Implicative dilemmas are closely related to the notion of conflict. An implicative dilemma arises when a desired change on one construct is associated with an undesired implication on another construct. E. g. a timid subject may want to become more socially skilled but associates being socially skilled with different negative characteristics (selfish, insensitive etc.). Hence, he may anticipate that becoming less timid will also make him more selfish (cf. Winter, 1982). As a consequence, the subject will resist to the change if the negative presumed implications will threaten the patients identity and the predictive power of his construct system. From this stance the resistance to change is a logical consequence coherent with the subjects construct system (Feixas, Saul, & Sanchez, 2000). The investigation of the role of cognitive dilemma in different disorders in the context of PCP is a current field of research (e.g. Feixas & Saul, 2004, Dorough et al. 2007).

## Usage

```
indexDilemma(
x,
self = 1,
ideal = ncol(x),
diff.mode = 1,
diff.congruent = NA,
diff.discrepant = NA,
diff.poles = 1,
r.min = 0.35,
exclude = FALSE,
digits = 2,
show = FALSE,
output = 1,
index = TRUE,
trim = 20
)
```

## Arguments

- x
A

`repgrid`

object.- self
Numeric. Index of self element.

- ideal
Numeric. Index of ideal self element.

- diff.mode
Numeric. Method adopted to classify construct pairs into congruent and discrepant. With

`diff.mode=1`

, the minimal and maximal score difference criterion is applied. With`diff.mode=0`

the Mid-point rating criterion is applied. Default is`diff.mode=1`

.- diff.congruent
Is used if

`diff.mode=1`

. Maximal difference between element ratings to define construct as congruent (default`diff.congruent=1`

). Note that the value needs to be adjusted by the user according to the rating scale used.- diff.discrepant
Is used if

`diff.mode=1`

. Minimal difference between element ratings to define construct as discrepant (default`diff.discrepant=3`

). Note that the value needs to be adjusted by the user according to the rating scale used.- diff.poles
Not yet implemented.

- r.min
Minimal correlation to determine implications between constructs.

- exclude
Whether to exclude the elements self and ideal self during the calculation of the inter-construct correlations. (default is

`FALSE`

).- digits
Numeric. Number of digits to round to (default is

`2`

).- show
Whether to additionally plot the distribution of correlations to help the user assess what level is adequate for

`r.min`

.- output
The type of output to return.

- index
Whether to print index numbers in front of each construct (default is

`TRUE`

).- trim
The number of characters a construct (element) is trimmed to (default is

`20`

). If`NA`

no trimming is done. Trimming simply saves space when displaying the output.

## Details

The detection of implicative dilemmas happens in two steps. First the constructs are classified as being 'congruent' or 'discrepant'. Secondly, the correlation between a congruent and discrepant construct pair is assessed if it is big enough to indicate an implication.

**Classifying the construct**

To detect implicit dilemmas the construct pairs are first identified as 'congruent' or 'discrepant'. The assessment is based on the rating differences between the elements 'self' and 'ideal self'. A construct is 'congruent' if the construction of the 'self' and the preferred state (i.e. ideal self) are the same or similar. A construct is discrepant if the construction of the 'self' and the 'ideal' is dissimilar.

There are two popular accepted methods to identify congruent and discrepant constructs:

"Scale Midpoint criterion" (cf. Grice 2008)

"Minimal and maximal score difference" (cf. Feixas & Saul, 2004)

*"Scale Midpoint criterion" (cf. Grice 2008)*

As reported in the Idiogrid (v. 2.4) manual: "... The Scale Midpoint uses the scales as the 'dividing line' for discrepancies; for example, if the actual element is rated above the midpoint, then the discrepancy exists (and vice versa). If the two selves are the same as the actual side of the scale, then a discrepancy does not exist". As an example:

Assuming a scoring range of 1-7, the midpoint score will be 4, we then look at self and ideal-self scoring on any given construct and we proceed as follow:

If the scoring of Self AND Ideal Self are both < 4: construct is "Congruent"

If the scoring of Self AND Ideal Self are both > 4: construct is "Congruent"

If the scoring of Self is < 4 AND Ideal Self is > 4 (OR vice versa): construct is "discrepant"

If scoring Self OR Ideal Self = 4 then the construct is NOT Discrepant and it is "Undifferentiated"

*Minimal and maximal score difference criterion (cf. Feixas & Saul, 2004)*

This other method is more conservative and it is designed to minimize Type I errors by a) setting a default minimum
correlation between constructs of `r=.34`

; b) discarding cases where the ideal Self and self are neither congruent
or discrepant; c) discarding cases where ideal self is "not oriented", i.e. scored at the midpoint.

E.g. suppose the element 'self' is rated 2 and 'ideal self' 5 on a scale from 1 to 6. The ratings differences are 5-2 = 3. If this difference is smaller than e.g. 1 the construct is 'congruent', if it is bigger than 3 it is 'discrepant'.

The values used to classify the constructs 'congruent' or 'discrepant' can be determined in several ways (cf. Bell, 2009):

They are set 'a priori'.

They are implicitly derived by taking into account the rating differences to the other constructs. (Not yet implemented)

The value mode is determined via the argument `diff.mode`

.

If no 'a priori' criteria to determine whether the construct is congruent or discrepant is supplied as an argument, the values are chosen according to the range of the rating scale used. For the following scales the defaults are chosen as:

Scale | 'A priori' criteria |

1 2 | –> con: <=0 disc: >=1 |

1 2 3 | –> con: <=0 disc: >=2 |

1 2 3 4 | –> con: <=0 disc: >=2 |

1 2 3 4 5 | –> con: <=1 disc: >=3 |

1 2 3 4 5 6 | –> con: <=1 disc: >=3 |

1 2 3 4 5 6 7 | –> con: <=1 disc: >=4 |

1 2 3 4 5 6 7 8 | –> con: <=1 disc: >=5 |

1 2 3 4 5 6 7 8 9 | –> con: <=2 disc: >=5 |

1 2 3 4 5 6 7 8 9 10 | –> con: <=2 disc: >=6 |

**Defining the correlations**

As the implications between constructs cannot be derived from a rating grid directly, the correlation between two
constructs is used as an indicator for implication. A large correlation means that one construct pole implies the
other. A small correlation indicates a lack of implication. The minimum criterion for a correlation to indicate
implication is set to .35 (cf. Feixas & Saul, 2004). The user may also choose another value. To get a an impression
of the distribution of correlations in the grid, a visualization can be prompted via the argument `show`

. When
calculating the correlation used to assess if an implication is given or not, the elements under consideration (i.
e. self and ideal self) can be included (default) or excluded. The options will cause different correlations (see
argument `exclude`

).

**Example of an implicative dilemma**

A depressive person considers herself as 'timid' and wished to change to the opposite pole she defines as 'extraverted'. This construct is called discrepant as the construction of the 'self' and the desired state (e.g. described by the 'ideal self') on this construct differ. The person also considers herself as 'sensitive' (preferred pole) for which the opposite pole is 'selfish'. This construct is congruent, as the person construes herself as she would like to be. If the person now changed on the discrepant construct from the undesired to the desired pole, i.e. from timid to extraverted, the question can be asked what consequences such a change has. If the person construes being timid and being sensitive as related and that someone who is extraverted will not be timid, a change on the first construct will imply a change on the congruent construct as well. Hence, the positive shift from timid to extraverted is presumed to have a undesired effect in moving from sensitive towards selfish. This relation is called an implicative dilemma. As the implications of change on a construct cannot be derived from a rating grid directly, the correlation between two constructs is used as an indicator of implication.

## References

Bell, R. C. (2009). *Gridstat version 5 - A Program for Analyzing the Data of A Repertory Grid*
(manual). University of Melbourne, Australia: Department of Psychology.

Dorough, S., Grice, J. W., & Parker, J. (2007). Implicative dilemmas and psychological well-being. *Personal
Construct Theory & Practice*, (4), 83-101.

Feixas, G., & Saul, L. A. (2004). The Multi-Center Dilemma Project: an investigation on the role of cognitive
conflicts in health. *The Spanish Journal of Psychology, 7*(1), 69-78.

Feixas, G., Saul, L. A., & Sanchez, V. (2000). Detection and analysis of implicative dilemmas: implications for
the therapeutic process. In J. W. Scheer (Ed.), *The Person in Society: Challenges to a Constructivist Theory*.
Giessen: Psychosozial-Verlag.

Winter, D. A. (1982). Construct relationships, psychological disorder and therapeutic change. *British Journal of
Medical Psychology, 55* (Pt 3), 257-269.

Grice, J. W. (2008). Idiogrid: Idiographic Analysis with Repertory Grids (Version 2.4). Oklahoma: Oklahoma State University.

