semi.phd {hierSDR}

Semiparametric PHD SDR fitting function

Description

fits semiparametric SDR models (PHD approach)

Usage

semi.phd(
  x,
  y,
  d = 5L,
  maxit = 100L,
  h = NULL,
  opt.method = c("lbfgs.x", "bfgs", "lbfgs2", "bfgs.x", "lbfgs", "spg", "ucminf", "CG",
    "nlm", "nlminb", "newuoa"),
  nn = 0.95,
  init.method = c("random", "phd"),
  optimize.nn = FALSE,
  verbose = TRUE,
  n.samples = 100,
  degree = 2,
  vic = TRUE,
  ...
)

Arguments

x

an n x p matrix of covariates, where each row is an observation and each column is a predictor

y

vector of responses of length n

d

an integer representing the structural dimension

maxit

maximum number of iterations

h

bandwidth parameter. By default, a reasonable choice is selected automatically

opt.method

optimization method to use. Available choices are c("lbfgs2", "lbfgs.x", "bfgs.x", "bfgs", "lbfgs", "spg", "ucminf", "CG", "nlm", "nlminb", "newuoa")

nn

nearest neighbor parameter for locfit.raw

init.method

method for parameter initialization. Either "random" for random initialization or "phd" for a principle Hessian directions initialization approach

optimize.nn

should nn be optimized? Not recommended

verbose

should results be printed along the way?

n.samples

number of samples for the random initialization method

degree

degree of kernel to use

vic

logical value of whether or not to compute the VIC criterion for dimension determination

...

extra arguments passed to locfit.raw

Value

A list with the following elements

• beta estimated sufficient dimension reduction matrix

• beta.init initial sufficient dimension reduction matrix – do not use, just for the sake of comparisons

• cov variance covariance matric for the covariates

• sqrt.inv.cov inverse square root of the variance covariance matrix for the covariates. Used for scaling

• solver.obj object returned by the solver/optimization function

• vic the penalized VIC value. This is used for dimension selection, with dimension chosen to minimize this penalized vic value that trades off model complexity and model fit