140-2008: Data Mining Application of Non-Linear Mixed Modeling in Water Quality Analysis

In regression analysis, non-linearity in fixed and random effects can adversely affect efficiency of regression parameter estimates. Successful non-linear time series modeling would improve regression parameter estimates and produce a richer notion of water quality than linear time series models allow. In addition multiple independent variables make each point in space a finite dimensional vector, non-linear in two dimensions jointly. The SAS/STAT procedure, NLMIXED fits non-linearity successfully in any time series using maximum likelihood-based methods. In this data mining study spatial and temporal variations of total phosphorus concentration (TP) in Truckee River, Nevada, sampled monthly (from January 1997 to December 2004) over six sites were modeled as a function of soluble total phosphorus concentration (STP), stream flow (SF), seasonality (Summer), man-made intervention (X1), alkalinity, pH, temperature (Temp), dissolved organic carbon (DOC), and dissolved oxygen(DO) using the non-linear regression capabilities provided with the NLMIXED procedure in SAS® after successfully identifying non linearity in data. Likelihood ratio tests were conducted for model specification, and for tests of various hypotheses on individual cross sections. Results of parameter estimates, model diagnostics, and residual analyses were compared to that obtained from a linear mixed model fitted to the same data using PROC MIXED. Non linear model fitted data better. All independent variables influenced TP significantly (p<0.0001). Tests of cross sectional effects showed significant contributions of TP from all sites (p<0.0001) into Truckee River. Non-linearity in data can influence time series regression parameter estimates significantly.