Effect of Rancher’s Management Philosophy, Grazing Practices, and Personal Characteristics on Sustainability Indices for North Central Texas Rangeland Page: 78
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validation as a useful tool to identify if the model derived from the study can be used to predict
the outcome in a different sample. Two methods can be used to do this: Shrinkage and Data
The manner in which regression weights are computed guarantee that they will provide
an optimal fit with respect to the least square criterion for the existing set of data. Prediction
using a different data set leads to regression weights that are no longer optimal. This loss in
predictive power is referred to as shrinkage (Stockburger, 2006).
In SPSS adjusted R2 indicates shrinkage when variance is applied to other populations,
while R2 explains the variance in Y accounted for from the sample in the study. SPSS uses
Wherry's formula to derive at the adjusted R2. A much better indication of cross validation is
Steins's formula (Yin and Fan, 2001). Because of this fact, all adjusted R2 were recalculated by
hand then inserted in place of Wherry's formula for the most parsimonious block of the
hierarchical regression analysis. Whereas, Stein's formula is as follows, where n = number of
cases, and k is the number of predictors:
adjustedR2= 1 -[(n- 1/n- k- 1)(n-2/n- k- 2)(n+1/n)](1 -R2)
Data splitting is a good technique, but Field (2005) explains that researchers rarely have
enough cases t make splitting the data set practical. The procedure would be simply splitting the
cases in the study, computing a regression equation on two halves and comparing the results.
An alternative cross-validation method to simple data splitting is K-fold cross-validation.
With this method k- folds are randomly removed from the data set. (Starkweather, 2011 e) The
original data set is randomly divided into K subsamples. A single subsample is retained as the
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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/m1/89/: accessed February 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .