Description
Correlation measures
The correlations between constructs are used in a lot of occasions,
indices etc, and present a standard statistic. Several types of
correlations can be requested via the function
constructCor.
- Pearson or Product-moment correlation (PMC)
- Kendall’s tau rank correlation
- Spearman’s rank correlation
Root mean square correlation
Also, the Root mean square (RMS) correlation, also known as
‘quadratic mean’ of the inter-construct correlations, can be calculated
using the function constructRmsCor. The RMS serves as a
simplification of the correlation table. It reflects the average
relation of one construct with all other constructs. Note that as the
correlations are squared during its calculation, the RMS is not affected
by the sign of the correlation (cf. Fransella, Bell & Bannister,
2003, p. 86).
Somers’ D
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 Somers’ D in
OpenRepGrid is prompted via the function
constructD.
R-Code
Correlation measures
constructCor(mackay1992)
#
# ##############################
# Correlation between constructs
# ##############################
#
# Type of correlation: pearson
#
# 1 2 3 4 5 6
# Quick - *Slow 1 0.38 0.77 0.13 0.52 0.29
# *Satisfied - Bitter 2 0.18 0.82 0.56 0.29
# Talkative - *Quiet 3 0.14 0.72 0.58
# *Succesful - Loser 4 0.64 0.47
# Emotional - *Calm 5 0.92
# *Caring - Selfish 6you can select between the different types of correlation by setting
the argument method to "pearson",
"kendall" or "spearman". To request a Spearman
rank correlation type
constructCor(mackay1992, method = "spearman")
#
# ##############################
# Correlation between constructs
# ##############################
#
# Type of correlation: spearman
#
# 1 2 3 4 5 6
# Quick - *Slow 1 0.50 0.83 0.00 0.56 0.19
# *Satisfied - Bitter 2 0.09 0.56 0.64 0.13
# Talkative - *Quiet 3 0.00 0.39 0.21
# *Succesful - Loser 4 0.69 0.49
# Emotional - *Calm 5 0.81
# *Caring - Selfish 6To format the output several arguments are available. See
?print.constructCor for more printing options.
r <- constructCor(mackay1992)
print(r, digits = 5, col.index = F)
#
# ##############################
# Correlation between constructs
# ##############################
#
# Type of correlation: pearson
#
# 1 2 3 4 5 6
# Quick - *Slow 0.37709 0.77226 0.12913 0.51682 0.28911
# *Satisfied - Bitter 0.18383 0.81969 0.56239 0.28917
# Talkative - *Quiet 0.13771 0.71984 0.57656
# *Succesful - Loser 0.63623 0.47133
# Emotional - *Calm 0.92394
# *Caring - SelfishRoot mean square correlation
To calulate the RMS correlation
constructRmsCor(fbb2003)
#
# ##########################################
# Root-mean-square correlation of constructs
# ##########################################
#
# RMS
# (1) clever - not bright 0.66
# (2) disorganized - organized 0.58
# (3) listens - doesn't hear 0.61
# (4) no clear view - clear view of life 0.46
# (5) understands me - no understanding 0.53
# (6) ambitious - no ambition 0.30
# (7) respected - not respected 0.62
# (8) distant - warm 0.25
# (9) rather aggressive - not aggressive 0.29
#
# Average of statistic 0.48
# Standard deviation of statistic 0.15Somers’ D
Somers’ D is an asymmetric measure. As a default the columns are the dependent the rows the independent variables.
constructD(fbb2003)
#
# ############################
# Somers' D between constructs
# ############################
#
# Direction: columns are set as dependent
# 1 2 3 4 5 6 7 8 9
# (1) clever - not bright 1 1.0 -0.6 0.9 -0.5 0.6 0.2 0.8 0.0 -0.1
# (2) disorganized - organized 2 -0.7 1.0 -0.6 0.4 -0.3 -0.2 -0.7 -0.1 -0.4
# (3) listens - doesn't hear 3 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 4 -0.6 0.4 -0.5 1.0 -0.2 -0.6 -0.5 -0.2 -0.2
# (5) understands me - no understandin 5 0.8 -0.3 0.9 -0.2 1.0 0.0 0.6 0.0 -0.2
# (6) ambitious - no ambition 6 0.2 -0.2 0.1 -0.5 0.0 1.0 0.3 0.2 0.1
# (7) respected - not respected 7 0.8 -0.7 0.7 -0.4 0.5 0.3 1.0 -0.1 0.0
# (8) distant - warm 8 0.0 -0.1 0.0 -0.2 0.0 0.2 -0.1 1.0 0.5
# (9) rather aggressi - not aggressive 9 -0.1 -0.4 -0.2 -0.2 -0.2 0.1 0.0 0.5 1.0To set the rows as dependent, type
constructD(fbb2003, dep = "r")The returned data is in all cases a matrix or a
data.frame, so you can easily extract the data you need for
further calculations.
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.