corrcheck: Checking correlations for feasibility

In GenOrd: Simulation of Discrete Random Variables with Given Correlation Matrix and Marginal Distributions

Description

The function returns the lower and upper bounds of the correlation coefficients of each pair of discrete variables given their marginal distributions, i.e., returns the range of feasible bivariate correlations.

Usage

corrcheck(marginal, support = list(), Spearman = FALSE)

Arguments

marginal	a list of k elements, where k is the number of variables. The i-th element of marginal is the vector of the cumulative probabilities defining the marginal distribution of the i-th component of the multivariate variable. If the i-th component can take k_i values, the i-th element of marginal will contain k_i-1 probabilities (the k_i-th is obviously 1 and shall not be included).
support	a list of k elements, where k is the number of variables. The i-th element of support is the vector containing the ordered values of the support of the i-th variable. By default, the support of the i-th variable is 1,2,...,k_i
Spearman	TRUE if we consider Spearman's correlation, FALSE (default) if we consider Pearson's correlation

Value

The functions returns a list of two matrices: the former contains the lower bounds, the latter the upper bounds of the feasible pairwise correlations (on the extra-diagonal elements)

Author(s)

Alessandro Barbiero, Pier Alda Ferrari

See Also

contord, ordcont, ordsample

Examples

# four variables
k <- 4
# with 2, 3, 4, and 5 categories (Likert scales, by default)
kj <- c(2,3,4,5)
# and these marginal distributions (set of cumulative probabilities)
marginal <- list(0.4, c(0.6,0.9), c(0.1,0.2,0.4), c(0.6,0.7,0.8,0.9))
corrcheck(marginal) # lower and upper bounds for Pearson's rho
corrcheck(marginal, Spearman=TRUE) # lower and upper bounds for Spearman's rho
# change the supports
support <- list(c(0,1), c(1,2,4), c(1,2,3,4), c(0,1,2,5,10))
corrcheck(marginal, support=support) # updated bounds

Example output

Loading required package: mvtnorm
Loading required package: Matrix
Loading required package: MASS
[[1]]
4 x 4 Matrix of class "dsyMatrix"
           [,1]       [,2]       [,3]       [,4]
[1,]  1.0000000 -0.9128709 -0.5687111 -0.8660254
[2,] -0.9128709  1.0000000 -0.9641540 -0.5270463
[3,] -0.5687111 -0.9641540  1.0000000 -0.9850366
[4,] -0.8660254 -0.5270463 -0.9850366  1.0000000

[[2]]
4 x 4 Matrix of class "dsyMatrix"
          [,1]      [,2]      [,3]      [,4]
[1,] 1.0000000 0.6085806 0.8530667 0.5773503
[2,] 0.6085806 1.0000000 0.5191599 0.9486833
[3,] 0.8530667 0.5191599 1.0000000 0.4925183
[4,] 0.5773503 0.9486833 0.4925183 1.0000000

[[1]]
4 x 4 Matrix of class "dsyMatrix"
           [,1]       [,2]       [,3]       [,4]
[1,]  1.0000000 -0.9759001 -0.6429904 -0.9607689
[2,] -0.9759001  1.0000000 -0.9883037 -0.6250763
[3,] -0.6429904 -0.9883037  1.0000000 -0.9961464
[4,] -0.9607689 -0.6250763 -0.9961464  1.0000000

[[2]]
4 x 4 Matrix of class "dsyMatrix"
          [,1]      [,2]      [,3]      [,4]
[1,] 1.0000000 0.6506000 0.9644856 0.6405126
[2,] 0.6506000 1.0000000 0.6274944 0.9844952
[3,] 0.9644856 0.6274944 1.0000000 0.6177652
[4,] 0.6405126 0.9844952 0.6177652 1.0000000

[[1]]
4 x 4 Matrix of class "dsyMatrix"
           [,1]       [,2]       [,3]       [,4]
[1,]  1.0000000 -0.8017837 -0.5687111 -0.7056563
[2,] -0.8017837  1.0000000 -0.9553936 -0.3771892
[3,] -0.5687111 -0.9553936  1.0000000 -0.9682511
[4,] -0.7056563 -0.3771892 -0.9682511  1.0000000

[[2]]
4 x 4 Matrix of class "dsyMatrix"
          [,1]      [,2]      [,3]      [,4]
[1,] 1.0000000 0.5345225 0.8530667 0.4704375
[2,] 0.5345225 1.0000000 0.4559833 0.9499579
[3,] 0.8530667 0.4559833 1.0000000 0.4013146
[4,] 0.4704375 0.9499579 0.4013146 1.0000000

GenOrd documentation built on May 2, 2019, 8:16 a.m.