Conflict measure for grids (Bassler et al., 1992) based on correlations.
Source:R/measures.r
indexConflict2.RdThe function calculates the conflict measure as devised by Bassler et al. (1992). It is an improved version of the
ideas by Slade and Sheehan (1979) that have been implemented in the function indexConflict1(). The new approach
also takes into account the magnitude of the correlations in a trait to assess whether it is balanced or imbalanced.
As a result, small correlations that are psychologically meaningless are considered accordingly. Also, correlations
with a small magnitude, i. e. near zero, which may be positive or negative due to chance alone will no longer
distort the measure (Bassler et al., 1992).
Details
Description of the balance / imbalance assessment:
Order correlations of the triad by absolute magnitude, so that \( r_{max} > r_{mdn} > r_{min}\), \(r_{max} > r_{mdn} > r_{min}\).
Apply Fisher's Z-transformation and division by 3 to yield values between 1 and -1 (\( Z_{max} > Z_{mdn} > Z_{min}, Z_{max} > Z_{mdn} > Z_{min}\)).
Check whether the triad is balanced by assessing if the following relation holds:
If \(Z_{max} Z_{mdn} > 0, Z_{max} x Z_{mdn} > 0\), the triad is balanced if \(Z_{max} Z_{mdn} - Z_{min} <= crit\), \(Z_{max} x Z_{mdn} - Z_{min} <= crit\).
If \(Z_{max} Z_{mdn} < 0, Z_{max} x Z_{mdn} < 0\), the triad is balanced if \(Z_{min} - Z_{max} Z_{mdn} <= crit\), \(Z_{min} - Z_{max} x Z_{mdn} <= crit\).
Personal remarks (MH)
I am a bit suspicious about step 2 from above. To devide by 3 appears pretty arbitrary.
The r for a z-values of 3 is 0.9950548 and not 1.
The r for 4 is 0.9993293. Hence, why not a value of 4, 5, or 6?
Denoting the value to devide by with a, the relation for the
first case translates into \(a Z_{max} Z_{mdn} <= \frac{crit}{a} + Z_{min}\),
\(a x Z_{max} x Z_{mdn} =< crit/a + Z_{min}\). This shows that a bigger value of a
will make it more improbable that the relation will hold.
References
Bassler, M., Krauthauser, H., & Hoffmann, S. O. (1992). A new approach to the identification of cognitive conflicts in the repertory grid: An illustrative case study. Journal of Constructivist Psychology, 5(1), 95-111.
Slade, P. D., & Sheehan, M. J. (1979). The measurement of 'conflict' in repertory grids. British Journal of Psychology, 70(4), 519-524.
See also
See indexConflict1() for the older version of this measure; see indexConflict3() for a measure based
on distances instead of correlations.
Examples
indexConflict2(bell2010)
#>
#> ###############################
#> Conflicts based on correlations
#> ###############################
#>
#> As devised by Bassler et al. (1992)
#>
#> Total number of triads: 84
