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

Author

Listed:
  • E. Andres Houseman

    (Harvard School of Public Health)

  • Brent Coull

    (Harvard School of Public Health)

  • James Shine

    (Harvard School of Public Health)

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.

Suggested Citation

  • E. Andres Houseman & Brent Coull & James Shine, 2004. "A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor," Harvard University Biostatistics Working Paper Series 1017, Berkeley Electronic Press.
    • Handle: RePEc:bep:hvdbio:1017
    Note: oai:bepress.com:harvardbiostat-1017
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    References listed on IDEAS

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    Keywords

    Boston Harbor; Enterococcus; Fourier series; Negative-binomial; Penalized spline; Poisson-gamma; Overdispersion; Semiparametric regression; Smoothing; Water monitoring;
    All these keywords.

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