Effect of Rancher’s Management Philosophy, Grazing Practices, and Personal Characteristics on Sustainability Indices for North Central Texas Rangeland Page: 75
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models that are likely to be the best, using "approximate posterior model probability." This
means finding the post regression probability that each variable is non-zero (Raftery et al., 2011).
It then averages variables, over the best models in the model class (Raftery, 1995; Raftery et al.,
This function is capable of selecting the best set of predictor variables for a linear
prediction model by building a normal curve distribution of how frequently a predictor is coming
up in a significant model. The model with the best fit is determined by the model with the
largest posterior probability and the lowest Bayesian information criterion (BIC) (Starkweather,
201 id). When estimating model parameters, it is possible to "overfit", or superficially improve
the outcome, by continually adding additional parameters. This method of model selection
protects against the possibility of"overfitting" by introducing a penalty for additional parameters
as opposed to simply maximizing for the amount of variance explained (McQuarrie, 1998).
To determine predictors impact on the sustainability indexes created from sections 2, 4,
and 5, impact was assessed from each set of predictors (variables) in section 1, 3, 6 and "other
variables". Whereas, the sustainability index from section 2 becomes the first dependent
variable, all variables identified in prior PCA computations are then inputted into the "bicreg"
function using the BMA package in R version 2.13.0. The same holds true for section 4, and
then section 5. This necessarily means that 3 separate analyses must be run, one for each
dependent variable: the sustainability indices. Output indicated which variables should be
inserted into ordinary least squares regression. The variables which have been identified as
returning the best model was accepted (Raftery, 1995).
Hierarchical Regression Analysis
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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/m1/86/: accessed February 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .