Development of a static headspace gas chromatographic procedure for the routine analysis of volatile fatty acids in wastewaters

An optimised procedure has been developed for the routine analysis of volatile fatty acids in wastewater matrices, using static headspace gas chromatography with flame ionisation detection. Factors such as sample volume, sample pre-treatment and the time and temperature of sample equilibration have been included in an optimisation model designed to provide maximum detector response for acetic, propionic, iso- and n-butyric and iso- and n-valeric acids in the concentration range 0-1000 mg/l. Optimal headspace conditions were observed when equilibrating at 85 degrees C for 30 min, using a 2.0 ml sample volume with the addition of 1.0 ml of NaHSO4 (62%, w/v) into standard 22.3 ml vials. 2-Ethylbutyric acid was used as an internal standard. The suitability of ordinary least squares regression and weighted least squares regression models for the purposes of calibration and quantification were investigated. A weighted least squares linear regression model applied to the heteroscedastic data provided lower detection limits, e.g. 3.7 and 3.3 mg/l for acetic and propionic acids.     

Comparison of regression techniques for linear calibration

A recently presented regression technique for linear calibration, which is based on a variance component model for univariate quantitative measurement data, is compared with the conventional and far spread regression techniques ordinary least squares regression and weighted least squares regression. The associated statistical models and estimations are represented. Its application is demonstrated at some practical examples. With consideration of special variation causes, like matrix influence or the influence of several operating conditions on the measurement response, it can be shown that the application of the variance component model is an advantage.     

Uncertainties in Determination of pH

 A statistical analysis of multi-point calibration procedure for practical measurement of pH under laboratory conditions is given. The procedure is shown to provide the necessary elements for simple assignment of an uncertainty to a pH measurement – an essential element of quality control. Performance of ordinary least squares regression for prediction of confidence limits is compared to orthogonal regression, inverse regression and Monte Carlo simulations. In case of pH measurement by multi-point calibration procedure, methods considering uncertainties in both axes are found to be statistically more satisfactory than ordinary least squares regression. By analysis of 50 pH calibration data, randomly selected from 250 5-point glass electrode calibrations, it is found that the practical differences, however, are of minor importance. The significance of uncertainty in pH is demonstrated for an example from metal ion speciation in aqueous solution. Received September 20, 1999. Revision April 19, 2000.     

Limits of detection and decision. Part 3

It has been shown that the MARLAP (Multi-Agency Radiological Laboratory Analytical Protocols) for estimating the Currie detection limit, which is based on ‘critical values of the non-centrality parameter of the non-central t distribution’, is intrinsically biased, even if no calibration curve or regression is used. This completed the refutation of the method, begun in Part 2. With the field cleared of obstructions, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system (CMS) having heteroscedastic, Gaussian measurement noise and using weighted least squares (WLS) processing, was then derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, “hockey stick” and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.     

Problems of calibration in trace, in situ-micro and surface analysis

Summary A systematic survey will be given on different strategies of calibration in dependence on given analytical and statistical conditions, particularly on several procedures of least squares regression (ordinary, orthogonal, unweighted and weighted LSR), of robust regression, addition methods and multicomponent calibration. In this connection calibration by means of latent variables (principal component regression PCR, partial least squares PLS) will be dealt with. The special conditions in the case of microanalysis and surface analysis will be considered under practical analytical as well as chemometrical aspects. Problems of homogeneity, representativness of samples and sample regions will be treated.     

