fit.csim: A Constrained single index model (workhorse function)
In syhyunpark/csim: Constrained single index models (CSIM)

Description Usage Arguments Details Value Author(s) See Also

fit.csim is the workhorse function for fitting CSIM. CSIM uses pre-treatment covariates X for modeling the treatment-specific scalar-valued treatment outcomes y. The single index variable is defined to be a linear combinations of X. The differnetial treatment effect is estimated by treatment-specific nonparametrically-defined link functions on the single index variable. For simultaneous covariate selection for the treatment effect modifiers, fit.csim returns a matrix of sparse single index coefficient vectors obtained via a L1 regularization.

fit.csim(y, Tr, X, ortho.constr = TRUE, sparse = TRUE, type = "BIC",
  lam.by = 0.03, n.lam = 100, n.max = 10, eps = 10^-4,
  it.max = 50, trace = F, nbasis.t = NULL, rho.grid = c(0, 0.25,
  0.5), eff.aug = FALSE, X.aug = NULL, linear.link = FALSE,
  coef.ini = NULL, i.fx = NULL, mc.ini = FALSE, unit.norm = 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
`X`	pre-treatment covarate matrix, n-by-p matrix
`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`.
`sparse`	if `TRUE`, apply L1 regularization when estimating the single index coefficients; the default is `TRUE`.
`type`	when `sparse=TRUE`, can choose bewteen `"CV"` and `"BIC"`, for the sparsity tuninig parameter selection.
`lam.by`	a value specifying the grid of the sparsity tuning parameters [1, 1+lam.by, ... 1 + n.lam*lam.by].
`n.lam`	a value specifying the grid of the sparsity tuning parameters [1, 1+lam.by, ... 1 + n.lam*lam.by].
`n.max`	a maximum number of nonzero (active) coeffients in CSIM.
`eps`	a value specifying the converge criterion of algorithm.
`it.max`	an integer value specifying the maximum number of iterations for each coordinate.
`trace`	if `TRUE`, show the trace of the fitting procedure; the default is `FALSE`.
`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.
`eff.aug`	if `TRUE`, perform efficiency augmentation (using a L1 regularized linear regression for the main effects of X); the default is `FALSE`.
`X.aug`	a design matrix to be used for efficinecy augmentation; the default is `NULL`.
`linear.link`	if `TRUE`, restrict the link functions to be linear functions; the default is `FALSE`.
`coef.ini`	an initial solution for alpha.coef.
`i.fx`	a value of the index to be fixed throughout the estimation for model identifiability; the default is `NULL`, hence it is estimated.
`mc.ini`	if `TRUE`, use an estimate obtained from the modified covariate method as an initial solution; this is only applicable for K=2 case; the default is `FALSE`.
`unit.norm`	if `TRUE`, set the estimated coefficient vector to have a unit norm for model identifiability; the default is to set the component with the largest magnitude to be 1.

The sequence of the model coefficients implied by the tuning paramters lam is fit by block coordinate descent algorithm.

a list of information of the fitted models including

`coef`	a matrix of the estimated single index coefficients, in which each row corresponds to the coefficients given each value of the tuning parameters `lam`.
`coef.pst`	a matrix of the re-fitted single index coefficients, in which each row corresponds to each value of the tuning parameters `lam`; the single index coefficients is re-fitted without regularization given a set of selected covariates implied by the nonzero components of `coef`, and store in `coef.pst`.
`eta.coef`	the estimated main effect coefficients if `eff.aug=TRUE`.
`intercept.y`	a list of the treatment-specific intercepts of the model
`center.X`	a vector whose elements are the means of the pretreatment covariates.
`scale.X`	a vector whose elements are the standard deviations of the pretreatment covariates.