Least median of squares: a robust method for outlier and model error detection in regression and calibration

The least median of squares method is a robust regression method, which means that it is not sensitive to outliers or other violations of the assumption of the usual normal model. This contrasts with the conventional regression method, which minimizes the sum of squares. It is demonstrated that the proposed method can be used to detect or correct for outliers or model errors in calibration applications and in comparing two procedures.     

Least-squares support vector machines and near infrared spectroscopy for quantification of common adulterants in powdered milk

This paper proposes the use of the least-squares support vector machine (LS-SVM) as an alternative multivariate calibration method for the simultaneous quantification of some common adulterants (starch, whey or sucrose) found in powdered milk samples, using near-infrared spectroscopy with direct measurements by diffuse reflectance. Due to the spectral differences of the three adulterants a nonlinear behavior is present when all groups of adulterants are in the same data set, making the use of linear methods such as partial least squares regression (PLSR) difficult. Excellent models were built using LS-SVM, with low prediction errors and superior performance in relation to PLSR. These results show it possible to built robust models to quantify some common adulterants in powdered milk using near-infrared spectroscopy and LS-SVM as a nonlinear multivariate calibration procedure.     

Systematic and statistical errors in quantitative evaluation in TLC and HPTLC. 3. The determination of the primary statistical errors

The paper describes the measurement and calculation of the primary statistical errors in the evaluation of TLC or HPTLC using in situ reflectance measurements. The primary errors are the errors of the sample volume spotted onto the plate, errors caused by the chromatographic process itself, the positioning error of the plate with respect to the centre of the light beam and the error in the light measurement. By scanning the same spot, the same track or the same plate under different conditions, the various errors can be determined.     

Statistical comparison of calibration methods in multicomponent analysis

Spectrophotometric multicomponent analysis is considerd on the basis of inverse multivariate calibration with linear methods (ordinary least squares, principal component, ridge and partial least squares regression) and with the non-linear methods ACE and the non-linear partial least squares. The performance of the different methods is compared by paired F-tests. As an estimate of the error variance the residual mean sum of squares in the analysis of variance table is used. The comparison is demonstrated for the infrared spectrometric analysis of the hydroxyl group content of brown coal measured in diffuse reflectance. Although the error variances among the calibration methods differ gradually, the differences are much less pronounced at statistical level.     

复方氯丙那林质量检控的近红外光谱快速分析

基于近红外光纤漫反射技术,利用偏最小二乘法分别建立了复方氯丙那林胶囊的三种药效成分盐酸氯丙那林、盐酸溴己新和盐酸去氯羟嗪的快速同时测定方法。所建立的盐酸氯丙那林、盐酸溴己新和盐酸去氯羟嗪的定量分析多元校正模型的相关系数分别为99.7%、99.4%和99.0%,校正集的均方根残差分别为0.028、0.145和0.250,预测均方根误差分别为0.055、0.120和0.210。由于该方法是在不经任何预处理的情况下的光纤快速同时分析,因此可用于复方氯丙那林的过程质量控制。     

Selection of Wavelength Range and Number of Factors to be Used in the PLS Treatment of Spectrophotometric Data

Abstract

A procedure for selection of wavelength range and number of factors to be used in partial least square calibration that involves the calculation of prediction residual sum of squares (PRESS) in different conditions is proposed. The best model takes into account the minimum PRESS value that does not show significant differences with respect to the corresponding model with fewer factors. The ability of the proposed method to minimize errors in partial least squares (PLS) prediction is demonstrated by applying it to the resolution of phenytoine (DPH) and phenobarbital (PB) binary mixtures with errors less than 2.8%; the results are compared with those obtained using another wavelength selection procedure. The ensuing method, which was validated by high performance liquid chromatography (HPLC), also gives good results with real samples (pharmaceutical preparations).     