Application of maximum likelihood multivariate curve resolution to noisy data sets

In this work, two different maximum likelihood approaches for multivariate curve resolution based on maximum likelihood principal component analysis (MLPCA) and on weighted alternating least squares (WALS) are compared with the standard multivariate curve resolution alternating least squares (MCR‐ALS) method. To illustrate this comparison, three different experimental data sets are used: the first one is an environmental aerosol source apportionment; the second is a time‐course DNA microarray, and the third one is an ultrafast absorption spectroscopy. Error structures of the first two data sets were heteroscedastic and uncorrelated, and the difference between them was in the existence of missing values in the second case. In the third data set about ultrafast spectroscopy, error correlation between the values at different wavelengths is present. The obtained results confirmed that the resolved component profiles obtained by MLPCA‐MCR‐ALS are practically identical to those obtained by MCR‐WALS and that they can differ from those resolved by ordinary MCR‐ALS, especially in the case of high noise. It is shown that methods that incorporate uncertainty estimations (such as MLPCA‐ALS and MCR‐WALS) can provide more reliable results and better estimated parameters than unweighted approaches (such as MCR‐ALS) in the case of the presence of high amounts of noise. The possible advantage of using MLPCA‐MCR‐ALS over MCR‐WALS is then that the former does not require changing the traditional MCR‐ALS algorithm because MLPCA is only used as a preliminary data pretreatment before MCR analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimizing performance in Spectrophotometric Multicomponent Analysis with the partial least-squares method

Summary Optimizing Performance in Spectrophotometric Multicomponent Analysis with the Partial Least-Squares Method Simultaneous analysis of three and five component systems is performed in the ultra-violet spectral range by means of multivariate calibration and data reduction with the partial least squares method (PLS). By applying fractional factorial designs the number of calibrating solutions is minimized to 4 for analysis of coffeine, propyphenazone and phenacetine in their mixtures. Furthermore, the superiority of the PLS-method over ordinary least squares regression and over calibrations based on pure spectra is demonstrated for a five component system.     

Appropriate calibration functions for capillary electrophoresis II. Heteroscedasticity and its consequences

If ordinary least squares regression methods are to be used, the standard deviation of the signal should not depend on the sample concentration, but this is not true in CE. Results indicate, that the signal standard deviation is approximately proportional to the sample concentration. Therefore weighted least squares regression must be used, if the standard deviation within the concentration range differs by more than the factor 50. It is advised to use this regression method down to the factor 5, where the difference to ordinary least squares calculations is still significant. This is demonstrated by comparing experimental and simulated data. These considerations are valid for other analytical techniques as well, if their characteristics of calibration and variance function are similar.     

The application of multiple linear regression to the measurement of the median particle size of drugs and pharmaceutical excipients by near-infrared spectroscopy.

A number of powdered drugs and pharmaceutical excipients were used to demonstrate the ability of near-infrared spectroscopy to measure median particle size (d50). Sieved fractions and bulk samples of aspirin, anhydrous caffeine, paracetamol, lactose monohydrate and microcrystalline cellulose were particle sized by forward angle laser light scattering (FALLS) and scanned by fibre-optic probe FT-NIR spectroscopy. Two-wavenumber multiple linear regression (MLR) calibrations were produced using: NIR reflectance; absorbance and Kubelka-Munk function data with each of median particle size, reciprocal median particle size and the logarithm of median particle size. Best calibrations were obtained using reflectance data versus the logarithm of median particle size (NIR predicted lnd50 versus ln(FALLS d50) for microcrystalline cellulose and lactose monohydrate sieve fraction calibrations: r = 0.99 in each case). Working calibrations for lactose monohydrate (median particle size range: 19.2-183 microns) and microcrystalline cellulose (median particle size range: 24-406 microns) were set-up using combinations of machine sieve-fractions and bulk samples. This approach was found to produce more robust calibrations than just the use of sieved fractions. The method has been compared with single wavenumber quadratic least squares regression using reflectance and mean-corrected reflectance data with median particle size. Correlation between NIR predicted and FALLS values was significantly better using the MLR method.     

