Multivariate Analysis of Variance for Stream Classification in Texas Eric S. Hersh CE397 Statistics in Water Resources Term Project Cinco de Mayo, 2009 Can we quantitatively regionalize the streams of Texas? Hersh, E.S., Maidment, D.R., and W.S. Gordon. An Integrated Stream Classification System to Support Environmental Flow Analyses in Texas. J. Am. Water Res. Assoc. Submitted November 2008. Revisited - the question posed Can we improve the way in which we perform the regionalization and thus (potentially) increase its classification strength? Analysis of Variance ANOVA Purpose: test whether group means are different MANOVA Multivariate Analysis of Variance Purpose: ANOVA with several dependent variables Multiple metric dependent variables (n=18) Based on categorical (non-metric) independent variables (n=5 regions) Manipulate independent variables to determine effect on dependent variables using SAS PROC GLM (general linear model) Region = DO Temp TSS pH Cond AirTemp Precip PET MAQ MAV BFI ZeroQ IQR Slope Substrate Sand Silt Clay The Model ANOVAMANOVA == = where: p = parameter (dependent variable) k = factor (independent variable) Data Gaps Total number of subbasins in Texas = 205 Number with complete data = 103 Uh oh! This test is going to lose a lot of value. Unless Can we fill in the gaps somehow? Data Gaps Some of the subbasins in Texas have no rivers. Many have no gages. Many have no WQ sampling stations. Synthetic data would be difficult and poor. But, the MANOVA test requires complete matrices. Solution: fill in gaps with parameter means Dilutes strength of classification (regions tend toward others) Hypothesis Test Null Hypothesis: (vectors of) the group means are equal Of course not! Thats preposterous! There would be no regionalization! But we dont care. (PRISM, ) West East Evaluating the Model Pillais trace considered most robust S.S. Pillai, , Indian mathematician Revision Methodology 1.Identify bordering subbasins (n=50, but 10 border multiple, so 60 trials total) 2.Switch one subbasin, check for increase in test stat, record and reset (21 deemed beneficial) 3.Rank by improvement 4.Implement changes in order, discard if decline (18 kept) 5.View in geographic context, apply decision rules (no islands or peninsulas, 15 kept) OLDNEW SWITCHED Possible Future Work Write final report