# find_w12bic: Internal mixedCCA function finding w1 and w2 given R1, R2 and... In mixedCCA: Sparse Canonical Correlation Analysis for High-Dimensional Mixed Data

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```find_w12bic( n, R1, R2, R12, lamseq1, lamseq2, w1init, w2init, BICtype, maxiter = 100, tol = 0.01, trace = FALSE, lassoverbose = FALSE ) ```

## 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`.

## 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.

## 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>.

mixedCCA documentation built on March 21, 2021, 1:07 a.m.