Advances in Mathematical Chemistry and Applications

Volume: 2

“Advances in Mathematical Chemistry and Applications, Volume 2” highlights the emerging discipline of mathematical chemistry, or, more precisely, discrete mathematical chemistry. This volume is ...
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Linear Regression, Model Averaging, and Bayesian Techniques for Predicting Chemical Activities from Structure

Pp. 125-147 (23)

Jarad B. Niemi and Gerald J. Niemi

Abstract

A primary goal of quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs) is to predict chemical activities from chemical structure. Chemical structure can be quantified in many ways resulting in hundreds, if not thousands, of measurements for every chemical. Chemical activities measures how the chemical interacts with other chemicals, e.g. toxicity, biodegradability, boiling point, and vapor pressure. Typically there are more chemical structure measurements than chemicals being measured, the so-called large-p, small-n problem. Here we review some of the statistical procedures that have been commonly used to explore these problems in the past and provide several examples of their use. Finally, we peek into the future to discuss two areas that we believe will see dramatically increased attention in the near future: model averaging and Bayesian techniques.

Keywords:

AIC, Bayesian analysis, BIC, cross-validation, elastic net, k-means clustering, LASSO, model averaging, model selection, modeling, partial least squares, prediction, principal component analysis, principal component regression, regression, ridge regression.

Affiliation:

Department of Statistics, Iowa State University, Ames, IA 50011- 1210, USA.