Conflict or inconsistency measure for grids (Bell, 2004) based on distances.
Source:R/measures.r
indexConflict3.RdMeasure of conflict or inconsistency as proposed by Bell (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, 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.
Usage
indexConflict3(
x,
p = 2,
e.out = NA,
e.threshold = NA,
c.out = NA,
c.threshold = NA,
trim = 20
)Arguments
- x
repgridobject.- p
The power of the Minkowski distance.
p=2(default) will result in euclidean distances,p=1in city block distances.- e.out
Numeric. A vector giving the indexes of the elements for which detailed stats (number of conflicts per element, discrepancies for triangles etc.) are prompted (default
NA, i.e. no detailed stats for any element).- e.threshold
Numeric. Detailed stats are prompted for those elements with a an attributable percentage to the overall conflicts higher than the supplied threshold (default
NA).- c.out
Numeric. A vector giving the indexes of the constructs for which detailed stats (discrepancies for triangles etc.) are prompted (default
NA, i. e. no detailed stats).- c.threshold
Numeric. Detailed stats are prompted for those constructs with a an attributable percentage to the overall conflicts higher than the supplied threshold (default
NA).- trim
The number of characters a construct (element) is trimmed to (default is
10). IfNAno trimming is done. Trimming simply saves space when displaying the output.
Value
A list (invisibly) containing:
potential: number of potential conflictsactual: count of actual conflictsoverall: percentage of conflictive relationse.count: number of involvements of each element in conflictive relationse.perc: percentage of involvement of each element in total of conflictive relationsc.count: number of involvements of each construct in conflictive relationc.perc: percentage of involvement of each construct in total of conflictive relationse.stats: detailed statistics for prompted elementsc.stats: detailed statistics for prompted constructse.threshold: threshold percentage. Used by print methodc.threshold: threshold percentage. Used by print methodenames: trimmed element names. Used by print methodcnames: trimmed construct names. Used by print method
Details
Status: working; output for euclidean and manhattan distance
checked against Gridstat output.
TODO: standardization and z-test for discrepancies;
Index of Conflict Variation.
output
For further control over the output see print.indexConflict3().
References
Bell, R. C. (2004). A new approach to measuring inconsistency or conflict in grids. Personal Construct Theory & Practice, (1), 53-59.
See also
See indexConflict1() and indexConflict2() for conflict measures based on triads of correlations.
Examples
# calculate conflicts
indexConflict3(bell2010)
#>
#> ##########################################################
#> CONFLICT OR INCONSISTENCIES BASED ON TRIANGLE INEQUALITIES
#> ##########################################################
#>
#> Potential conflicts in grid: 360
#> Actual conflicts in grid: 123
#> Overall percentage of conflict in grid: 34.17 %
#>
#> ELEMENTS
#> ########
#>
#> Percent of conflict attributable to element:
#>
#> percentage
#> 1 self 162.60
#> 2 closest friend of th 1382.11
#> 3 the unhappiest perso 406.50
#> 4 A person of the oppo 650.41
#> 5 A teacher you respec 1056.91
#> 6 Mother (or the perso 1138.21
#> 7 A person of the oppo 813.01
#> 8 The most confident p 1788.62
#> 9 A person you work we 1138.21
#> 10 A teacher you did no 1463.41
#>
#> Chi-square test of equal count of conflicts for elements.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$e.count
#> X-squared = 27.488, df = 9, p-value = 0.001161
#>
#>
#> CONSTRUCTS
#> ##########
#>
#> Percent of conflict attributable to construct:
#>
#> percentage
#> 1 relaxed - worried & 10.16
#> 2 not so sma - smart (aca 11.38
#> 3 dislikes s - loves spor 13.01
#> 4 not intera - loves peop 10.57
#> 5 not transp - transparen 12.60
#> 6 insensitiv - sensitive 12.20
#> 7 fearful&ti - fearless 10.16
#> 8 rough - gentle 11.38
#> 9 accept as - loves to a 8.54
#>
#> Chi-square test of equal count of conflicts for constructs.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$c.count
#> X-squared = 3.5122, df = 8, p-value = 0.8982
#>
# show additional stats for elements 1 to 3
indexConflict3(bell2010, e.out = 1:3)
#>
#> ##########################################################
#> CONFLICT OR INCONSISTENCIES BASED ON TRIANGLE INEQUALITIES
#> ##########################################################
#>
#> Potential conflicts in grid: 360
#> Actual conflicts in grid: 123
#> Overall percentage of conflict in grid: 34.17 %
#>
#> ELEMENTS
#> ########
#>
#> Percent of conflict attributable to element:
#>
#> percentage
#> 1 self 162.60
#> 2 closest friend of th 1382.11
#> 3 the unhappiest perso 406.50
#> 4 A person of the oppo 650.41
#> 5 A teacher you respec 1056.91
#> 6 Mother (or the perso 1138.21
#> 7 A person of the oppo 813.01
#> 8 The most confident p 1788.62
#> 9 A person you work we 1138.21
#> 10 A teacher you did no 1463.41
#>
#> Chi-square test of equal count of conflicts for elements.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$e.count
#> X-squared = 27.488, df = 9, p-value = 0.001161
#>
#>
#> CONSTRUCTS
#> ##########
#>
#> Percent of conflict attributable to construct:
#>
#> percentage
#> 1 relaxed - worried & 10.16
#> 2 not so sma - smart (aca 11.38
#> 3 dislikes s - loves spor 13.01
#> 4 not intera - loves peop 10.57
#> 5 not transp - transparen 12.60
#> 6 insensitiv - sensitive 12.20
#> 7 fearful&ti - fearless 10.16
#> 8 rough - gentle 11.38
#> 9 accept as - loves to a 8.54
#>
#> Chi-square test of equal count of conflicts for constructs.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$c.count
#> X-squared = 3.5122, df = 8, p-value = 0.8982
#>
#>
#>
#> CONFLICTS BY ELEMENT
#> ####################
#>
#>
#> ### Element: 1 self
#>
#> Number of conflicting construct pairs: 2
#>
#> Construct conflict discrepancies:
#>
#> 1 2 3 4 5 6 7 8 9
#> 1
#> 2 <NA>
#> 3 <NA> <NA>
#> 4 <NA> <NA> <NA>
#> 5 <NA> <NA> <NA> <NA>
#> 6 <NA> <NA> 0.03 <NA> 0.33
#> 7 <NA> <NA> <NA> <NA> <NA> <NA>
#> 8 <NA> <NA> <NA> <NA> <NA> <NA> <NA>
#> 9 <NA> <NA> <NA> <NA> <NA> <NA> <NA> <NA>
#>
#> Percent of conflict attributable to each construct:
#>
#> percentage
#> 1 relaxed - worried & 0
#> 2 not so sma - smart (aca 0
#> 3 dislikes s - loves spor 25
#> 4 not intera - loves peop 0
#> 5 not transp - transparen 25
#> 6 insensitiv - sensitive 50
#> 7 fearful&ti - fearless 0
#> 8 rough - gentle 0
#> 9 accept as - loves to a 0
#>
#> Av. level of discrepancy: 0.01
#>
#> Std. dev. of discrepancies: 0.176
#>
#>
#> ### Element: 2 closest friend of th
#>
#> Number of conflicting construct pairs: 17
#>
#> Construct conflict discrepancies:
#>
#> 1 2 3 4 5 6 7 8 9
#> 1
#> 2 0.53
#> 3 <NA> 1.35
#> 4 0.19 <NA> 1.81
#> 5 <NA> 0.55 <NA> 1.51
#> 6 0.37 <NA> 1.17 <NA> 0.33
#> 7 <NA> 1.59 <NA> 1.75 <NA> 0.03
#> 8 0.47 <NA> 0.62 <NA> 0.17 <NA> <NA>
#> 9 <NA> 0.55 <NA> 0.8 <NA> <NA> <NA> <NA>
#>
#> Percent of conflict attributable to each construct:
#>
#> percentage
#> 1 relaxed - worried & 11.76
#> 2 not so sma - smart (aca 14.71
