Mathematical Sciences: Random Coefficient Models and Robust Analysis

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Proposal: DMS 95-05290 Principal investigator: Douglas G. Simpson Institution: University of Illinois Title: RANDOM COEFFICIENT MODELS AND ROBUST ANALYSIS Abstract: Random coefficient models have found wide application for modeling correlation, incorporating laboratory or study effects, and in developing Bayesian estimates and inferences. Marginal analysis is an alternative approach in which models are developed directly for marginal distributions (integrated over random effects), and the inferences are at the level of population average effects rather than at the level of individual experimental units. Connections and contrasts between these general modeling strategies and robust statistics will be developed. The aim is to develop fresh ideas for attacking hard problems in applied statistics. Among the problems to be attacked: robust generalized linear modeling and graphical data analysis; environmental exposure risk assessment combining information from multiple studies with varying protocols and endpoint measurements; inferences for random function data arising from spectral measurement instruments. With the wide availability of powerful computers, increasingly complex data are being collected. In analytical chemistry it is now routine to qtore separation spectra electronically. In environmental toxicology large databases are being assembled on potentially hazardous pollutants. The proposed research is directed at the development of statistical methods for such data. In combining information from multiple exposure--response studies, it is possible to model uncertainty due to things such as interlaboratory effects or species differences using modern computational techniques and new statistical paradigms. In environmental chemistry, fluctuations in the amount of material assayed and in the measuring instrument itself lead to extra randomness in the measurement. Adjusting for this effect is critical to the success of the metho ds, particularly as the number of features measured, e.g., peaks on a mass spectrum, becomes large. The proposed research will develop toolkits for analysis, inference and diagnostics. Key components of the work are algorithm development, simulation studies, asymptotic analysis, testing of the methodology, and software development. The major applications driving this research are in environmental risk assessment (combining information) and environmental monitoring (spectral measurements), targeting strategic national concerns in environmental management. ??