- Title
- Diagnostic tools and remedial methods for collinearity in linear regression models with spatially varying coefficients
- Author
- Wheeler, David C
- Degree
- Doctor of Philosophy, Ohio State University,
Geography, 2006.
- Advisor
- Morton O'Kelly
- Pages
- 150p.
- Abstract
- The realization in the statistical and geographical sciences that a relationship between an explanatory variable and a response variable in a linear regression model is not always constant across a study area has lead to the development of regression models that allow for spatially varying coefficients. Two competing models of this type are geographically weighted regression (GWR) and Bayesian regression models with spatially varying coefficient processes (SVCP). In the application of these spatially varying coefficient models, marginal inference on the regression coefficient spatial processes is typically of primary interest. In light of this fact, there is a need to assess the validity of such marginal inferences, since these inferences may be misleading in the presence of explanatory variable collinearity. The presence of local collinearity in the absence of global collinearity necessitates the use of diagnostic tools in the local regression model building process to highlight areas in which the results are not reliable for statistical inference. The method of ridge regression and the lasso can also be integrated into the GWR framework to constrain and stabilize regression coefficients and lower prediction error. This dissertation presents numerous diagnostic tools and remedial methods for GWR and demonstrates the utility of these techniques with example datasets. In addition, I present the results of simulation studies designed to evaluate the sensitivity of the spatially varying coefficients in the competing models to various levels of collinearity. The results of the simulation studies show that the Bayesian regression model produces more accurate inferences overall on the regression coefficients than does GWR. In addition, the Bayesian regression model is fairly robust in terms of marginal coefficient inference to moderate levels of collinearity, while GWR degrades more substantially with strong collinearity. The simulation study results also show that penalized versions of GWR models produce lower prediction and estimation error of the response variable than does GWR. In addition, penalized versions of GWR also lower the estimation error of the regression coefficients compared to GWR, particularly in the presence of collinearity.
- Subject Headings
- Statistics ; Geography
- Keywords
- regression; GWR; spatial statistics; collinearity; Bayesian statistics
Document number: osu1155413322.
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