#> 3 dislikes s - loves spor 11.76
#> 4 not intera - loves peop 14.71
#> 5 not transp - transparen 11.76
#> 6 insensitiv - sensitive 11.76
#> 7 fearful&ti - fearless 8.82
#> 8 rough - gentle 8.82
#> 9 accept as - loves to a 5.88
#>
#> Av. level of discrepancy: 0.34
#>
#> Std. dev. of discrepancies: 0.583
#>
#>
#> ### Element: 3 the unhappiest perso
#>
#> Number of conflicting construct pairs: 5
#>
#> Construct conflict discrepancies:
#>
#> 1 2 3 4 5 6 7 8 9
#> 1
#> 2 <NA>
#> 3 <NA> <NA>
#> 4 <NA> <NA> <NA>
#> 5 <NA> <NA> 0.11 <NA>
#> 6 <NA> <NA> 0.03 <NA> <NA>
#> 7 <NA> 0.4 1.27 <NA> <NA> <NA>
#> 8 <NA> <NA> <NA> <NA> <NA> <NA> <NA>
#> 9 <NA> <NA> <NA> <NA> <NA> <NA> 1.18 <NA>
#>
#> Percent of conflict attributable to each construct:
#>
#> percentage
#> 1 relaxed - worried & 0
#> 2 not so sma - smart (aca 10
#> 3 dislikes s - loves spor 30
#> 4 not intera - loves peop 0
#> 5 not transp - transparen 10
#> 6 insensitiv - sensitive 10
#> 7 fearful&ti - fearless 30
#> 8 rough - gentle 0
#> 9 accept as - loves to a 10
#>
#> Av. level of discrepancy: 0.07
#>
#> Std. dev. of discrepancies: 0.556
# show additional stats for constructs 1 and 5
indexConflict3(bell2010, c.out = c(1, 5))
#>
#> ##########################################################
#> CONFLICT OR INCONSISTENCIES BASED ON TRIANGLE INEQUALITIES
#> ##########################################################
#>
#> Potential conflicts in grid: 360
#> Actual conflicts in grid: 123
#> Overall percentage of conflict in grid: 34.17 %
#>
#> ELEMENTS
#> ########
#>
#> Percent of conflict attributable to element:
#>
#> percentage
#> 1 self 162.60
#> 2 closest friend of th 1382.11
#> 3 the unhappiest perso 406.50
#> 4 A person of the oppo 650.41
#> 5 A teacher you respec 1056.91
#> 6 Mother (or the perso 1138.21
#> 7 A person of the oppo 813.01
#> 8 The most confident p 1788.62
#> 9 A person you work we 1138.21
#> 10 A teacher you did no 1463.41
#>
#> Chi-square test of equal count of conflicts for elements.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$e.count
#> X-squared = 27.488, df = 9, p-value = 0.001161
#>
#>
#> CONSTRUCTS
#> ##########
#>
#> Percent of conflict attributable to construct:
#>
#> percentage
#> 1 relaxed - worried & 10.16
#> 2 not so sma - smart (aca 11.38
#> 3 dislikes s - loves spor 13.01
#> 4 not intera - loves peop 10.57
#> 5 not transp - transparen 12.60
#> 6 insensitiv - sensitive 12.20
#> 7 fearful&ti - fearless 10.16
#> 8 rough - gentle 11.38
#> 9 accept as - loves to a 8.54
#>
#> Chi-square test of equal count of conflicts for constructs.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$c.count
#> X-squared = 3.5122, df = 8, p-value = 0.8982
#>
#>
#>
#> CONFLICTS BY CONSTRUCT
#> ######################
#>
#>
#> ### Construct: 1 relaxed - worried &
#>
#> Element-construct conflict discrepancies:
#>
#> e1 e2 e3 e4 e5 e6 e7 e8 e9 e10
#> c1
#> c2 <NA>
#> c3 <NA> <NA>
#> c4 <NA> 0.19 <NA>
#> c5 <NA> <NA> <NA> <NA>
#> c6 <NA> 0.37 <NA> <NA> <NA>
#> c7 <NA> <NA> <NA> <NA> <NA> 1
#> c8 <NA> 0.47 <NA> <NA> 0.47 <NA> 0.47
#> c9 <NA> <NA> <NA> <NA> <NA> <NA> <NA> 3.44
#>
#> Av. level of discrepancy: 0.38
#>
#> Std. dev. of discrepancies: 0.973
#>
#>
#> ### Construct: 5 not transp - transparen
#>
#> Element-construct conflict discrepancies:
#>
#> e1 e2 e3 e4 e5 e6 e7 e8 e9 e10
#> c1
#> c2 <NA>
#> c3 <NA> <NA>
#> c4 <NA> 1.51 <NA>
#> c5 <NA> <NA> <NA> <NA>
#> c6 0.33 0.33 <NA> 1.51 <NA>
#> c7 <NA> <NA> <NA> <NA> 0.3 2.75
#> c8 <NA> 0.17 <NA> 1.33 0.17 <NA> <NA>
#> c9 <NA> <NA> <NA> <NA> <NA> 1.8 <NA> 0.59
#>
#> Av. level of discrepancy: 0.32
