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.

If you are not intested in CCA, but would like to estimate rank-based correlations with latent Gaussian copula models, we recommend to use a new stand-alone package latentcor available here that incorpotaes all continuous/binary/ternary/zero-inflated(truncated) cases.

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)