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Interrelationship Digraph (ID) using SAS/IML®

Started ‎07-30-2014 by
Modified ‎04-04-2022 by
Views 1,603

This program uses PROC IML, SAS Data Steps, and the %DSCONT macro to construct the Interrelationship Digaph (ID) or Relations Diagram in Graphical and Tabulated Matrix formats.


The Interrelationship Digraph (ID) is one of seven Quality Management and Planning toods described by Mizuno (1988). IDs are used to explore cause and effect relationships between ideas, items, or issues; prioritizing choices when decision makers have difficulty reaching concensus, and sorting out issues involved in project planning, especially when credible data may not exist.


The IML module, ID(K,W), expresses relationships of issues in matrix format using values of -1, 0, or +1 where "-1" denotes "incoming" arrows (or influence effects from column item j into row item i); "0" denotes no relationship between row-column items i and j; and "+1" denotes "outgoing" arrows (or causal effects from row item i out to column item j).


Matrix operators and functions of PROC IML produce the matrix ID computed from the adjacency matix, K = A(i,j), and strength of relationship matrix W, denoting relationship weights between node pairs of row item i and column item j.  Relationship strengths have values of 1 (weak or equal strength), 3 (Meduim strength), or 9 (Significant or Strong strength).


The ID(K,W) module returns an output matrix, idmatrix, that includes column vectors that identifies the key drivers (or causal effects) represented as the largest values in the "Total Out (+1)" column. Key effects or outcome are the maximum values in the "Total  In(-1)" column, and largest Strength weight (in the Strength column).


The benefit of the ID is that it pinpoints and prioitizes the areas where to focus quality improvement efforts first.



1.  Mizuno, S. (1988), Management for Quality Improvement: The 7 New QC Tools, Cambridge, MA, Productivity Press, Inc.

2. Milchalski, W.J., and King D.G., (2005), Six Sigma Tool Navigator: The Master Guide for Teams, Tool 141,

3. Hoerl, R. and Snee, R. (2012), Statistical Thinking: Improving Business Performance, 2nd. ed., John Wiley & Sons: Hoboken, NJ, pp. 185-188.

4. Alexander, M. (2013), "When Little Objective Data Are Available, Find Root Causes and Effects with Interrelationship Digraphs and JMP", SESUG 2013: The Proceeding of the SouthEast SAS Users Group, St.Pete Beach, Fl, 2013,

Version history
Last update:
‎04-04-2022 03:17 PM
Updated by:


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