## Examples

```
id <- indexDilemma(boeker, self = 1, ideal = 2)
id
#>
#> ####################
#> Implicative Dilemmas
#> ####################
#>
#> -------------------------------------------------------------------------------
#>
#> SUMMARY:
#>
#> No. of Implicative Dilemmas (IDs): 4
#> No. of possible construct pairs: 91
#> Percentage of IDs (PID): 4.4% (4/91)
#> Intensity of IDs (IID): 61.3
#> Proportion of the intensity of constructs of IDs (PICID): 2.7
#>
#> -------------------------------------------------------------------------------
#>
#> PARAMETERS:
#>
#> Self: Element No. 1 = self
#> Ideal: Element No. 2 = ideal self
#>
#> Correlation Criterion: >= 0.35
#> Note: Correlation calculated including elements Self & Ideal
#>
#> Criteria (for construct classification):
#> Discrepant if Self-Ideal difference: >= 3
#> Congruent if Self-Ideal difference: <= 1
#>
#> -------------------------------------------------------------------------------
#>
#> CLASSIFICATION OF CONSTRUCTS:
#>
#> Note: Constructs aligned so 'Self' corresponds to left pole
#>
#> Construct Self Ideal Difference Classification
#> 1 balanced - get along with conflicts 1 4 3 discrepant
#> 2 isolated - sociable 3 6 3 discrepant
#> 3 closely integrated - excluded 2 2 0 congruent
#> 4 passive - discursive 3 6 3 discrepant
#> 5 open minded - indifferent 2 1 1 congruent
#> 6 dispassionate - dreamy 3 2 1 congruent
#> 7 practically oriented - depressed 2 1 1 congruent
#> 8 serious - playful 3 2 1 congruent
#> 9 socially minded - selfish 2 1 1 congruent
#> 10 peaceful - quarrelsome 2 2 0 congruent
#> 11 technical - artistic 2 6 4 discrepant
#> 12 scientific - emotional 2 1 1 congruent
#> 13 extrovert - introvert 3 2 1 congruent
#> 14 wanderlust - home oriented 1 1 0 congruent
#>
#> -------------------------------------------------------------------------------
#>
#> IMPLICATIVE DILEMMAS:
#>
#> Note: Congruent constructs on the left - Discrepant constructs on the right
#>
#> Congruent Discrepant R
#> 1 5. open minded - indifferent 1. balanced - get along with conflicts 0.53
#> 2 9. socially minded - selfish 1. balanced - get along with conflicts 0.36
#> 3 10. peaceful - quarrelsome 1. balanced - get along with conflicts 0.84
#> 4 14. wanderlust - home oriented 1. balanced - get along with conflicts 0.72
#> RexSI
#> 1 0.63
#> 2 0.43
#> 3 *Not implemented
#> 4 0.79
#>
#> R = Correlation including Self & Ideal
#> RexSI = Correlation excluding Self & Ideal
#> R was used as criterion
# adjust minimal correlation
indexDilemma(boeker, self = 1, ideal = 2, r.min = .5)
#>
#> ####################
#> Implicative Dilemmas
#> ####################
#>
#> -------------------------------------------------------------------------------
#>
#> SUMMARY:
#>
#> No. of Implicative Dilemmas (IDs): 3
#> No. of possible construct pairs: 91
#> Percentage of IDs (PID): 3.3% (3/91)
#> Intensity of IDs (IID): 69.6
#> Proportion of the intensity of constructs of IDs (PICID): 2.3
#>
#> -------------------------------------------------------------------------------
#>
#> PARAMETERS:
#>
#> Self: Element No. 1 = self
#> Ideal: Element No. 2 = ideal self
#>
#> Correlation Criterion: >= 0.5
#> Note: Correlation calculated including elements Self & Ideal
#>
#> Criteria (for construct classification):
#> Discrepant if Self-Ideal difference: >= 3
#> Congruent if Self-Ideal difference: <= 1
#>
#> -------------------------------------------------------------------------------
#>
#> CLASSIFICATION OF CONSTRUCTS:
#>
#> Note: Constructs aligned so 'Self' corresponds to left pole
#>
#> Construct Self Ideal Difference Classification
#> 1 balanced - get along with conflicts 1 4 3 discrepant
#> 2 isolated - sociable 3 6 3 discrepant
#> 3 closely integrated - excluded 2 2 0 congruent
#> 4 passive - discursive 3 6 3 discrepant
#> 5 open minded - indifferent 2 1 1 congruent
#> 6 dispassionate - dreamy 3 2 1 congruent
#> 7 practically oriented - depressed 2 1 1 congruent
#> 8 serious - playful 3 2 1 congruent
#> 9 socially minded - selfish 2 1 1 congruent
#> 10 peaceful - quarrelsome 2 2 0 congruent
#> 11 technical - artistic 2 6 4 discrepant
#> 12 scientific - emotional 2 1 1 congruent
#> 13 extrovert - introvert 3 2 1 congruent
#> 14 wanderlust - home oriented 1 1 0 congruent
#>
#> -------------------------------------------------------------------------------
#>
#> IMPLICATIVE DILEMMAS:
#>
