Description Usage Arguments Details Value Calculations Author(s) References See Also Examples
Calculate powertransformed Hartmann distances.
1 2 3 4 5 6 7  distanceNormalized(
x,
reps = 1000,
prob = NULL,
progress = TRUE,
distributions = TRUE
)

x 

reps 
Number of random grids to generate to produce
sample distribution for Hartmann distances
(default is 
prob 
The probability of each rating value to occur.
If 
progress 
Whether to show a progress bar during simulation
(default is 
distributions 
Wether to additionally return the values of the simulated
distributions (Slater etc.) The default is 
Hartmann (1992) suggested a transformation of Slater (1977) distances to make
them independent from the size of a grid. Hartmann distances are supposed to
yield stable cutoff values used to determine 'significance' of interelement
distances. It can be shown that Hartmann distances are still affected by grid
parameters like size and the range of the rating scale used (Heckmann, 2012).
The function distanceNormalize
applies a BoxCox (1964) transformation to the
Hartmann distances in order to remove the skew of the Hartmann distance
distribution. The normalized values show to have more stable cutoffs
(quantiles) and better properties for comparison across grids of different
size and scale range.
The function distanceNormalize
can also return
the quantiles of the sample distribution and only the element distances
consideres 'significant' according to the quantiles defined.
A matrix containing the standardized distances.
Further data is contained in the object's attributes:

A list of several parameters
including 

Quantiles for Slater, Hartmann and power transformed distance distribitions. 

List with values of the
simulated distributions, if 
The 'power tranformed Hartmann distance' are calulated as follows: The simulated Hartmann distribution is added a constant as the BoxCox transformation can only be applied to positive values. Then a range of values for lambda in the BoxCox transformation (Box & Cox, 1964) are tried out. The best lambda is the one maximizing the correlation of the quantiles with the standard normal distribution. The lambda value maximizing normality is used to transform Hartmann distances. As the resulting scale of the power transformation depends on lambda, the resulting values are ztransformed to derive a common scaling.
The code for the calculation of the optimal lambda was written by Ioannis Kosmidis.
Mark Heckmann
Box, G. E. P., & Cox, D. R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society. Series B (Methodological), 26(2), 211252.
Hartmann, A. (1992). Element comparisons in repertory grid technique: Results and consequences of a Monte Carlo study. International Journal of Personal Construct Psychology, 5(1), 4156.
Heckmann, M. (2012). Standardizing interelement distances in grids  A revision of Hartmann's distances, 11th Biennal Conference of the European Personal Construct Association (EPCA), Dublin, Ireland, Paper presentation, July 2012.
Slater, P. (1977). The measurement of intrapersonal space by Grid technique. London: Wiley.
distanceHartmann
and distanceSlater
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  ## Not run:
### basics ###
distanceNormalized(bell2010)
n < distanceNormalized(bell2010)
n
# printing options
print(n)
print(n, digits=4)
# 'significant' distances only
print(n, p=c(.05, .95))
# access cells of distance matrix
n[1,2]
### advanced ###
# histogram of Slater distances and indifference region
n < distanceNormalized(bell2010, distributions=TRUE)
l < attr(n, "distributions")
hist(l$bc, breaks=100)
## End(Not run)

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