indexDilemma: Detect implicative dilemmas (conflicts).
In OpenRepGrid: Tools to analyse repertory grid data

Description Usage Arguments Details Value Author(s) References Examples

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).

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

`x`	`repgrid` object.
`self`	Numeric. Index of self element.
`ideal`	Numeric. Index of ideal self element.
`diff.mode`	Numeric. Mode to classify construct pairs into congruent and discrepant. `diff.mode=1` will use the difference in ratings between the self and the ideal element to determine if the construct is congruent or discrepant. No other modes have yet been implemented.
`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`).
`output`	The type of output printed to the console. `output=1` prints classification of the construct into congruent and discrepant and the detected dilemmas. `output=1` only prints the latter. `output=0` will surpress printing. Note that the type of output does not affect the object that is returned invisibly which will be the same in any case (see value).
`show`	Whether to additionally plot the distribution of correlations to help the user assess what level is adequate for `r.min`.
`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.
`digits`	Numeric. Number of digits to round to (default is `2`).

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 & Saul, 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.

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

Mark Heckmann

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.

## Not run: 

indexDilemma(boeker, self=1, ideal=2)
indexDilemma(boeker, self=1, ideal=2, out=2)

# additionally show correlation distribution
indexDilemma(boeker, self=1, ideal=2, show=T)

# adjust minimal correlation
indexDilemma(boeker, 1, 2, r.min=.25)

# adjust congruence and discrepance ranges
indexDilemma(boeker, 1, 2, diff.con=0, diff.disc=4)


## End(Not run)