Calibration by orthogonal and common least squares — Theoretical and practical aspects

Consequences resulting from a three-dimensional calibration model introduced in [5] are investigated. Accordingly, there exists a different statistical background for the calibration, the analytical evaluation and the validation step. If the errors of the concentration values are not negligible compared with the errors of the measured values, orthogonal calibration models have to be used instead of the common Gaussian least squares (GLS). Four different approximation models of orthogonal least squares, Wald's approximation (WA), Mandel's approximation (MA), Geometrical mean (GM), and Principal component estimation (PC) are investigated and compared with each other and with GLS by simulations and by real analytical applications. From the simulations it can be seen that GLS is affected by bias in the estimates of both slope and intercept in the case of increasing concentration error. On the other hand, the orthogonal models estimate the calibration parameter better. The best fit is obtained by Wald's approximation. It is shown by simulations and real analytical calibration problems that orthogonal calibration has to be used in all cases in which the concentration errors cannot be neglected compared to the errors of the measured values. This is in particular relevant in recovery experiments for validation by means of comparison of methods. In such cases orthogonal least squares methods have always to be applied where the use of WA is recommended. The situation is different in the case of ordinary calibration experiments. The examples considered show small existing differences between the classical GLS and the orthogonal procedures. In doubtful cases both GLS and WA should be computed where the latter should be used if significant differences appear.     

Determination of the percentage of milk (cow's, ewe's and goat's) in cheeses with different ripening times using near infrared spectroscopy technology and a remote reflectance fibre-optic probe

In the present work we studied the use of near infrared spectroscopy (NIRS) technology employing a remote reflectance fibre-optic probe (with a 5 cm × 5 cm quartz window) for the analysis of the percentage of milk (cow's, ewe's and goat's) used in the elaboration of cheeses with different ripening times. To do so, cheeses with known and varying percentages of cow's, ewe's and goat's milk were elaborated (112 samples with milk collected in winter and 112 samples with milk collected in summer) and used as reference material, and ripening controls were performed over 6 months. The method allows immediate control of the cheese without prior sample treatment or destruction by direct application of the fibre-optic probe to the sample. The regression method employed was modified partial least squares (MPLS). Of all the samples (224), 200 formed to so-called calibration set and the other 24 were used for external validation. The calibration results obtained using 200 samples of cheese allowed the percentage of cow's, ewe's and goat's milk to be measured. The multiple correlation coefficients (RSQ) and prediction corrected standard errors (SEP(C)) obtained were respectively, 0.834 and 11.6% for cow's milk; 0.871 and 9.8% for goat's milk; 0.880 and 10.6% for ewe's milk. The ratio performance deviation (RPD) values obtained indicate that the NIRS equations can be applied to unknown samples.     

Fitting multiple datasets in kinetics: n‐butane + OH → products

Offsets due to systematic calibration errors are a common feature of the literature on temperature‐dependent rate constants. We present a formalism for dealing with these offsets within the context of least‐squares fitting, using a priori parameter constraints based on the estimated accuracy of individual studies. This methodology not only eliminates biases caused by calibration errors, it also ensures that the metric used to compare different studies is their accuracy, not their precision. Consequently, studies with single measurements at room temperature can be meaningfully compared with studies comprising dozens of measurements spanning a wide temperature range. We apply this procedure to the complete literature dataset for two reactions: OH + propane and OH + n‐butane, after first presenting new data for OH + n‐butane spanning the temperature range 180–300 K and extending the low‐temperature limit of the literature by 50 K. There is outstanding agreement among a very large set of studies, including relative measurements of the propane:n‐butane rate constant ratio. We present new reduced transition state theory fits for each reaction that accurately reproduce the observed rate constants between 180 and 1000 K, and argue that these two reactions are the optimal reference reactions for many relative rate studies. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 259–272, 2004     

近红外光谱测定复方对乙酰氨基酚片的有效成分

复方对乙酰氨基酚是临床上常用的解热镇痛药,常用剂型有片剂和注射剂,其片剂含有对乙酰氨基酚、阿司匹林和咖啡因等三种有效成分。对于该制剂的质量控制,《中国药典》[1]利用分光光度法测定对乙酰氨基酚的含量,用氢氧化钠标准溶液、高氯酸标准溶液分别滴定阿司匹林和咖啡因从而     

Determination of Quercetin in Extracts of Ginkgo biloba L. Leaves by Near‐Infrared Reflectance Spectroscopy Based on Interval Partial Least‐Squares (iPLS) Model

Abstract

This paper developed a multivariate method of analysis of quercetin in Ginkgo biloba leaf extracts, based on reflectance NIR measurements and partial least squares regression. In order to give a better correlation with the results obtained by HPLC, multiplicative scatter correction (MSC) was utilized to correct scattering effect and interval partial least squares (iPLS) to select optimum wavelength region. In general, good calibration statistics were obtained for the prediction of quercetin content, as demonstrated by some figures of merit, namely linearity, repeatability, and accuracy. And the iPLS model was more reliable than the full model.     

