forw.cd: A coordinate descent function
In syhyunpark/csim: Constrained single index models (CSIM)

Description Usage Arguments Details Value See Also

forw.cd implements an ordinary (not a block-) coordinate descent to opitmize the single index coefficients, given an initial single index variable u = alpha'X.

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forw.cd(w.a, u, y, Tr, X.a, nbasis.t = c(6, 6, 8), rho.grid = c(0,
  0.25, 0.5), it.max = 60, eps = 10^-4, trace = F,
  linear.link = FALSE, ortho.constr = TRUE, i.fx = NULL)

`w.a`	an initial estimate of the single index coefficient vector.
`u`	a vector of the current singe index variable, u = alpha'X.
`y`	treatment outcomes, n-by-1 vector.
`Tr`	treatment indicators, n-by-1 vector; each element represents one of the K available treatment options.
`X.a`	a matrix of the pre-treatment covarates, associated with the single index coefficients.
`nbasis.t`	a length K+1 vector; each element specifies the number of B-spline basis funtions used in approximating the treatment-specific link function; the last element is for the "main effect" link function.
`rho.grid`	a grid vector of (ridge-type) smoothing parameters for approximating the link functions.
`it.max`	an integer value specifying the maximum number of iterations for each coordinate.
`eps`	a value specifying the converge criterion of algorithm.
`trace`	if `TRUE`, show the trace of the fitting procedure; the default is `FALSE`.
`linear.link`	if `TRUE`, restrict the link functions to be linear functions; 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`.
`i.fx`	a value of the index to be fixed throughout the estimation for model identifiability; the default is `NULL`, hence it is estimated.

This function can be used to fit an un-regularized constrained single index model. This function is also used in obtaining the "post-selected" (re-fitted) single index coefficients, cfs.pst; see fit.csim and block.cd; see also Radchenko (2015) for the post-selected single index coefficient estimator.

a list of information of the optimized single index coefficients including