Predictor-independent linear models relating lognormally distributed Escherichia coli and fecal coliforms

Following an EPA recommendation many states switched to Escherichia coli (EC) water-quality standards. However, past data is still in terms of fecal coliforms (FC). EC-FC models are therefore necessary to understand long-term water-quality trends. The predominant method develops a linear relationship between log EC and log FC by minimizing the errors of log EC. These models are difficult to interpret as they are nonlinear. This method also leads to biased model coefficients as log FC is assumed to be error free. The present study develops linear models that do not require predictor identification. The models were developed by minimizing the errors in the logarithmic domain. Linear and log-log models with and without predictor identification were developed for EC-FC data from 10 sites in the lower Passaic River at Paterson, New Jersey. The Nash-Sutcliffe efficiencies (NSEs) of all model types are similar. The authors recommend the use of linear models that do not require predictor identification due to ease of interpretation and better estimate of the true relationship between EC and FC.