### 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
1.0000000           0.5876060           0.2809003
(4) Father          (5) Spouse (6) Disliked person
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