Effect of Rancher’s Management Philosophy, Grazing Practices, and Personal Characteristics on Sustainability Indices for North Central Texas Rangeland Page: 70
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loss function can be used as total discrepancy index or criteria for determining acceptability of
cases. Smaller loss equates to more closely achieving bilinearizability a discrepancy index of 0
would be perfect. This is not realistic for real-life applications. In fact, de Leeuw et al. (1999)
mention that we may be able to successfully approximate bilinearizability in ordinal data but it is
very unlikely in purely nominal variables. Still, minimization using LINEALS, even with
nominal data leads to a lower discrepancy compared to other optimal scaling techniques.
Therefore, if the aim is to achieve bilinearization, LINEALS should be considered (Mair and de
Continuous variables were not optimally scaled. Instead these were removed from the
data set prior to optimization. The discretized variables and the continuous variables were then
recombined into a data set and used for further the analysis. Handling of the continuous data in
this manner is similar to ordinal regression as carried out by SPSS (SPSS Inc, 2009b).
Principal Component Analysis
With 214 original variables, it was necessary to methodically select a subset of variables,
based on which original variables have the highest correlations with the principal component
factors within each section of the survey. The subsets retain only those variables with
meaningful relationships to the structure of the survey (Garson, 2011 b).
When attempting to measure a construct with multiple predictors, the items must measure
the same thing or measurement error will be present. Also, measurement error would increase
standard error in subsequent regression analysis (Garson, 2011 c). Because of this, some form of
variable reduction must occur. This can be accomplished with principal component analysis
(PCA), which is a preferred method for data reduction, (StatSoft Inc., 2011).
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Becker, Wayne. Effect of Rancher’s Management Philosophy, Grazing Practices, and Personal Characteristics on Sustainability Indices for North Central Texas Rangeland, dissertation, December 2011; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc103289/m1/81/: accessed April 29, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .