fit.link.fn.gcv: A wrapper function for the link function estimator
In syhyunpark/csim: Constrained single index models (CSIM)

Description Usage Arguments Value See Also

This is a wrapper function that fits the (B-spline approximated) link functions, given the current single index u = alpha'X. An optimal smoothing parameter, rho.opt, is chosen by minimizing the generalized cross validation (GCV) for prediction errors.

1 2	fit.link.fn.gcv(y, Tr, u, nbasis.t = NULL, rho.grid = c(0, 0.25, 0.5), linear.link = FALSE, ortho.constr = TRUE, ini = FALSE)

`y`	treatment outcomes, n-by-1 vector.
`Tr`	treatment indicators, n-by-1 vector; each element represents one of the K available treatment options.
`u`	a vector of the current singe index variable, u = alpha'X.
`nbasis.t`	a length K+1 vector; each element specifies the number of B-spline basis funtions for approximating the treatment-specific link function; the last element is for the "main effect" link function; the default is `nbasis.t=NULL`, and will be determined depending on the sample size.
`rho.grid`	a grid vector of (ridge-type) smoothing parameters for approximating the link functions.
`linear.link`	if `TRUE`, restrict the link functions to be linear funtions; the default is `FALSE`.
`ortho.constr`	the constraint that separates the interaction effects from the main effect (without this, the interaction effect can be confounded by the main effect); the default is `TRUE`.
`ini`	if `TRUE`, calculate the MSE using the interaction-effect component only.

`beta.t.coef`	a vector of the estimated treatment-specific B-spline coefficients vectors.
`beta.0.coef`	a vector of the estimated B-spline coefficients fitted regardless of the treatment indicators.
`smoother`	the `smoother` object obtained from `smoother.fn` used in fitting the link functions.
`resid`	a vector of the residuals from the current fitted constrained single index model.
`working.resid`	a vector of the residuals from the current fitted constrained single index model, which accounts for the fitted main effects implied by `beta.0.coef`.
`Q`	the criterion value (a MSE estimate) of the current fitted constrained single index model.
`rho.opt`	the optimized smoothing parameter used in fitting the link functions.