Effect of Rancher’s Management Philosophy, Grazing Practices, and Personal Characteristics on Sustainability Indices for North Central Texas Rangeland Page: 73
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analysis is working best. Likewise, low communalities may indicate that a predictor is not
working well and should be removed from the model. However, this is not always necessarily
so. Communalities must be interpreted in relation to the interpretability of the
factors/components. A communality of 0.75, which seems high, could actually be meaningless if
the component is not interpretable. On the other hand, a low communality may be meaningful if
it contributes to a well defined factor. Therefore, what is most important, more so than the actual
value, is the extent to which it contributes to the interpretation of the factor (Garson, 2011 b).
Communalities are reported in this section of the results, so as to not lose sight of that fact, and
to aid in interpretation of variables.
Once the number of components, to be accepted as relevant is determined, component
loadings must be interpreted. Interpretation involves selecting variables which contribute to each
component's identity. There is some subjectivity involved when interpreting component
loadings. Various researches follow different rules of thumb. In confirmatory factor analysis, as
opposed to PCA, loadings should be 0.7 or higher to confirm that independent variables
identified a priori are represented by a particular factor. Reasoning is such that the 0.7 level
corresponds to about half of the variance in the indicator being explained by the factor. With
many data sets, the .7 standard is a high one and often data cannot meet this criterion. Often,
especially for exploratory purposes (PCA), researchers will use a lower level such as .4 for the
central factor and .25 for other factors (Raubenheimer, 2004). One example, Hair et al. (1998),
call loadings above 0.6 "high" and those below 0.4 "low". Factor/component loadings must be
interpreted in the light of theory, not by arbitrary cutoff levels (Garson, 2011 b).
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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/m1/84/: accessed October 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .