In markheckmann/OpenRepGrid: Tools to Analyze Repertory Grid Data

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Conflict measures bases on correlations

Description

The first approach to mathematically derive a conflict measure based on grid data was presented by [-@slade_measurement_1979]. They based their operationalization on an approach by @lauterbach_assessing_1975 who applied Heider's [-@heider_attitudes_1946] balance theory for a quantitative assessment of psychological conflict. The measure uses inter-construct correlation as a basis. It assess via the sign of the correlations of a triad of constructs if the constructs triad is balanced or imbalanced. A triad is imbalanced if one or three of the correlations are negative, i. e. when they leading to contrary implications [@slade_measurement_1979]. The function indexConflict1 in OpenRepGrid calculates the proportion of conflictive triads in the grid as devised by Slade and Sheehan.

Slade and Sheehan’s approach has several drawbacks, as it does not take into account the magnitude of the inter-construct correlations. As a consequence significant and insignificant correlations are not differentiated. Also, correlations of small magnitude, i.e. near zero, which may have a positive or negative signe due to chance alone distort the measure [@winter_construct_1982; @bassler_new_1992]. An improved version of the index that overcomes these shortcomings was proposed by [-@bassler_new_1992] and incorporated into the program CT (correlation test). The index enhances the identification of imbalanced triads by using a criterion that incorporates the magnitudes of correlations. From a psychological viewpoint, it remains unclear though what is measured. Connections to the concept of cognitive differentiation have been presumed [@krauthauser_new_1994]. The function indexConflict2 in OpenRepGrid calculates the proportion of conflictive triads in the grid as devised by [-@bassler_new_1992].

Calculation

@slade_measurement_1979 approach

Multiply all correlations from a triad (formed by the constructs A, B and C) $r_{AB} r_{AC} r_{BC}$. If the sign of the result is negative, the triad is imbalanced.

The table below shows when a triad made up of the constructs A, B, and C is balanced and imbalanced.

$r_{AB}$ | $r_{AC}$ | $r_{BC}$ | Triad characteristic --------- | --------- | ---- | ----- + | + | + | balanced + | + | - | imbalanced + | - | + | imbalanced + | - | - | balanced - | + | + | imbalanced - | + | - | balanced - | - | + | balanced - | - | - | imbalanced

@bassler_new_1992 approach

Order correlations of the triad by absolute magnitude, so that $r_{max} > r_{mdn} > r_{min}$.

Apply Fisher's Z-transformation and devision by 3 to yield values between 1 and -1 Check whether the triad is balanced by assessing if the following relation holds:

If $Z_{max} Z_{mdn} > 0$, the triad is balanced if $Z_{max} Z_{mdn} - Z_{min} <= crit$
If $Z_{max} Z_{mdn} < 0$, the triad is balanced if $Z_{min} - Z_{max} Z_{mdn} <= crit$

R-Code

To use the Slade and Sheehan approach use

indexConflict1(boeker)

For the Bassler et al. approach use

indexConflict2(boeker)
indexConflict2(boeker, crit =.05)   # change critical value

Conflict measures based on distances

Description

Measure of conflict or inconsistency as proposed by @bell_new_2004. The identification of conflict is based on distances rather than correlations as in other measures of conflict indexConflict1 and indexConflict2. It assesses if the distances between all components of a triad, made up of one element and two constructs, satisfies the "triangle inequality" [cf. @bell_new_2004]. If not, a triad is regarded as conflictive. An advantage of the measure is that it can be interpreted not only as a global measure for a grid but also on an element, construct, and element by construct level making it valuable for detailed feedback. Also, differences in conflict can be submitted to statistical testing procedures.