#>
#> Std. dev. of discrepancies: 0.761
# finetune output
## change number of digits
x <- indexConflict3(bell2010)
print(x, digits = 4)
#>
#> ##########################################################
#> CONFLICT OR INCONSISTENCIES BASED ON TRIANGLE INEQUALITIES
#> ##########################################################
#>
#> Potential conflicts in grid: 360
#> Actual conflicts in grid: 123
#> Overall percentage of conflict in grid: 34.1667 %
#>
#> ELEMENTS
#> ########
#>
#> Percent of conflict attributable to element:
#>
#> percentage
#> 1 self 162.6016
#> 2 closest friend of th 1382.1138
#> 3 the unhappiest perso 406.5041
#> 4 A person of the oppo 650.4065
#> 5 A teacher you respec 1056.9106
#> 6 Mother (or the perso 1138.2114
#> 7 A person of the oppo 813.0081
#> 8 The most confident p 1788.6179
#> 9 A person you work we 1138.2114
#> 10 A teacher you did no 1463.4146
#>
#> Chi-square test of equal count of conflicts for elements.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$e.count
#> X-squared = 27.488, df = 9, p-value = 0.001161
#>
#>
#> CONSTRUCTS
#> ##########
#>
#> Percent of conflict attributable to construct:
#>
#> percentage
#> 1 relaxed - worried & 10.1626
#> 2 not so sma - smart (aca 11.3821
#> 3 dislikes s - loves spor 13.0081
#> 4 not intera - loves peop 10.5691
#> 5 not transp - transparen 12.6016
#> 6 insensitiv - sensitive 12.1951
#> 7 fearful&ti - fearless 10.1626
#> 8 rough - gentle 11.3821
#> 9 accept as - loves to a 8.5366
#>
#> Chi-square test of equal count of conflicts for constructs.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$c.count
#> X-squared = 3.5122, df = 8, p-value = 0.8982
#>
#> NULL
## omit discrepancy matrices for constructs
x <- indexConflict3(bell2010, c.out = 5:6)
print(x, discrepancies = FALSE)
#>
#> ##########################################################
#> CONFLICT OR INCONSISTENCIES BASED ON TRIANGLE INEQUALITIES
#> ##########################################################
#>
#> Potential conflicts in grid: 360
#> Actual conflicts in grid: 123
#> Overall percentage of conflict in grid: 34.17 %
#>
#> ELEMENTS
#> ########
#>
#> Percent of conflict attributable to element:
#>
#> percentage
#> 1 self 162.60
#> 2 closest friend of th 1382.11
#> 3 the unhappiest perso 406.50
#> 4 A person of the oppo 650.41
#> 5 A teacher you respec 1056.91
#> 6 Mother (or the perso 1138.21
#> 7 A person of the oppo 813.01
#> 8 The most confident p 1788.62
#> 9 A person you work we 1138.21
#> 10 A teacher you did no 1463.41
#>
#> Chi-square test of equal count of conflicts for elements.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$e.count
#> X-squared = 27.488, df = 9, p-value = 0.001161
#>
#>
#> CONSTRUCTS
#> ##########
#>
#> Percent of conflict attributable to construct:
#>
#> percentage
#> 1 relaxed - worried & 10.16
#> 2 not so sma - smart (aca 11.38
#> 3 dislikes s - loves spor 13.01
#> 4 not intera - loves peop 10.57
#> 5 not transp - transparen 12.60
#> 6 insensitiv - sensitive 12.20
#> 7 fearful&ti - fearless 10.16
#> 8 rough - gentle 11.38
#> 9 accept as - loves to a 8.54
#>
#> Chi-square test of equal count of conflicts for constructs.
#>
#> Chi-squared test for given probabilities
#>
#> data: x$c.count
#> X-squared = 3.5122, df = 8, p-value = 0.8982
#>
#>
#>
#> CONFLICTS BY CONSTRUCT
#> ######################
#>
#>
#> ### Construct: 5 not transp - transparen
#>
#> Av. level of discrepancy: 0.32
#>
#> Std. dev. of discrepancies: 0.761
#>
#>
#> ### Construct: 6 insensitiv - sensitive
#>
#> Av. level of discrepancy: 0.32
#>
#> Std. dev. of discrepancies: 0.929