A Statistical View of Some Chemometrics Regression Tools

TLDR

Chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis and has also generated several new data‑analytical methods borrowed from statistics and engineering. This article examines partial least squares and principal components regression from a statistical perspective, aiming to understand their successes, when they work well, and how they compare to other statistical methods for those situations. The methods discussed include ordinary least squares, variable subset selection, and ridge regression.

Abstract

Chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis. In addition to borrowing many techniques from the statistics and engineering literatures, chemometrics itself has given rise to several new data-analytical methods. This article examines two methods commonly used in chemometrics for predictive modeling—partial least squares and principal components regression—from a statistical perspective. The goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations. These methods include ordinary least squares, variable subset selection, and ridge regression.