# Comparisons of prediction abilities of augmented classical least squares and partial least squares with realistic simulated data : effects of uncorrelated and correlated errors with nonlinearities.

## Abstract

A manuscript describing this work summarized below has been submitted to Applied Spectroscopy. Comparisons of prediction models from the new ACLS and PLS multivariate spectral analysis methods were conducted using simulated data with deviations from the idealized model. Simulated uncorrelated concentration errors, and uncorrelated and correlated spectral noise were included to evaluate the methods on situations representative of experimental data. The simulations were based on pure spectral components derived from real near-infrared spectra of multicomponent dilute aqueous solutions containing glucose, urea, ethanol, and NaCl in the concentration range from 0-500 mg/dL. The statistical significance of differences was evaluated using the Wilcoxon signed rank test. The prediction abilities with nonlinearities present were similar for both calibration methods although concentration noise, number of samples, and spectral noise distribution sometimes affected one method more than the other. In the case of ideal errors and in the presence of nonlinear spectral responses, the differences between the standard error of predictions of the two methods were sometimes statistically significant, but the differences were always small in magnitude. Importantly, SRACLS was found to be competitive with PLS when component concentrations were only known for a single component. Thus, SRACLS has a distinct advantage over standard CLSmore »

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 993880

- Report Number(s):
- SAND2003-2454J

TRN: US201024%%144

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Journal Article

- Journal Name:
- Proposed for publication in Applied Spectroscopy.

- Additional Journal Information:
- Journal Name: Proposed for publication in Applied Spectroscopy.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97 MATHEMATICAL METHODS AND COMPUTING; COMPARATIVE EVALUATIONS; LEAST SQUARE FIT; DATA COVARIANCES; MATHEMATICAL MODELS; FORECASTING; MULTIVARIATE ANALYSIS; INFRARED SPECTRA; GLUCOSE; UREA; ETHANOL; SODIUM CHLORIDES; AQUEOUS SOLUTIONS; SPECTROMETERS; CALIBRATION; SPECTRAL RESPONSE

### Citation Formats

```
Haaland, David Michael, and Melgaard, David Kennett.
```*Comparisons of prediction abilities of augmented classical least squares and partial least squares with realistic simulated data : effects of uncorrelated and correlated errors with nonlinearities.*. United States: N. p., 2003.
Web.

```
Haaland, David Michael, & Melgaard, David Kennett.
```*Comparisons of prediction abilities of augmented classical least squares and partial least squares with realistic simulated data : effects of uncorrelated and correlated errors with nonlinearities.*. United States.

```
Haaland, David Michael, and Melgaard, David Kennett. Sun .
"Comparisons of prediction abilities of augmented classical least squares and partial least squares with realistic simulated data : effects of uncorrelated and correlated errors with nonlinearities.". United States.
```

```
@article{osti_993880,
```

title = {Comparisons of prediction abilities of augmented classical least squares and partial least squares with realistic simulated data : effects of uncorrelated and correlated errors with nonlinearities.},

author = {Haaland, David Michael and Melgaard, David Kennett},

abstractNote = {A manuscript describing this work summarized below has been submitted to Applied Spectroscopy. Comparisons of prediction models from the new ACLS and PLS multivariate spectral analysis methods were conducted using simulated data with deviations from the idealized model. Simulated uncorrelated concentration errors, and uncorrelated and correlated spectral noise were included to evaluate the methods on situations representative of experimental data. The simulations were based on pure spectral components derived from real near-infrared spectra of multicomponent dilute aqueous solutions containing glucose, urea, ethanol, and NaCl in the concentration range from 0-500 mg/dL. The statistical significance of differences was evaluated using the Wilcoxon signed rank test. The prediction abilities with nonlinearities present were similar for both calibration methods although concentration noise, number of samples, and spectral noise distribution sometimes affected one method more than the other. In the case of ideal errors and in the presence of nonlinear spectral responses, the differences between the standard error of predictions of the two methods were sometimes statistically significant, but the differences were always small in magnitude. Importantly, SRACLS was found to be competitive with PLS when component concentrations were only known for a single component. Thus, SRACLS has a distinct advantage over standard CLS methods that require that all spectral components be included in the model. In contrast to simulations with ideal error, SRACLS often generated models with superior prediction performance relative to PLS when the simulations were more realistic and included either non-uniform errors and/or correlated errors. Since the generalized ACLS algorithm is compatible with the PACLS method that allows rapid updating of models during prediction, the powerful combination of PACLS with ACLS is very promising for rapidly maintaining and transferring models for system drift, spectrometer differences, and unmodeled components without the need for recalibration. The comparisons under different noise assumptions in the simulations obtained during this investigation emphasize the need to use realistic simulations when making comparisons between various multivariate calibration methods. Clearly, the conclusions of the relative performance of various methods were found to be dependent on how realistic the spectral errors were in the simulated data. Results demonstrating the simplicity and power of ACLS relative to PLS are presented in the following section.},

doi = {},

journal = {Proposed for publication in Applied Spectroscopy.},

number = ,

volume = ,

place = {United States},

year = {2003},

month = {6}

}