An analytic method frequently used in geography and many other scientific disciplines is to calculate the statistical expression of an "expected" relationship and then to compare measurements of actual observations with values that would be expected if the statistical expression was accurate. Differences between the real and expected values are termed residuals; through analysis of the pattern of residuals, investigators often can detect other systematic regularities in the relationships among different variables. This project will explore new methods of measuring and analyzing the regularities in residuals, focusing on different types of systematic variation that commonly occur in data gathered at different time periods for different geographic locations or for other observational units. Techniques have been developed for dealing with heteroscedasticity and autocorrelation, two situations in which normal statistical assumptions related to the independence of observations and their variances are violated. Relatively little attention has been given to a third form of systematic variability, contemporaneous correlation, which measures how observations for specific observational units vary together over time. The investigator will focus his attention in this project on the refinement of statistics for measuring cross-sectional heteroscedasticity, longitudinal autocorrelation, and contemporaneous correlation. Development of these statistics will focus on their application for two lines of inquiry: (1) empirical modelling of interstate migration rates, and (2) estimation of future expected warranty claims based on actuarial approaches. This project will advance statistical methods for the analysis of data relating three or more dimensions, especially longitudinal spatial data. It will result in new measures for evaluating patterns of residuals, measures that will be useful for retroactive modelling and for forecasting. Although primarily methodological in emphasis, the project also will generate new insights into specific types of inquiries. It will provide a means for relating gravity models and Markovian models in migration studies, and it will enhance the utility of cross-sectional data in the determination of warranty contracts.
