estimate_corr_bounds: Estimation of bounds of indirect correlations

In AlessandroDeCarlo27/mvlognCorrEst: Sampling from a multivariate Log-Normal distribution using Log-Normal parameters and Estimation of Indirect Correlations

Estimation of bounds of indirect correlations

Description

This function returns the ranges of indirect correlations to be estimated. estimate_corr_bounds receives in input a correlation matrix where indirect correlations to be estimated must be identified with NA values. From input correlation structure the associated graph is derived. For each indirect correlation between a generic couple of variables (X1,X2), all the possible paths in the graph that links X1 and X2 visiting one node at most once are considered.

The cost of each path is computed by multiplying the correlations met along the path and, the minimum and the maximum costs are used to identify the indirect correlation range. If there is not any path between two nodes, maximum and minimum values will be set to NA. If there is a unique path, the bound is computed considering cost +/- widen_factor*cost, where cost is the cost of the unique existing path. The default value of widen_factor is 0.2.

Usage

estimate_corr_bounds(corrMat, widen_factor = 0.2)

Arguments

corrMat	Matrix Object which represents a correlation matrix. Indirect correlations to be estimated must be indicated by NA. This matrix must be symmetric, thus it must contain at least two NA values.
widen_factor	number between 0 and 1. If there is a unique path, the range for that indirect correlation is computed considering cost +/- widen_factor*cost where cost is the cost of the unique existing path. Default value is 0.2.

Value

A matrix object with N(= number of indirect correlations) rows and 4 columns reporting:

• var1: numerical index of X1, the first variable of the couple for which the indirect correlation has to be estimated

• var2: numerical index of X2, the second variable of the couple for which the indirect correlation has to be estimated

• lower: lower bound for the range of indirect correlation between var1 and var2

• upper: upper bound for the range of indirect correlation between var1 and var2.

Author(s)

Alessandro De Carlo [e-mail]

See Also

graph_from_adjacency_matrix

all_simple_paths

Examples

# create a correlation matrix, define some correlations
c_start <- diag(rep(1,6))
c_start[1,2] <- -0.6
c_start[1,3] <- -0.75
c_start[2,3] <-0.95
c_start[2,4] <- 0.75
c_start[2,6] <- -0.6
c_start <- c_start+t(c_start)-diag(rep(1,ncol(c_start)))
#set to NA indirect correlations
c_start[c_start==0]<-NA
#plot correlation graph
plot_graph_corr(c_start,"Graph of Correlation Matrix")
#get bounds of correlations
estimate_corr_bounds(c_start)

#output: variable 5 is not directly correlated with any of the other variables so it
#is impossible to establish a path to it. Bounds of indirect correlation involving variable 5 are set to NA

#       var1 var2     lower   upper
#[1,]    1    4 -0.534375 -0.4500
#[2,]    1    5        NA      NA
#[3,]    1    6  0.360000  0.4275
#[4,]    2    5        NA      NA
#[5,]    3    4  0.337500  0.7125
#[6,]    3    5        NA      NA
#[7,]    3    6 -0.570000 -0.2700
#[8,]    4    5        NA      NA
#[9,]    4    6 -0.540000 -0.3600
#[10,]    5    6        NA      NA

AlessandroDeCarlo27/mvlognCorrEst documentation built on March 23, 2023, 10:11 a.m.