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Description

As a measure for element similarity correlations between elements are frequently used. Note that product moment correlations as a measure of similarity are flawed as they are not invariant to construct reflection (Bell, 2010; Mackay, 1992). A correlation index invariant to construct reflection is Cohen’s rc measure (1969), which can be calculated using the argument rc=TRUE which is the default option.

R-Code

As a default the construct reflection invariant correlation Cohen’s rc is calculated.

Note how the values change when the simple product-moment correlation is used instaed of Cohen’s rc. Make sure you know what you are doing when setting rc=FALSE.

elementCor(mackay1992, rc = F)
# 
# ############################
# Correlation between elements
# ############################
# 
# Type of correlation:  pearson 
# Note: Standard correlations are not invariant to scale reflection.
# 
#                         1     2     3     4     5     6
# (1) Self            1     -0.37 -0.19  0.32 -0.75  0.96
# (2) Ideal self      2           -0.71 -0.56 -0.26 -0.30
# (3) Mother          3                  0.63  0.57 -0.12
# (4) Father          4                        0.05  0.38
# (5) Spouse          5                             -0.74
# (6) Disliked person 6

Although nor recommended different measures, not invariant to construct relfection, can be prompoted, when setting rc=FALSE.

  • Pearson or Product-moment correlation (PMC)
  • Kendall’s tau rank correlation
  • Spearman’s rank correlation

To request these types of correlations use the method argument plus rc=FALSE.

elementCor(mackay1992, rc = FALSE, meth = "kendall") # Kendalls tau correlation
elementCor(mackay1992, rc = FALSE, meth = "spearman") # Spearman rank correlation

Several arguments to format the output are available.

elementCor(mackay1992, index = F, trim = 6)
# 
# ############################
# Correlation between elements
# ############################
# 
# Type of correlation:  Cohens's rc (invariant to scale reflection) 
# 
#            1     2     3     4     5     6
# Self   1      0.59  0.28  0.29 -0.61 -0.62
# Ideal  2           -0.04 -0.20 -0.38 -0.81
# Mother 3                  0.63  0.37 -0.43
# Father 4                        0.00  0.00
# Spouse 5                              0.00
# Dislik 6

If the correlations are calculated for further processing, the correlations can be saved.

r <- elementCor(mackay1992)

The object is matrix, so you can eassily acces the results. E.g. all correlations with the element Self.

r[1, ]
#            (1) Self      (2) Ideal self          (3) Mother          (4) Father          (5) Spouse (6) Disliked person 
#           1.0000000           0.5876060           0.2809003           0.2909572          -0.6123724          -0.6182840

Literature

Bell, R. C. (2010). A note on aligning constructs. Personal Construct Theory & Practice, 7, 42–48.
Cohen, J. (1969). Rc: A profile similarity coefficient invariant over variable reflection. Psychological Bulletin, 71(4), 281–284. doi:10.1037/h0026865
Mackay, N. (1992). Identification, reflection, and correlation: Problems in the bases of repertory grid measures. International Journal of Personal Construct Psychology, 5(1), 57–75. doi:10.1080/08936039208404941