OPTICAL PROPERTIES OF SMALL GRAINS FOR RAPID AND OBJECTIVE ASSESSMENT OF QUALITY AND SAFETY
Title: LEAST-SQUARES MEANS MULTIPLE COMPARISON TESTING OF REFERENCE VERSUS PREDICTED RESIDUALS FOR EVALUATION OF PARTIAL LEAST SQUARES (PLS) SPECTRAL CALIBRATIONS
Submitted to: Near Infrared Spectroscopy Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: August 11, 2006
Publication Date: September 19, 2006
Citation: Reeves III, J.B., Delwiche, S.R., Reeves, V.B. 2006. Least-squares means multiple comparison testing of reference versus predicted residuals for evaluation of partial least squares (pls) spectral calibrations. Near Infrared Spectroscopy Journal. 14:371-377.
Interpretive Summary: At the heart of quantitative near- and mid-infrared spectroscopy are the linear or non-linear mathematical equations that are used to predict the concentration of a component, given the spectrum of the matrix. For example, very accurate multiple linear regression models can be developed for determining the level of protein in a food substance, in which protein concentration, determined by a reference chemical procedure (e.g., Kjeldahl, combustion) is related to a near-infrared spectrum of the substance. However, often model accuracy can suffer from sample-to-sample variations in the physical structure of the substance, which causes variation in the spectral response. Additionally, larger and broader absorption bands often obscure spectral responses caused by weak absorbers that happen to be vital for the constituent being modeled. Both of these effects can be mitigated by use of mathematical transformations performed on the spectra before regression modeling. Known as spectral pre-treatments, these transformations include smoothes, derivatives (first- or second-, most often), and normalizations. Although highly developed commercial software is available to perform pre-treatments and regression analysis (especially true for linear regression), the act of finding the best pre-treatment transformation is cumbersome, empirical, and time-consuming. To address the need of the spectroscopist or scientist in charge of model development, a procedure was developed that will systematically and automatically examine any reasonable number (2 to 25) pre-treatments used in conjunction with partial least squares regression models. By an analysis of variance (mixed effect) and a least square means multiple comparison, this procedure has the ability to identify the pre-treatments that produce the best, statistically significant quantitative models for a given component. Though demonstrated on partial least squares regression equations, this procedure can be used in conjunction with all other linear and non-linear regression models.
It is common to use data pre-treatments such as scatter correction, derivatives, mean centering, and variance scaling, prior to the development of near- and mid-infrared spectral calibrations. As a result, it is possible to generate a multitude of calibrations, many of which will have similar statistical properties, as measured by the coefficient of determination (R-squared) and the residual error. With respect to validation data sets, calibration equations have the tendency to provide the most optimistic modeling statistics on the set of data to which they were developed; however, the absolute best calibration out of a number of pre-treatments examined may not be the best for determining the values of future samples, and therefore, not the most robust calibration. If several calibrations are found to be statistically the same, then other criteria could be used to determine which one to use (e.g., one with fewest PLS factors or based on past experience) or further investigations could be carried out on the more limited set of calibrations deemed to represent the best of all those originally developed. However, there has been no accepted statistical procedure for determining which calibrations are statistically the same and which are not from a large group of calibrations. We propose the use of least squares means multiple comparisons testing of squared reference-versus-predicted residuals for determining the statistical similarity of multiple PLS calibrations. A program has been developed using common commercial statistical software (SAS, Mixed procedure) which computes and summarizes comparisons of PLS calibrations. This method is also applicable to other calibration methods (e.g., PCR, MLR, ANN) as it only requires a list of reference and predicted values for each calibration as input.