Effect of Rancher’s Management Philosophy, Grazing Practices, and Personal Characteristics on Sustainability Indices for North Central Texas Rangeland Page: 71
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Traditional PCA is a variable reduction technique which maximizes the amount of
variance accounted for in the observed variables by identifying a smaller group of variables
called components (Starkweather, 2010a).
Principle component analysis was used as a means of identifying a subset of variables
based on which original variables have the highest correlation with the principal components,
also known as component loadings (Garson, 2011 b; StatSoft Inc., 2011). The analysis was run
using SPSS 18.0. Data was loaded into SPSS after optimal scaling. Sections, 1, 3, and 6 were
analyzed with PCA separately. An extra, fourth PCA was also conducted using variables that
did not help to maximize Crobach's Alpha and were therefore not used in resulting sustainability
Selection of Components
According to Field (2005) a scree plot should be used to determine number of factors in
instances where the number of variables is between 30 and 250, which is consistent with the data
derived from the questionnaire. However, he also explains that the sample size needs to be
greater than 200, which is not consistent with this study.
Another method beginning to gain popularity for determining the number of principal
components is the use of "Parallel Engine Analysis". This analysis is based on parameters
provided by the researcher. It calculates eigenvalues from randomly generated correlation
matrices. These can be then compared with eigenvalues extracted from the researcher's dataset.
The number of factors to retain will be the number of eigenvalues that are larger than the
corresponding random eigenvalues (Horn, 1965). A parallel analysis engine to aid determining
number of factors to retain is available online at: http://ires.ku.edu/~smishra/parallelengine.htm/.
The engine utilizes a SAS-based code written by O'Connor (2000).
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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/m1/82/: accessed May 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .