PLS modeling

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

The PLS calibration set was built mixing in an agate mortar different amounts of Mancozeb standard with kaolin, a coadjuvant usually formulated in agrochemicals. Cluster analysis was employed for sample classification and to select the adequate PLS model acording with the characteristics of the sample matrix and the presence of other components. 

PLS metliod applied to speetral data provides exeellent quantitative analytieal results. It offers more aeeurate and robust predietion eompared with the results obtained by LR method. Therefore, the Ca(OH) determination by FTIR using a PLS model ealibration has demonstrated to be an adequate tool, despite the disadvantages of quantitative analysis using FTIR speetroseopie teehnique. 

The optimal PLS models obtained for the prediction of %DE using the five different spectral sources are listed in Table 2 (see also Fig. 5). The models... 

The optimal spectroscopic PLS models for the degree of esterification of amidated... 

Figure 7. PLS model for (left) pH and (right) Ca2 using the FTIR DR ensemble.

Let us now consider a new set of values measured for the various X-variables, collected in a supplementary row vector x. From this we want to derive a row vector y of expected T-values using the predictive PLS model. To do this, the same sequence of operations is followed transforming x into a set of factor scores r, t 2, t A pertaining to this new observation. From these t -scores y can be... 

Here we summarize the steps needed to compute the PLS model... 

S. Wold, N. Kettaneh-Wold and B.Skagerberg, Nonlinear PLS modeling. Chemom. Intell. Lab. Syst., 7 (1989) 53-65. 

A typical performance behaviour is shown in Fig. 44.16b. The increase of the NSE for the monitoring set is a phenomenon that is called overtraining. This phenomenon can be compared to fitting a curve with a polynomial of a too high order or with a PCR or PLS model with too many latent variables. It is caused by the fact that after a certain number of iterations, the noise present in the training set is modelled by the network. The network acts then as a memory, able to recall... 

Wold, S., Nonlinear PLS modeling II spline inner relation, Chemom. Intell. Lab. Sys., 14, 71-84 (1992). 

Helminen J, Leppamaki M, Paatero E and Minkkinen (1998) Monitoring the Kinetics of the Ion-exchange Resin Catalysed Esterification of Acetic Acid with Ethanol Using Near Infrared Spectroscopy with Partial Least Squares (PLS) Model, Chemometr Intell Lab Syst, 44 341. 

More generally, the comparison is represented in Fig. 6.24 where the RMSP values of 14 calibration models (n = 349 test persons) are given. In most cases the RBF models greatly surpasses the PLS models. 

Using our dataset which includes all of the descriptors mentioned so far, we conducted a PLS analysis using SIMCA software [34], In the initial PLS model, MW, V, and a (Alpha) were removed because they are in each case highly correlated with CMR (r > 0.95). SIMCA s VIP function selected only qmin (Qnegmin) for removal on the basis of it making no important contribution to the model. In the second model, 2q+/a (SQpos A) and ECa/a (SCa A) coincided nearly exactly in the three-component space of these two, we decided to keep only ECa/a in the third and final model. This model consisted of three components and accounted for 75% of the variance in log SQ the Q2 value was 0.66. 

Furthermore, there are two other aspects to the extrapolation problem one structural and one statistical. An illustrative example of these various cases can be found in a dataset of benzamides (S16.1). that one of the present authors (U.N.) published some time ago [44]. If one develops a PLS model based on the same descriptors and the same, experimental design-based, training set (compounds 1-16) augmented by compound 17 (Table 16.8) in order to prove the points raised above [the prediction limit (1.502) set to two times the overall RSD of the model (0.751) which roughly gives 95% confidence interval], one can observe the following with respect to predictions on the remaining test set compounds ... 

An examination of the results of the external predictions shows interesting findings. The compounds ofTable 17.1 that are projected in the Discriminant Analysis-PLS model made with the training set compounds are shown in Fig. 17.2 (the... 

While I am no longer working in this field, and cannot easily do simulations, I think that a 2 factor PCR or PLS model would fully model the simulated spectra. At any wavelength in your simulation, a second degree power series applies, which is linear in coefficients, and the coefficients of a 2 factor PCR or PLS model will be a linear function of the coefficients of the power series. (This assumes an adequate number of calibration spectra, that is, at least as many spectra as factors and a sufficient number of wavelength, which the full spectrum method assures.) The PCR or PLS regression should find the linear combination of these PCR/PLS coefficients that is linear in concentration. 

While I am no longer working in this field, and cannot easily do simulations, I think that a 2 factor PCR or PLS model would fully model the simulated spectra. (Fred Cahn)... 

Richard Kramer, Patrick Wiegand, and Paul Chabot suggested that a one-factor PLS model should reject the data from the nonlinear wavelength and therefore also provide a perfect fit to the constituent . I offered to provide the data as an EXCEL spreadsheet to these responders Paul accepted the offer, and I e-mailed the data to him. We will see the results at an appropriate stage. 

Based on the values of the correlation coefficients, then, we can find the following comparisons between the two algorithms as several of the responders indicated, the PLS model did provide improved results over the PCR model. On the other hand, the degree of improvement was not the major effect that at least some of the responders expected. As Richard Kramer expected,... 

PCR is an alternative method to the much more used regression method PLS (Section 4.7). PCR is a strictly defined method and the model often gives a very similar performance as a PLS model. Usually PCR needs more components than PLS because no information ofy is used for the computation of the PCA scores this is not necessarily a disadvantage because more variance of X is considered and the model may gain stability. 

FIGURE 4.24 PLS as a multiple linear regression method for prediction of a property y from variables xi,..., xm, applying regression coefficients b1,...,bm (mean-centered data). From a calibration set, the PLS model is created and applied to the calibration data and to test data. 

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