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

Description Usage Arguments Details Value See Also

Given a vector of responses y and a smoother object obtained from smoother.fn, fit.link.fn computes the treatment-specific link functions of the constrained single index model.

1	fit.link.fn(y, smoother, ortho.constr = TRUE, ini = FALSE)

`y`	treatment outcomes, n-by-1 vector.
`smoother`	a smoother object obtained from `smoother.fn`.
`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.

This is a subfunction that fits the (B-spline approximated) link functions gt, 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.

a list of information of the fitted link functions given the current single index variable including

`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`.
`MSE`	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.