A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

E. Andres Houseman, Brent Coull and James Shine
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E. Andres Houseman: Harvard School of Public Health
Brent Coull: Harvard School of Public Health
James Shine: Harvard School of Public Health

No 1017, Harvard University Biostatistics Working Paper Series from Berkeley Electronic Press

Abstract: Boston Harbor has had a history of poor water quality, including by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. We propose a negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we motivate the use of a Fourier basis to represent it and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treament Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Keywords: Boston Harbor; Enterococcus; Fourier series; Negative-binomial; Penalized spline; Poisson-gamma; Overdispersion; Semiparametric regression; Smoothing; Water monitoring (search for similar items in EconPapers)
Date: 2004-10-18
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