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only show subset of element to fit pdf page
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markheckmann committed Dec 29, 2023
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5 changes: 3 additions & 2 deletions paper.Rmd
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Expand Up @@ -31,7 +31,7 @@ pre {

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, comment = "")
options(width = 200)
options(width = 100)
library(OpenRepGrid)
```

Expand Down Expand Up @@ -106,7 +106,8 @@ pvrect(s, max.only = FALSE)
Inter-element distances are a commonly applied measure in the statistical analysis of grid data [@fransella_manual_2004]. As already shown in the biplot example above, distances between elements indicate which elements (i.e. persons) are construed as similar. One distance of particular intererest in psychotherapy research is the self-ideal distance as it may provide useful clinical indications [e.g. @taylor_investigating_2020]. But also in other areas, for example, in market research element distances are frequently used in the analysis [e.g. @hauser_measuring_2011]. In most cases, the Euclidean distance is selected as a distance measure. As the maximal Euclidean distances between two elements depends on the rating scale and the number of constructs in a grid, several approaches to standardizing inter-element distances have been suggested. One well known approach which has come to be known as *Slater distances*, divides the inter-element distance by its expected value [@slater_measurement_1977]. However, @hartmann_element_1992 showed in a simulation study that Slater distances have a skewed distribution, as well as a mean and a standard deviation depending on the number of elicited constructs. Hartmann suggested an improvement measure by applying a transformation to standardize Slater distances across different grid sizes. This development serves as another example of above mentioned situation, as to the best of my knowledge, Hartmann distances are currently only implemented in OpenRepGrid and no other grid software. Hartmann distances can be calculated using the following code.

```{r hartmann, echo=T}
distanceHartmann(boeker)
ss <- boeker[, 1:8] # show only subset of elements, to fit PDF page
distanceHartmann(ss)
```

The last feature example concers the detection of implicative dilemmas. Implicative dilemmas represent a form of cognitive conflict. An implicative dilemma arises when a desired change on one construct is associated with an undesired change on another construct. For example, a *timid* person may wish to become more *socially skilled* but associates being more socially skilled with several negative characteristics (selfish, insensitive etc.). The person might, for example, construe the implication of becoming less timid (desired) as becoming more selfish (undesired) at the same time [@winter_construct_1982]. As a consequence, the person may resist to the desired change if the presumed implications will threaten the person's identity and the predictive power of his construct system. The investigation of the role of implicative dilemmas in different mental disorders is an active field of research in Personal Construct Psychology [e.g. @feixas_multi-center_2004; @dorough_implicative_2007; @rouco_measurement_2019]. Implicative dilemma can be detected using the `indexDilemma` function. For the dataset above, the results show that a desired change on the discrepant contruct *balanced - get along with conflicts* towards the *get along with conflicts* pole implies four undesired changes, for example, to become more *indifferent* and less *peaceful*.
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28 changes: 11 additions & 17 deletions paper.md
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Expand Up @@ -106,7 +106,8 @@ Inter-element distances are a commonly applied measure in the statistical analys


```r
distanceHartmann(boeker)
ss <- boeker[, 1:8] # show only subset of elements, to fit PDF page
distanceHartmann(ss)
```

```
Expand All @@ -117,22 +118,15 @@ Distances between elements
Distance method: Hartmann (standardized Slater distances)
Normalized:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(1) self 1 -0.28 1.58 1.92 0.80 -1.33 1.20 -0.29 -0.04 2.62 -5.24 2.66 2.87 2.28 2.89
(2) ideal self 2 -0.78 1.36 -0.47 -2.09 -0.56 0.12 -1.02 0.12 -3.69 -1.50 -1.45 -1.63 -1.71
(3) mother 3 1.70 2.99 0.22 2.82 1.15 2.27 2.09 -3.84 1.91 1.06 1.44 1.92
(4) father 4 2.31 -1.04 2.23 0.55 1.00 1.92 -4.39 0.96 0.50 0.08 0.63
(5) kurt 5 0.63 2.72 1.27 2.69 1.74 -3.37 1.30 0.35 0.79 1.01
(6) karl 6 0.29 1.63 2.14 -0.66 0.10 -1.21 -1.53 -0.60 -1.04
(7) george 7 0.45 2.19 1.17 -3.39 1.70 0.54 0.42 1.35
(8) martin 8 2.03 1.22 -1.85 -0.67 -0.73 -0.13 -0.53
(9) elizabeth 9 0.76 -2.07 -0.08 -0.91 -0.29 0.05
(10) therapist 10 -4.91 2.20 2.35 1.97 2.22
(11) irene 11 -5.47 -5.65 -4.79 -5.52
(12) childhood self 12 3.66 3.16 4.22
(13) self before illness 13 3.60 3.79
(14) self with delusion 14 3.52
(15) self as dreamer 15
1 2 3 4 5 6 7 8
(1) self 1 -0.32 0.86 1.49 0.14 -1.48 0.69 -0.78
(2) ideal self 2 -1.32 0.73 -1.00 -3.01 -1.27 -0.75
(3) mother 3 0.89 2.23 -0.49 2.14 0.38
(4) father 4 1.72 -2.03 1.51 -0.56
(5) kurt 5 -0.25 1.97 0.31
(6) karl 6 -0.58 0.85
(7) george 7 -0.62
(8) martin 8
For calculation the parameters from Hartmann (1992) were used. Use 'method=new' or method='simulate' for a more accurate version.
```
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