Theory of reflectance measurements in quantitative evaluation in TLC and HPTLC. 1. Multilayer model of reflectance and transmittance

In the approach described in this paper, the layer of adsorbent is divided into n sublayers. The radiation density in each sublayer is given by the sum of the transmittance and the reflectance of the adjacent sublayers. Absorption of light by the layer or the substance will diminish this radiation density. Depending upon the factors of reflectance and transmittance some light will pass to the adjacent sublayers. Two polynomials are derived from this readily understood formulation to calculate the reflectance or the transmittance of a layer of finite thickness. The algorithms given describe the reflectance and transmittance encountered in practical measurements with large amounts of substance per spot, as well as with small amounts. There are no restrictions with respect to nonideal scattering or reflection by the adsorbent layer support.     

Four-way calibration applied to the simultaneous determination of folic acid and methotrexate in urine samples

First-, second- and third-order calibration methods were investigated for the simultaneous determination of folic acid and methotrexate. The interest in the determination of these compounds is related to the fact that methotrexate inhibits the body’s absorption of folic acid and prolonged treatment with methotrexate may lead to folic acid deficiency, and to the use of folic acid to cope with toxic side effects of methotrexate. Both analytes were converted into highly fluorescent compounds by oxidation with potassium permanganate, and the kinetics of the reaction was continuously monitored by recording the kinetics curves of fluorescence emission, the evolution with time of the emission spectra and the excitation–emission matrices (EEMs) of the samples at different reaction times. Direct determination of mixtures of both drugs in urine was accomplished on the basis of the evolution of the kinetics of EEMs by fluorescence measurements and four-way parallel-factor analysis (PARAFAC) or multiway partial least squares (N-PLS) chemometric calibration. The core consistency diagnostic (CORCONDIA) was employed to determine the correct number of factors in PARAFAC and the procedure converged to a choice of three factors, attributed to folic acid, methotrexate and to the sum of fluorescent species present in the urine.      

Lifetime of the traceability chain in chemical measurement

Since the uncertainty of each link in the traceability chain (measuring analytical instrument, reference material or other measurement standard) changes over the course of time, the chain lifetime is limited. The lifetime in chemical analysis is dependent on the calibration intervals of the measuring equipment and the shelf-life of the certified reference materials (CRMs) used for the calibration of the equipment. It is shown that the ordinary least squares technique, used for treatment of the calibration data, is correct only when uncertainties in the certified values of the measurement standards or CRMs are negligible. If these uncertainties increase (for example, close to the end of the calibration interval or shelf-life), they are able to influence significantly the calibration and measurement results. In such cases regression analysis of the calibration data should take into account that not only the response values are subjects to errors, but also the certified values. As an end-point criterion of the traceability chain destruction, the requirement that the uncertainty of a measurement standard should be a source of less then one-third of the uncertainty in the measurement result is applicable. An example from analytical practice based on the data of interlaboratory comparisons of ethanol determination in beer is discussed. Received: 5 October 2000 Accepted: 3 December 2000     

Quantitative determination of drugs by in situ spectrophotometry of chromatograms for pharmacokinetic studies. I. Sulpiride and other benzamides, vincamine, naftazone (author's transl)

Assays are proposed for sulpiride and other benzamides, vincamine and naftazone in plasma (or blood) and urine with direct UV reflectance spectrophotometry on this are applied directly on TLC along with a calibration curve on each plate. Plasma (or total blood) samples are extracted, and an internal standard is added before aplication; slopes of the obtained calibration curves do not change significantly from plate to plate, thus allowing several determinations on the same plate. The sensitivity is 2 microgram in a 1-ml sample (amount applied 30 ng) for sulpiride and related compounds and about the same for vincamine. Naftazone is determined in plasma with simultaneous reflectance and transmittance spectrophotometric measurements at 520 nm on chromatoplates sprayed with lead acetate, the sensitivity reached is 10 ng in a 1-ml sample (amount applied 0.5 ng). For all drugs studied, the proposed techniques are specific, reliable and sensitive enough and can be used to perform pharmacokinetic studies in human or in animal after administration of doses in the therapeutic range.     