Simultaneous Anodic Stripping Voltammetric Determination of Pb and Cd,Using a Vibrating Gold Microwire Electrode,Assisted by Chemometric Techniques

Simultaneous anodic stripping voltammetric determination of Pb and Cd is restricted on gold electrodes as a result of the overlapping of these two peaks. This work describes the quantitative determination of a binary mixture system of Pb and Cd, at low concentration levels (up to 15.0 and 10.0 µg L^?1 for Pb and Cd, respectively) by differential pulse anodic stripping voltammetry (DPASV; deposition time of 30 s), using a green electrode (vibrating gold microwire electrode) without purging in a chloride medium (0.5 M NaCl) under moderate acidic conditions (HCl 1.0 mM), assisted by chemometric tools. The application of multivariate curve resolution alternating least squares (MCR‐ALS) for the resolution and quantification of both metals is shown. The optimized MCR‐ALS models showed good prediction ability with concentration prediction errors of 12.4 and 11.4 % for Pb and Cd, respectively. The quantitative results obtained by MCR‐ALS were compared to those obtained with partial least squares (PLS) and classical least squares (CLS) regression methods. For both metals, PLS and MCR‐ALS results are comparable and superior to CLS. For Cd, as a result of the peak shift problem, the application of CLS was unsuitable. MCR‐ALS provides additional advantage compared to PLS since it estimates the pure response of the analytes signal. Finally, the built up multivariate calibration models, based either in MCR‐ALS or PLS regression, allowed to quantify concentrations of Pb and Cd in surface river water samples, with satisfactory results.     

Weighted least squares in calibration: estimating data variance functions in high-performance liquid chromatography

For minimum-variance estimation of parameters by the method of least squares, heteroscedastic data should be weighted inversely as their variance, w(i) proportional, variant 1/sigma(i)2. Here the instrumental data variance for a commercial high-performance liquid chromatography (HPLC) instrument is estimated from 5 to 11 replicate measurements on more than 20 samples for each of four different analytes. The samples span a range of over four orders of magnitude in concentration and HPLC peak area, over which the sampling variance estimates s2 are well represented as a sum of a constant term and a term proportional to the square of the peak area. The latter contribution is dominant over most of the range used in routine HPLC analysis and represents approximately 0.2% of peak area for all four analytes studied here. It includes a contribution from uncertainty in the syringe injection volume, which is found to be +/-0.008 microL. The dominance of proportional error justifies the use of 1/x2 or 1/y2 weighting in routine calibration with such data; however, the constant variance term means that these weighting formulas are not correct in the low-signal limit relevant for analysis at trace levels. Least-squares methods for both direct and logarithmic fitting of variance sampling estimates are described. Since such estimates themselves have proportional uncertainty, direct fitting requires iterative adjustment of the weights, while logarithmic fitting does not.     

Liquid chromatography with tandem mass spectrometry method for the determination of nicotine and minor tobacco alkaloids in electronic cigarette refill liquids and second‐hand generated aerosol

A liquid chromatography with tandem mass spectrometry method for the simultaneous quantification of nicotine and seven minor tobacco alkaloids in both refill liquids for electronic cigarettes and their generated aerosol was developed and validated. The limit of detection and limit of quantification values were 0.3–20.0 and 1.0–31.8 ng/mL, respectively. Within‐laboratory reproducibility was 8.2–14.2% at limit of quantification values and 4.8–12.7% at other concentration levels. Interday recovery was 75.8–116.4%. The method was applied to evaluate the compliance of commercial liquids (n = 95) with their labels and to assess levels of minor alkaloids. Levels of nicotine and its corresponding compounds were also evaluated in generated aerosol. About 47% of samples showed differences above ±10 % of the stated nicotine concentration. About 78% of the “zero nicotine” liquids showed traces in the range of 1.3 ± 0.1–254.0 ± 14.6 μg/mL. Nicotine‐N ′‐oxides, myosmine, and anatabine were the most common minor alkaloids in liquids containing nicotine. Nicotine and N ′‐oxides were detected in all air samples when aerosol was generated from liquids containing nicotine. Nicotine average emissions from electronic cigarette (2.7 ± 0.9 μg/m³) were significantly lower (p < 0.01, t‐test) with respect to conventional cigarette (30.2 ± 1.5 μg/m³).     

