Checking correlations for feasibility
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.
corrcheck(marginal, support = list(), Spearman = FALSE)
a list of $k$ elements, where $k$ is the number of variables.
The $i$-th element of
marginalis 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
marginalwill contain $k_i-1$ probabilities (the $k_i$-th is obviously 1 and shall not be included).
a list of $k$ elements, where $k$ is the number of variables. The $i$-th element of
supportis the vector containing the ordered values of the support of the $i$-th variable. By default, the support of the $i$-th variable is $1,2,...,k_i$
TRUEif we consider Spearman's correlation,
FALSE(default) if we consider Pearson's correlation
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)
# 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
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