find_w12bic: Internal mixedCCA function finding w1 and w2 given R1, R2 and R12

Description

Internal mixedCCA function finding w1 and w2 given R1, R2 and R12

Usage

find_w12bic(
  n,
  R1,
  R2,
  R12,
  lamseq1,
  lamseq2,
  w1init,
  w2init,
  BICtype,
  maxiter = 100,
  tol = 0.01,
  trace = FALSE,
  lassoverbose = FALSE
)

Value

find_w12bic returns a data.frame containing

w1: estimated canonical direction \(w1\).
w2: estimated canonical direction \(w2\).
w1trace: a matrix, of which column is the estimated canonical direction \(w1\) at each iteration. The number of columns is the number of iteration until the convergence.
w2trace: a matrix, of which column is the estimated canonical direction \(w2\) at each iteration. The number of columns is the number of iteration until the convergence.
lam1.iter: For each iteration, what lambda value is selected for \(w1\) is stored.
lam2.iter: For each iteration, what lambda value is selected for \(w2\) is stored.
obj: objective function value without penalty: \(w1^T * R12 * w2\). If lamseq1 and lamseq2 are scalar, then original objective function including penalty part will be used.

Arguments

n: Sample size
R1: Correlation matrix of dataset X1 (p1 by p1)
R2: Correlation matrix of dataset X2 (p2 by p2)
R12: Correlation matrix between the dataset X1 and the dataset X2 (p1 by p2)
lamseq1: A sequence of lambda values for the datasets X1. It can be a scalar (a vector of one value). should be the same length with lamseq2.
lamseq2: A sequence of lambda values for the datasets X2. It can be a scalar (a vector of one value). should be the same length with lamseq1.
w1init: An initial vector of length p1 for canonical direction \(w1\).
w2init: An initial vector of length p1 for canonical direction \(w2\).
BICtype: Either 1 or 2: For more details for two options, see the reference.
maxiter: The maximum number of iterations allowed.
tol: The desired accuracy (convergence tolerance).
trace: If trace = TRUE, progress per each iteration will be printed. The default value is FALSE.
lassoverbose: If lassoverbose = TRUE, all warnings from lassobic optimization regarding convergence will be printed. The default value is lassoverbose = FALSE.

References

Yoon G., Carroll R.J. and Gaynanova I. (2020) "Sparse semiparametric canonical correlation analysis for data of mixed types" <doi:10.1093/biomet/asaa007>.