Models of Regional Skew Based on Bayesian GLS Regression

The skew map developed by Hardison in 1974 was based on records of at least 25 years in lengths. It is still used today, over 30 years later. The first edition of Bulletin 17 states: "It is expected that Plate 1 [the skew map] will be revised as more data become available and more extensive studies are completed." Today, tremendous advances in computing power and spatial statistical methods allow for a much better analysis of the larger data set now available. This paper describes a Bayesian Generalized Least Squares (B-GLS) framework together with diagnostic statistics introduced by Reis et al. that can be used to develop regional skew relationships. An example using data from the Illinois River Basin illustrates useful diagnostic statistics including pseudo R², Bayesian plausibility, leverage, influence and σ-influence. The B-GLS framework and diagnostic statistics developed in this analysis are being applied to an ongoing study in the southeast United States which will produce a regional skew estimator.