Regression diagnostics applied in kinetic data processing: Outlier recognition and robust weighting procedures

An efficient protocol, based on advanced statistical diagnostics and robust fitting techniques applied to the least‐squares processing of kinetic data of chemical reactions, is presented and discussed. The procedure, which is aimed at obtaining highly accurate estimation of the fitting parameters, consists of the identification of the outliers that remarkably impair the fitting by means of the so‐called “leverage analysis” and some related diagnostics. This approach allows the elimination of the actually aberrant observations from the data set and/or their robust weighting to inhibit the negative effects induced on the data fitting, with consequent reduction of the bias introduced into the parameter estimates. It has been found that the proposed procedure, applied to experimental kinetic data, does yield to a significant improvement in the regression results. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 587–607, 2010     

A system for the neutron activation analysis of trace elements in samples of biological and environmental interest

A neutron activation, ion exchange group separation and iterative least squares γ-ray spectroscopy method has been evaluated. This technique is suitable for multiple trace element analysis in a wide range of biological and environmental materials, since the major contaminants,²⁴Na,³²P, and⁴²K, are removed by an anion exchange resin and do not interfere with the analysis of the majority of the trace elements present. The iterative least squares method was tested with a mixture of standards. The reproducibility and accuracy varied from 3 to 26%. The larger uncertainties resulted from (1) the limited statistical accuracy associated with a low counting rate, and (2) bias introduced by the contaminants in the library of standard spectra even though radiochemical purity exceeded 99.8%. The rigorous least squares method can accurately compensate for instrumental drifts so that the sensitivity approaches the limit imposed by the statistical accuracy of the data and of the standard spectra. Minor components of the complex γ-spectrum were resolved and proved to be present at levels as low as 0.8% of the integral counting rate.     

Determination of lanthanides in synthetic standards by reversed-phase high-performance liquid chromatography with the aid of a weighted least-squares regression model estimation of method sensitivities and detection limits

A reversed-phase liquid chromatography method was used for determining lanthanides in synthetic standards. The separation of lanthanide group was achieved in less than 15 min using a linear gradient program of alpha-hydroxyisobutyricacid eluent from 0.05 to 0.5 M (pH 3.8) with a UV-Vis detection system at 658 nm. A post-column reagent of Arsenazo III was employed for improving the sensitivity and selectivity of the method as well as for lowering the limits of detection (LODs). Linear calibration curves for all lanthanides were constructed using an ordinary least-squares (OLS) regression as well as a weighted least-squares (WLS) regression model for taking into account the heteroscedastic errors. The WLS model was successfully used for a better estimation of the sensitivities and the LODs of the RP-HPLC method than the conventional OLS model. The lanthanide sensitivity obtained from the slope of each calibration curve seems to be better for a lanthanide with an odd-atomic number compared to its neighboring element with an even-atomic number, as if nature is helping us to quantify the concentrations of the less abundant lanthanides. This observation was also confirmed when the LODs computed for all lanthanides were examined. The LODs observed for all lanthanides depicted a clear systematic "zigzag" pattern. This is actually the first time that the lanthanide detection limits determined by a HPLC method are shown to mimic the zigzag patterns for the concentration data in geological and cosmological materials. Such a "zigzag" pattern should be used as a standard criterion for evaluating the quality of detection limit data.     

A hybrid genetic algorithm for estimating the equilibrium potential of an ion-selective electrode

Non-linear equations can be used to model the measured potential of ion-selective electrodes (ISEs) as a function of time. This can be done by using non-linear least squares regression to fit parameters of non-linear equations to an ISE response curve. In iterative non-linear least squares regression (which can be considered as local optimisers), the determination of starting parameter estimates that yield convergence to the global optimum can be difficult. Starting values away from the global optimum can lead to either abortive divergence or convergence to a local optimum. To address this issue, a global optimisation technique was used to find initial parameter estimates near the global optimum for subsequent further refinement to the absolute optimum. A genetic algorithm has been applied to two non-linear equations relating the measured potential from selected ISEs to time. The parameter estimates found from the genetic algorithm were used as starting values for non-linear least squares regression, and subsequent refinement to the absolute optimum. This approach was successfully used for both expressions with measured data from three different ISEs; namely, calcium, chloride and lead ISEs.     

