Sparse Canonical Correlation Analysis for High-Dimensional Mixed Data

Semi-parametric approach for sparse canonical correlation analysis which can handle mixed data types: continuous, binary and truncated continuous. Bridge functions are provided to connect Kendall's tau to latent correlation under the Gaussian copula model. The methods are described in Yoon, Carroll and Gaynanova (2020) and Yoon, Mueller and Gaynanova (2021) .

mixedCCA: sparse CCA for data of mixed types

The R package mixedCCA implements sparse canonical correlation analysis for data of mixed types: continuous, binary or zero-inflated (truncated continuous). The corresponding reference is

Yoon G., Carroll R.J. and Gaynanova I. (2020). “Sparse semiparametric canonical correlation analysis for data of mixed types”. Biometrika.

The faster version of latent correlation computation part is now fully available and implemented to the R package mixedCCA. The corresponding reference is available on arXiv:

Yoon G., Müller C.L. and Gaynanova I., “Fast computation of latent correlations” JCGS.

Installation

devtools::install_github("irinagain/mixedCCA")

Example

library(mixedCCA)

### Simple example

# Data setting
n <- 100; p1 <- 15; p2 <- 10 # sample size and dimensions for two datasets.
maxcancor <- 0.9 # true canonical correlation

# Correlation structure within each data set
set.seed(0)
perm1 <- sample(1:p1, size = p1);
Sigma1 <- autocor(p1, 0.7)[perm1, perm1]
blockind <- sample(1:3, size = p2, replace = TRUE);
Sigma2 <- blockcor(blockind, 0.7)
mu <- rbinom(p1+p2, 1, 0.5)

# true variable indices for each dataset
trueidx1 <- c(rep(1, 3), rep(0, p1-3))
trueidx2 <- c(rep(1, 2), rep(0, p2-2))

# Data generation
simdata <- GenerateData(n=n, trueidx1 = trueidx1, trueidx2 = trueidx2, maxcancor = maxcancor,
                        Sigma1 = Sigma1, Sigma2 = Sigma2,
                        copula1 = "exp", copula2 = "cube",
                        muZ = mu,
                        type1 = "trunc", type2 = "trunc",
                        c1 = rep(1, p1), c2 =  rep(0, p2)
)
X1 <- simdata$X1
X2 <- simdata$X2

# Sparse semiparametric CCA with BIC1 criterion
mixedCCAresult <- mixedCCA(X1, X2, type1 = "trunc", type2 = "trunc", BICtype = 1)
mixedCCAresult$KendallR # estimated latent correlation matrix
mixedCCAresult$w1 # estimated canonical vector for X1
mixedCCAresult$w2 # estimated canonical vector for X2
mixedCCAresult$cancor # estimated canonical correlation

# Separate estimation of latent correlation matrix
estimateR(X1, type = "trunc")$R # For X1 only
estimateR_mixed(X1, X2, type1 = "trunc", type2 = "trunc")$R12 # For X = (X1, X2)