NIR spectroscopic measurement of moisture content in Scots pine seeds

When tree seeds are used for seedling production it is important that they are of high quality in order to be viable. One of the factors influencing viability is moisture content and an ideal quality control system should be able to measure this factor quickly for each seed. Seed moisture content within the range 3-34% was determined by near-infrared (NIR) spectroscopy on Scots pine (Pinus sylvestris L.) single seeds and on bulk seed samples consisting of 40-50 seeds. The models for predicting water content from the spectra were made by partial least squares (PLS) and ordinary least squares (OLS) regression. Different conditions were simulated involving both using less wavelengths and going from samples to single seeds. Reflectance and transmission measurements were used. Different spectral pretreatment methods were tested on the spectra. Including bias, the lowest prediction errors for PLS models based on reflectance within 780-2280 nm from bulk samples and single seeds were 0.8% and 1.9%, respectively. Reduction of the single seed reflectance spectrum to 850-1048 nm gave higher biases and prediction errors in the test set. In transmission (850-1048 nm) the prediction error was 2.7% for single seeds. OLS models based on simulated 4-sensor single seed system consisting of optical filters with Gaussian transmission indicated more than 3.4% error in prediction. A practical F-test based on test sets to differentiate models is introduced.     

Combined Experimental and Multivariate Model Approaches for Glycoalkaloid Quantification in Tomatoes

The intake of tomato glycoalkaloids can exert beneficial effects on human health. For this reason, methods for a rapid quantification of these compounds are required. Most of the methods for α-tomatine and dehydrotomatine quantification are based on chromatographic techniques. However, these techniques require complex and time-consuming sample pre-treatments. In this work, HPLC-ESI-QqQ-MS/MS was used as reference method. Subsequently, multiple linear regression (MLR) and partial least squares regression (PLSR) were employed to create two calibration models for the prediction of the tomatine content from thermogravimetric (TGA) and attenuated total reflectance (ATR) infrared spectroscopy (IR) analyses. These two fast techniques were proven to be suitable and effective in alkaloid quantification (R² = 0.998 and 0.840, respectively), achieving low errors (0.11 and 0.27%, respectively) with the reference technique.     

Prediction of sensory properties of espresso from roasted coffee samples by near-infrared spectroscopy

Thirty-five representative and suitably selected roasted coffee samples were characterised by near-infrared (NIR) spectroscopy and used to prepare the corresponding espresso samples to be subsequently subjected to sensory evaluation by trained panellists. The main purpose was to investigate the relationships between certain crucial sensory attributes of espresso coffees, including perceived acidity, mouthfeel, bitterness and aftertaste, and near-infrared spectra of original roasted coffee samples, in such a way that non-destructive near-infrared reflectance measurements would be used to predict all these sensory properties with a decisive influence from a quality assurance standpoint. Separate calibration models based on partial least squares regression (PLS), correlating NIR spectral data of roasted coffee samples with each sensory attribute of espresso samples studied, were developed. Wavelength selection was also performed applying iterative predictor weighting-PLS (IPW-PLS) in order to take into account only significant and characteristic spectral features, in an attempt to improve the quality of the final regression models constructed. Using IPW-PLS regression, prediction of the four sensory responses modelled was performed with high accuracy, with root mean square errors of the residuals in cross-validation (RMSECV) ranging from 4.7 to 7.0%. Thus, the results provided by the high-quality calibration models proposed in the present study, comparable in terms of accuracy to the evaluations provided by a trained sensory panel, are promising and prove the feasibility of using a similar methodology in on-line or routine applications to predict the sensory quality of unknown espresso coffee samples via their respective NIR roasted coffee spectra.     

应用遗传算法和PLS的近红外光谱预测玉米中淀粉含量的研究

以普通玉米籽粒为试验材料,在应用遗传算法结合偏最小二乘回归法对近红外光谱数据进行特征波长选择的基础上,应用偏最小二乘回归法建立了特征波长测定玉米籽粒中淀粉含量的校正模型．试验结果表明,基于11个特征波长所建立的校正模型,其校正误差（RMSEC）、交叉检验误差（RMSECV）和预测误差（RMSEP）分别为0.30％、0.35％和0.27％,校正数据集和独立的检验数据集的预测值与实际测定值之间的相关系数分别达到0.9279和0.9390,与全光谱数据所建立的预测模型相比,在预测精度上均有所改善,表明应用遗传算法和PLS进行光谱特征选择,能获得更简单和更好的模型,为玉米籽粒中淀粉含量的近红外测定和红外光谱数据的处理提供了新的方法与途径．