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SPEAKER: |
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TITLE: |
"Regression for Contaminant Concentration Data: Issues, Models and Analysis" |
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DAY: |
Wednesday, February 28, 2001 |
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TIME: |
3:30 p.m. [Tea & cookies in BSB-202 at 3:00 p.m.] |
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PLACE: |
BSB-108 |
In a large number of environmental applications involving the analysis of contaminant concentration data, the observed distributions are approximately lognormal. This feature is often justified by the fact that, in many situations, contaminant concentrations are the result of many slight dilutions. Thus the standard practice is to first transform the data to the logarithmic scale and then conduct the statistical analyses using methods for normally distributed data. However, regulatory rules such as those followed by the US Environmental Protection Agency require that risks should be characterized in terms of the mean contaminant concentration in the original scale. Furthermore, recent studies suggest that the lognormal distribution may exhibit heavier tails than required in practice for adequate description of contaminant concentrations. An added complication is the presence of observations below their detection limit. Keeping in mind the above issues and features, in this talk we discuss regression methods for contaminant concentration data. The methods are applicable when measurements on concomitant variables such as environmental factors are available. In one approach, we use log-regression with arbitrary error distributions as the underlying models and develop estimation and inferential methods for the moments of the contaminant concentration at a new set of experimental conditions. In another approach we use normal regression on the Box-Cox transformation of the data. We focus on maximum likelihood, E-M algorithm, bias correction, minimum variance unbiased estimation, nonparametric estimation and confidence intervals. To illustrate the methods we analyze data on calcium and magnesium concentrations in samples of water from the Fraser River, British Columbia, as well as data on PCB and dieldrin concentrations in samples of water from the Niagara River, Ontario. The talk is based on joint work with Abdel El-Shaarawi and Yongmin Yu.
Román Viveros-Aguilera is a professor in the Department of Mathematics and Statistics at McMaster University. He holds a BA from Universidad Verecruzana and an MA from the Instituto Politécnico Nacional, Mexico, and PhD from the University of Waterloo. He is interested in the theory and applications of statistics in the areas of environmetrics, reliability, survival analysis, latent variable methods and statistical process control.
The references below, suggested by the speaker as useful background for this talk, have been placed on reserve at Thode Library (STATS 770: Statistics Seminar).
El-Shaarawi, A.H. & Roman Viveros (1997) Inference About the Mean in Log-Regression with Environmental Applications, Environmentrics 8, pp. 569-582.
You could also read the description of the Niagara River Pollution Case Study on the Web, download the data, and try some exploratory analyses.