dependence {subcopem2D}

Dependence Measures

Description

Calculation of pairwise monotone and supremum dependence, monotone/supremum dependence ratio, and proportion of pairwise NAs.

Usage

dependence(mat, cont = NULL, sc.order = 0)

Arguments

mat

k-column matrix with n observations of a k-dimensional random vector (NA values are allowed).

cont

vector of column numbers to consider/coerce as continuous random variables (optional).

sc.order

order of subcopula approximation (continuous random variables). If 0 (default) then maximum order m = n is used. Often m = 50 is a good recommended value, higher values demand more computing time.

Details

Each of the random variables in the k-dimensional random vector under consideration may be of any kind (discrete, continuous, or mixed). NA values are allowed.

Value

A 3-dimensional array k\times k\times 4 with pairwise monotone and supremum dependence, monotone/supremum dependence ratio, and proportion of pairwise NAs.

Note

NA values are allowed.

Author(s)

Arturo Erdely https://sites.google.com/site/arturoerdely

References

Erdely, A. (2017) A subcopula based dependence measure. Kybernetika 53(2), 231-243. DOI: 10.14736/kyb-2017-2-0231

Nelsen, R.B. (2006) An Introduction to Copulas. Springer, New York.

See Also

subcopem, subcopemc

Examples

V <- runif(300)  # Continuous Uniform(0,1)
W <- V*(1-V)     # Continuous transform of V
# X given V=v as continuous Uniform(0,v)
X <- mapply(runif, rep(1, length(V)), rep(0, length(V)), V)
Y <- 1*(0.2 < X)*(X < 0.6)  # Discrete transform of X
Z <- X*(0.1 < X)*(X < 0.9) + 1*(X >= 0.9)  # Mixed transform of X
V[1:10] <- NA  # Introducing some NAs
W[3:12] <- NA  # Introducing some NAs
Y[5:25] <- NA  # Introducing some NAs
vector5D <- cbind(V, W, X, Y, Z)  # Matrix of 5-variate observations
# Monotone and supremum dependence, ratio and proportion of NAs:
(deparray <- dependence(vector5D, cont = c(1, 2, 3), 30))
# Pearson's correlations:
cor(vector5D, method = "pearson", use = "pairwise.complete.obs")
# Spearman's correlations:
cor(vector5D, method = "spearman", use = "pairwise.complete.obs") 
# Kendall's correlations:
cor(vector5D, method = "kendall", use = "pairwise.complete.obs")   
pairs(vector5D)  # Matrix of pairwise scatterplots