Nonparametric methods in the analysis of estuarine water quality data.

摘要

Environmental time series contain both cyclic and irregular sources of variation. For modeling estuarine water quality variables, harmonic regression analysis has long been the standard for dealing with periodicity. Generalized additive models (GAMs) allow more flexibility in the response function. They permit parametric, semiparametric, and nonparametric regression functions of the predictor variables. We compare harmonic regression, GAMs with cubic regression splines, and GAMs with cyclic regression splines in simulations and using water quality data collected from the National Estuarine Research Reserve System (NERRS). While the classical harmonic regression model works well for clean, near-sinusoidal data, the GAMs are competitive and are very promising for more complex data. The GAMs are also more adaptive and require less user-intervention.; Once the periodicity has been removed, there are often anomalies in the series. These unusual events in the data are ecologically interesting. We develop a data-driven event detection algorithm using Efron's (2006) idea of local false discovery rates to detect events in water quality time series. Two test statistics are used in the algorithm: a sum of squared residuals (Q*) and the minimum absolute error (V*) for a sequence of residuals. Based on a simulation study, Q* as a test statistic works well under Normal errors but is sensitive to non-Normal errors. The more nonparametric V* controls the false discovery rate for both Normal and non-Normal errors, but tends to have a low true discovery rate. The event detection algorithm is not sensitive to event frequency, but the shape of the event does affect its detectability (damped-cosine-wave shapes were more rarely detected than box shapes). A problem that we encounter with the event detection algorithm is the frequent numerical failure of the locfdr function in R. Moreover, for those water quality series from the ACE Basin NERRS reserve for which the locfdr function did not fail, results were sometimes highly intuitive but also at times were not. The false discovery rate detection threshold had to be set very low (0.0001) to avoid a very large number of signaled events in the real data, which may signal complexity in the true mean function.