# Dependence Measures Calculation of pairwise monotone and supremum dependence, monotone/supremum dependence ratio, and proportion of pairwise NAs. ```r 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. ## Returns A 3-dimensional array $k\times k\times 4$ with pairwise monotone and supremum dependence, monotone/supremum dependence ratio, and proportion of pairwise NAs. ## 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. ## Author(s) Arturo Erdely [https://sites.google.com/site/arturoerdely](https://sites.google.com/site/arturoerdely) ## Note NA values are allowed. ## See Also `subcopem`, `subcopemc` ## Examples ```r 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 ```

dependence function