### Description

*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, Saúl, & Sanchez, 2000). The
investigation of the role of cognitive dilemma in different disorders in
the context of PCP is a current field of research (Dorough, Grice, & Parker, 2007; e.g. Feixas &
Saúl, 2004).

### Process of detection

The detection of implicative dilemmas happens in two steps. First the constructs are classified as being ‘congruent’ or ‘discrepant’. Second 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. 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 if the construct is congruent or discrepant is supplied as an argument, the values are chosen acording 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 & Saúl, 2004). The user may also chose 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 selflish. 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 for implication.

### R-Code

To detect implicative dilemma use the function
`indexDilemma`

. It will output an overview over the arguments
used in the detection, a table of classifications of the construct and
the implicative dilemmas that have been detected.

```
indexDilemma(boeker, self = 1, ideal = 2)
#
# ####################
# 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 RexSI
# 1 5. open minded - indifferent 1. balanced - get along with conflicts 0.53 0.63
# 2 9. socially minded - selfish 1. balanced - get along with conflicts 0.36 0.43
# 3 10. peaceful - quarrelsome 1. balanced - get along with conflicts 0.84 *Not implemented
# 4 14. wanderlust - home oriented 1. balanced - get along with conflicts 0.72 0.79
#
# R = Correlation including Self & Ideal
# RexSI = Correlation excluding Self & Ideal
# R was used as criterion
```

To change the values for the classification of the constructs as
congruent and discrepant use the argument `diff.congruent`

.
The following output is identical to the Gridstat default.

```
indexDilemma(boeker, self = 1, ideal = 2, diff.congruent = 0)
#
# ####################
# Implicative Dilemmas
# ####################
#
# -------------------------------------------------------------------------------
#
# SUMMARY:
#
# No. of Implicative Dilemmas (IDs): 2
# No. of possible construct pairs: 91
# Percentage of IDs (PID): 2.2% (2/91)
# Intensity of IDs (IID): 77.9
# Proportion of the intensity of constructs of IDs (PICID): 1.7
#
# -------------------------------------------------------------------------------
#
# 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: <= 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 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 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
#
# Congruent Discrepant R RexSI
# 1 10. peaceful - quarrelsome 1. balanced - get along with conflicts 0.84 *Not implemented
# 2 14. wanderlust - home oriented 1. balanced - get along with conflicts 0.72 0.79
#
# R = Correlation including Self & Ideal
# RexSI = Correlation excluding Self & Ideal
# R was used as criterion
```

Several other argumnets can be modified. Type the following code into the R console to see the results.

```
indexDilemma(boeker, self = 1, ideal = 2, output = 2) # show identified dillemas only
indexDilemma(boeker, 1, 2, diff.disc = 0, diff.con = 4) # set classification parameters
indexDilemma(boeker, 1, 2, index = F) # no index numbers
indexDilemma(boeker, 1, 2, trim = 20) # trim construct labels
```

Called for console output. Invisibly returns a list containing the result dataframes and all results from the calculations.

```
r <- indexDilemma(boeker, self = 1, ideal = 2)
r$res1
r$res2
r$res3
r$res4
```

### Literature

*Personal Construct Theory & Practice*,

*4*, 83–101.

*The Spanish Journal of Psychology*,

*7*(1), 69–78. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/15139250

*The person in society: Challenges to a constructivist theory*. Giessen: Psychosozial-Verlag.

*The British Journal of Medical Psychology*,

*55 (Pt 3)*, 257–269. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/7126491