#> Number of imbalanced triads: 63
#>
#> Proportion of balanced triads: 25 %
#> Proportion of imbalanced triads: 75 %
x <- indexConflict2(bell2010)
print(x)
#>
#> ###############################
#> Conflicts based on correlations
#> ###############################
#>
#> As devised by Bassler et al. (1992)
#>
#> Total number of triads: 84
#> Number of imbalanced triads: 63
#>
#> Proportion of balanced triads: 25 %
#> Proportion of imbalanced triads: 75 %
# show conflictive triads
print(x, output = 2)
#>
#> ###############################
#> Conflicts based on correlations
#> ###############################
#>
#> As devised by Bassler et al. (1992)
#>
#> Total number of triads: 84
#> Number of imbalanced triads: 63
#>
#> Proportion of balanced triads: 25 %
#> Proportion of imbalanced triads: 75 %
#>
#> Constructs that form imbalanced triads:
#>
#> 1 1 2 4
#> 2 1 2 7
#> 3 1 2 8
#> 4 1 3 8
#> 5 1 3 9
#> 6 1 4 5
#> 7 1 4 6
#> 8 1 4 7
#> 9 1 4 8
#> 10 1 4 9
#> 11 1 5 8
#> 12 1 5 9
#> 13 1 6 7
#> 14 1 6 8
#> 15 1 7 8
#> 16 1 7 9
#> 17 1 8 9
#> 18 2 3 5
#> 19 2 3 6
#> 20 2 3 7
#> 21 2 3 8
#> 22 2 3 9
#> 23 2 4 5
#> 24 2 4 6
#> 25 2 4 7
#> 26 2 4 8
#> 27 2 4 9
#> 28 2 5 6
#> 29 2 5 7
#> 30 2 5 8
#> 31 2 5 9
#> 32 2 6 7
#> 33 2 6 8
#> 34 2 7 8
#> 35 2 7 9
#> 36 3 4 5
#> 37 3 4 6
#> 38 3 4 8
#> 39 3 4 9
#> 40 3 5 6
#> 41 3 5 8
#> 42 3 6 8
#> 43 3 6 9
#> 44 3 7 8
#> 45 3 7 9
#> 46 3 8 9
#> 47 4 5 7
#> 48 4 5 8
#> 49 4 6 7
#> 50 4 6 8
#> 51 4 6 9
#> 52 4 7 8
#> 53 4 8 9
#> 54 5 6 7
#> 55 5 6 8
#> 56 5 6 9
#> 57 5 7 8
#> 58 5 7 9
#> 59 5 8 9
#> 60 6 7 8
#> 61 6 7 9
#> 62 6 8 9
#> 63 7 8 9
# accessing the calculations for further use
x$total
#> [1] 84
x$imbalanced
#> [1] 63
x$prop.balanced
#> [1] 0.25
x$prop.imbalanced
#> [1] 0.75
x$triads.imbalanced
#> [,1] [,2] [,3]
#> [1,] 1 2 4
#> [2,] 1 2 7
#> [3,] 1 2 8
#> [4,] 1 3 8
#> [5,] 1 3 9
#> [6,] 1 4 5
#> [7,] 1 4 6
#> [8,] 1 4 7
#> [9,] 1 4 8
#> [10,] 1 4 9
#> [11,] 1 5 8
#> [12,] 1 5 9
#> [13,] 1 6 7
#> [14,] 1 6 8
#> [15,] 1 7 8
#> [16,] 1 7 9
#> [17,] 1 8 9
#> [18,] 2 3 5
#> [19,] 2 3 6
#> [20,] 2 3 7
#> [21,] 2 3 8
#> [22,] 2 3 9
#> [23,] 2 4 5
#> [24,] 2 4 6
#> [25,] 2 4 7
#> [26,] 2 4 8
#> [27,] 2 4 9
#> [28,] 2 5 6
#> [29,] 2 5 7
#> [30,] 2 5 8
#> [31,] 2 5 9
#> [32,] 2 6 7
#> [33,] 2 6 8
#> [34,] 2 7 8
#> [35,] 2 7 9
#> [36,] 3 4 5
#> [37,] 3 4 6
#> [38,] 3 4 8
#> [39,] 3 4 9
#> [40,] 3 5 6
#> [41,] 3 5 8
#> [42,] 3 6 8
#> [43,] 3 6 9
#> [44,] 3 7 8
#> [45,] 3 7 9
#> [46,] 3 8 9
#> [47,] 4 5 7
#> [48,] 4 5 8
#> [49,] 4 6 7
#> [50,] 4 6 8
#> [51,] 4 6 9
#> [52,] 4 7 8
#> [53,] 4 8 9
#> [54,] 5 6 7
#> [55,] 5 6 8
#> [56,] 5 6 9
#> [57,] 5 7 8
#> [58,] 5 7 9
#> [59,] 5 8 9
#> [60,] 6 7 8
#> [61,] 6 7 9
#> [62,] 6 8 9
#> [63,] 7 8 9