Somers' D for constructs

Description
As suggested by Hinkle (1965) the relationships between constructs may take several different forms (reciprocal, hierarchical etc.) Several authors have suggested the use of asymmetric measures of association as an indicator for the type of relationship present (cf. Fransella et al., 2003). Currently only the software Gridstat (Bell, 2009) allows to calculate the asymmetric measure Somers’ D (Somers, 1962). The calculation of Somer’s D in OpenRepGrid is prompted via the function constructD.

R-Code
Somers' D is an asymmetric measure. As a default the columns are the dependent the rows the independent variables.

> constructD(fbb2003)

Somers' D

Direction: columns are set as dependent 1   2    3    4    5    6    7    8    9 (1) clever - not bright               1.0 -0.6  0.9 -0.5  0.6  0.2  0.8  0.0 -0.1 (2) disorganized - organized        -0.7  1.0 -0.6  0.4 -0.3 -0.2 -0.7 -0.1 -0.4 (3) listens - doesn't hear           1.0 -0.5  1.0 -0.4  0.8  0.1  0.7  0.0 -0.2 (4) no clear view - clear view of l -0.6  0.4 -0.5  1.0 -0.2 -0.6 -0.5 -0.2 -0.2 (5) understands me - no understandin 0.8 -0.3  0.9 -0.2  1.0  0.0  0.6  0.0 -0.2 (6) ambitious - no ambition          0.2 -0.2  0.1 -0.5  0.0  1.0  0.3  0.2  0.1 (7) respected - not respected        0.8 -0.7  0.7 -0.4  0.5  0.3  1.0 -0.1  0.0 (8) distant - warm                   0.0 -0.1  0.0 -0.2  0.0  0.2 -0.1  1.0  0.5 (9) rather aggressi - not aggressive -0.1 -0.4 -0.2 -0.2 -0.2 0.1  0.0  0.5  1.0

To set the rows as dependent: > constructD(fbb2003, dep="r")

Somers' D

Direction: rows are set as dependent 1   2    3    4    5    6    7    8    9 (1) clever - not bright               1.0 -0.7  1.0 -0.6  0.8  0.2  0.8  0.0 -0.1 (2) disorganized - organized        -0.6  1.0 -0.5  0.4 -0.3 -0.2 -0.7 -0.1 -0.4 (3) listens - doesn't hear           0.9 -0.6  1.0 -0.5  0.9  0.1  0.7  0.0 -0.2 (4) no clear view - clear view of l -0.5  0.4 -0.4  1.0 -0.2 -0.5 -0.4 -0.2 -0.2 (5) understands me - no understandin 0.6 -0.3  0.8 -0.2  1.0  0.0  0.5  0.0 -0.2 (6) ambitious - no ambition          0.2 -0.2  0.1 -0.6  0.0  1.0  0.3  0.2  0.1 (7) respected - not respected        0.8 -0.7  0.7 -0.5  0.6  0.3  1.0 -0.1  0.0 (8) distant - warm                   0.0 -0.1  0.0 -0.2  0.0  0.2 -0.1  1.0  0.5 (9) rather aggressi - not aggressive -0.1 -0.4 -0.2 -0.2 -0.2 0.1  0.0  0.5  1.0

To surpress the console output and save the results in an object: d <- constructD(fbb2003, out=0, trim=6) d

Literature

 * Bell, R. C. (2009). Gridstat version 5 - A Program for Analyzing the Data of A Repertory Grid (manual). University of Melbourne, Australia: Department of Psychology.
 * Fransella, F., Bell, R. C., & Bannister, D. (2003). A Manual for Repertory Grid Technique (2. ed.). Chichester: John Wiley & Sons.
 * Hinkle, D. (1965). The Change of Personal Constructs from the Viewpoint of a Theory of Construct Implications (Unpublished Ph.D. thesis). Ohio State University, Ohio.
 * Somers, R. H. (1962). A New Asymmetric Measure of Association for Ordinal Variables. American Sociological Review, 27(6), 799-811.