A goodness-of-fit test for the bivariate necessary-but-not-sufficient relationship
Date
2020-07-31
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Abstract
In the social sciences, theory often casts bivariate relationships between constructs in terms of logical asymmetries. For example, in psychology, one theory is that intelligence is necessary but not sufficient for creativity. But as average-based linear models fail to accommodate nuances of logical asymmetries, a mismatch between theory and method is common in the literature. Recent methodological work proposed the Linear Ceiling and Floor Probability Region (LCFPR) model, which analyzes bivariate relationships in terms of necessity and sufficiency. However, an erroneous treatment of nested models and a lack of a formal goodness-of-fit test remain unaddressed in the LCFPR framework. In this thesis, I propose a goodness-of-fit test for LCFPR that addresses such shortcomings. A simulation study shows that, using a nonparametric quantile, the power and size of the test are largely acceptable. Analyses of real datasets demonstrate the proposed procedure. Conclusions and future directions are outlined in the final chapter.
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Keywords
logical asymmetries, goodness-of-fit, beta distribution, intelligence, creativity
Citation
Ilagan, M. (2020). A goodness-of-fit test for the bivariate necessary-but-not-sufficient relationship (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.