Extracting robust and physically meaningful pitzer parameters for thermodynamic properties of electrolytes from experimental data. Ridge regression as an aid to the problem of intercorrelation

The Pitzer interaction model for thermodynamic properties of electrolytes is reevaluated in view of available regression techniques for the statistical inference of Pitzer parameters from experimental data. It is concluded that ordinary least squares regression is not generally suited, because of the intrinsic correlations among the various predictor variables in the Pitzer model. The predictor variables all are some function of the concentration of the electrolyte considered. Ridge regression, a mathematically only slightly different procedure designed to overcome the problem of intercorrelations, often yields more robust estimates for the Pitzer parameters. The potential of RR is demonstrated by some examples for the system GaCl₃–HCl. The ridge estimates are expected to be closer to the physically true parameter values.     

Characterizing nonconstant instrumental variance in emerging miniaturized analytical techniques

Measurement variance is a crucial aspect of quantitative chemical analysis. Variance directly affects important analytical figures of merit, including detection limit, quantitation limit, and confidence intervals. Most reported analyses for emerging analytical techniques implicitly assume constant variance (homoskedasticity) by using unweighted regression calibrations. Despite the assumption of constant variance, it is known that most instruments exhibit heteroskedasticity, where variance changes with signal intensity. Ignoring nonconstant variance results in suboptimal calibrations, invalid uncertainty estimates, and incorrect detection limits. Three techniques where homoskedasticity is often assumed were covered in this work to evaluate if heteroskedasticity had a significant quantitative impact—naked-eye, distance-based detection using paper-based analytical devices (PADs), cathodic stripping voltammetry (CSV) with disposable carbon-ink electrode devices, and microchip electrophoresis (MCE) with conductivity detection. Despite these techniques representing a wide range of chemistries and precision, heteroskedastic behavior was confirmed for each. The general variance forms were analyzed, and recommendations for accounting for nonconstant variance discussed. Monte Carlo simulations of instrument responses were performed to quantify the benefits of weighted regression, and the sensitivity to uncertainty in the variance function was tested. Results show that heteroskedasticity should be considered during development of new techniques; even moderate uncertainty (30%) in the variance function still results in weighted regression outperforming unweighted regressions. We recommend utilizing the power model of variance because it is easy to apply, requires little additional experimentation, and produces higher-precision results and more reliable uncertainty estimates than assuming homoskedasticity.     

多元光度测定病态系统的岭回归估计

考察了含多种酚类的有机混合体系的同时测定，发现对于这类化学与光谱性质皆十分相近的混合物体系，最小二乘法和卡尔曼滤波方法都不能给出令人满意的结果，甚至出现负值，而脾岭回归估计方法对此类病态体系进行分析，所得结果明显优于最小二乘法与卡尔曼滤波方法。     

Quantification of amorphous content in maltitol by

A method was developed for the quantification of low levels of amorphous content in maltitol with StepScan DSC. The method was based on the fact that the change of specific heat at the glass transition is linearly proportional to the amorphous content. The influence of different measurement parameters of StepScan DSC was evaluated and two different calibration heating rates were tested. Synthetic mixtures with various proportions of crystalline and amorphous maltitol were prepared. Two different measurement methods were compared and the linear regression between ΔC_p and amorphous content was obtained. The limit of detection (LOD) and the limit of quantification (LOQ) values were for the fictive temperature 0.24% (amorphous content) and 0.81% and for the half point temperature 0.27 and 0.92%, respectively, (method 1) and for the fictive temperature 0.18 (amorphous content) and 0.61% and for the half point temperature 0.16 and 0.52%, respectively (method 2). Very low determination limits for the quantification of amorphous content could be attained with the StepScan DSC method. However, the realistic limit of quantification was somewhat higher (about 3%) because of noise in the StepScan measurement. The main advantage of the StepScan DSC method for quantification of amorphous content was that the glass transition and relaxation peaks are separated into different curves and the interpretation becomes easier.