, {\tt to}]\) versus
\(H_1: \theta \in [{\tt from}, {\tt to}]\). Y, X (and theta) can only be
one-dimensional. There are no restrictions on Z. The equivalence test can
also be performed on the conditional covariance scale directly (using
scale = "cov") or on the conditional correlation scale:
$$E[cov(X, Y | Z)] / \sqrt{E[Var(X | Z)]E[Var(Y | Z)]}$$,
using scale = "cor".