Method for stabilizing near-infrared models and determining their applicability

A method for developing a model for determining a property of interest of a test sample:

• (a) obtaining a plurality of samples of a material having known values of the property of interest;
• (b) collecting a near-infrared spectrum of each of the samples in the plurality of samples;
• (c) grouping the samples in the plurality of samples into a plurality of subsets;
• (d) determining a regression model for each subset from the near-infrared spectra of the samples forming such subset;
• (e) selecting regression models which have a standard error of calibration less than a predetermined value;
• (f) retaining regression models from the selected models which are relatively poorly correlated to each other;
• (g) averaging the retained models to determine a composite model;
• (h) determining a near-infrared spectrum of the test sample;
• and
• (i) determining the property of interest of the test sample by applying the composite model to the near-infrared spectrum of the test sample.

A method of determining the value of a property of interest of a test material, comprising:

• (a) obtaining a plurality of samples of the material, each such sample having a known value of the property of interest;
• (b) collecting a near-infrared spectrum for each sample in the plurality of samples using near-infrared radiation;
• (c) determining a separate regression model for a plurality of subsets of the plurality of samples;
• (d) selecting regression models having a standard error of calibration less than a predetermined value;
• (e) determining a residual for each sample and each selected regression model as the difference between a value of the property of interest determined by such selected regression model and a value determined by a primary measurement technique for the parameter of interest;
• (f) pairing the regression models having any common samples;
• (g) determining a correlation coefficient between residuals of common samples in each of the pairs of models;
• (h) selecting a subset of selected regression models, wherein the residuals of the regression models in the subset are the least correlated to one another;
• (i) averaging the models in the selected subset (Step h) to obtain a composite model;
• (j) estimating the degree of improvement of the composite model estimates using a B-statistic, wherein the B-statistic is defined as 1-R.sup.2, where R is the average correlation coefficient between residuals of the subset of the least-correlated models;
• (k) collecting a near-infrared spectrum of the test sample;
• and
• (l) computing the value of the parameter of interest of the test sample using the composite model.

A method for determining a property of interest of a test sample by utilizing a plurality of samples, each having a known value of the property, comprising:

• (a) subjecting each sample in the plurality of samples to a known light energy and collecting a corresponding spectrum for each such sample;
• (b) determining a composite model from the spectra of the plurality of samples;
• (c) determining a spectrum of the test sample;
• (d) determining the property of interest of the test sample by applying the composite model to the spectrum of the test sample;
• (e) determining whether the property of interest of the test sample is an outlier;
• and
• (f) determining an I-statistic for the parameter of interest of the test sample if the test sample is not an outlier, wherein the I-statistic is defined as a ratio of the variance of the subset models' estimates of the parameter of interest to the square of the average standard error of calibration of the subset models.
• (g) predicting the test sample to be an inlier if the value of the I-statistic of the parameter of interest of the test sample is greater than about 1.