#> Note: Congruent constructs on the left - Discrepant constructs on the right
#>
#> Congruent Discrepant R
#> 1 5. open minded - indifferent 1. balanced - get along with conflicts 0.53
#> 2 10. peaceful - quarrelsome 1. balanced - get along with conflicts 0.84
#> 3 14. wanderlust - home oriented 1. balanced - get along with conflicts 0.72
#> RexSI
#> 1 0.63
#> 2 *Not implemented
#> 3 0.79
#>
#> R = Correlation including Self & Ideal
#> RexSI = Correlation excluding Self & Ideal
#> R was used as criterion
# adjust congruence and discrepance ranges
indexDilemma(boeker, self = 1, ideal = 2, diff.congruent = 0, diff.discrepant = 4)
#>
#> ####################
#> Implicative Dilemmas
#> ####################
#>
#> -------------------------------------------------------------------------------
#>
#> SUMMARY:
#>
#> No. of Implicative Dilemmas (IDs): 0
#> No. of possible construct pairs: 91
#> Percentage of IDs (PID): 0.0% (0/91)
#> Intensity of IDs (IID): NaN
#> Proportion of the intensity of constructs of IDs (PICID): 0
#>
#> -------------------------------------------------------------------------------
#>
#> PARAMETERS:
#>
#> Self: Element No. 1 = self
#> Ideal: Element No. 2 = ideal self
#>
#> Correlation Criterion: >= 0.35
#> Note: Correlation calculated including elements Self & Ideal
#>
#> Criteria (for construct classification):
#> Discrepant if Self-Ideal difference: >= 4
#> Congruent if Self-Ideal difference: <= 0
#>
#> -------------------------------------------------------------------------------
#>
#> CLASSIFICATION OF CONSTRUCTS:
#>
#> Note: Constructs aligned so 'Self' corresponds to left pole
#>
#> Construct Self Ideal Difference Classification
#> 1 balanced - get along with conflicts 1 4 3 neither
#> 2 isolated - sociable 3 6 3 neither
#> 3 closely integrated - excluded 2 2 0 congruent
#> 4 passive - discursive 3 6 3 neither
#> 5 open minded - indifferent 2 1 1 neither
#> 6 dispassionate - dreamy 3 2 1 neither
#> 7 practically oriented - depressed 2 1 1 neither
#> 8 serious - playful 3 2 1 neither
#> 9 socially minded - selfish 2 1 1 neither
#> 10 peaceful - quarrelsome 2 2 0 congruent
#> 11 technical - artistic 2 6 4 discrepant
#> 12 scientific - emotional 2 1 1 neither
#> 13 extrovert - introvert 3 2 1 neither
#> 14 wanderlust - home oriented 1 1 0 congruent
#>
#> -------------------------------------------------------------------------------
#>
#> IMPLICATIVE DILEMMAS:
#>
#> Note: Congruent constructs on the left - Discrepant constructs on the right
#>
#> No implicative dilemmas detected
# print options (see ?print.indexDilemma for help)
print(id, output = "D") # dilemmas only
#>
#> ####################
#> Implicative Dilemmas
#> ####################
#>
#> -------------------------------------------------------------------------------
#>
#> IMPLICATIVE DILEMMAS:
#>
#> Note: Congruent constructs on the left - Discrepant constructs on the right
#>
#> Congruent Discrepant R
#> 1 5. open minded - indifferent 1. balanced - get along with conflicts 0.53
#> 2 9. socially minded - selfish 1. balanced - get along with conflicts 0.36
#> 3 10. peaceful - quarrelsome 1. balanced - get along with conflicts 0.84
#> 4 14. wanderlust - home oriented 1. balanced - get along with conflicts 0.72
#> RexSI
#> 1 0.63
#> 2 0.43
#> 3 *Not implemented
#> 4 0.79
#>
#> R = Correlation including Self & Ideal
#> RexSI = Correlation excluding Self & Ideal
#> R was used as criterion
print(id, output = "OD") # overview and dilemmas
#>
#> ####################
#> Implicative Dilemmas
#> ####################
#>
#> -------------------------------------------------------------------------------
#>
#> IMPLICATIVE DILEMMAS:
#>
#> Note: Congruent constructs on the left - Discrepant constructs on the right
#>
#> Congruent Discrepant R
#> 1 5. open minded - indifferent 1. balanced - get along with conflicts 0.53
#> 2 9. socially minded - selfish 1. balanced - get along with conflicts 0.36
#> 3 10. peaceful - quarrelsome 1. balanced - get along with conflicts 0.84
#> 4 14. wanderlust - home oriented 1. balanced - get along with conflicts 0.72
#> RexSI
#> 1 0.63
#> 2 0.43
#> 3 *Not implemented
#> 4 0.79
#>
#> R = Correlation including Self & Ideal
#> RexSI = Correlation excluding Self & Ideal
#> R was used as criterion
# plot dilemmas as network graph (see ?plot.indexDilemma for help)
# set a seed for reproducibility
plot(id, layout = "rows")
plot(id, layout = "circle")
plot(id, layout = "star")
```