The DEMATEL total-relation classification

Normalises the direct-influence matrix X by the larger of its greatest row sum and its greatest column sum (the standard DEMATEL normalisation, which keeps the Neumann series N + N^2 + N^3 + ... convergent), then solves the total-relation matrix T = N(I - N)^-1 in closed form rather than by truncating the series. D is each criterion's row sum of T (how much it influences the others, direct and indirect combined) and R its column sum (how much it is influenced). Prominence D + R is overall involvement in the system, while relation D - R is net direction, positive for a net cause and negative or zero for a net effect. The threshold is the arithmetic mean of every entry of T: relations at or above it are considered significant enough to draw in an influence diagram.

Usage

sframe_dematel_compute(x)

Arguments

x

A square numeric matrix of direct influence, zero diagonal.

Value

A list with normalised (N), total_relation (T), D, R, prominence (D + R), relation (D - R), threshold (mean of T), and role (a character vector, "cause" where relation > 0, else "effect").

Details

The series converges only when the spectral radius of N is below 1. Normalisation keeps the radius at or below 1, and it equals 1 when criteria influence each other in a closed group with equal totals. That case returns an error explaining it, and no truncated series is substituted.