How to construct a multiple regression model for data with missing elements and outlying objects

The aim of this study is to show the usefulness of robust multiple regression techniques implemented in the expectation maximization framework in order to model successfully data containing missing elements and outlying objects. In particular, results from a comparative study of partial least squares and partial robust M-regression models implemented in the expectation maximization algorithm are presented. The performances of the proposed approaches are illustrated on simulated data with and without outliers, containing different percentages of missing elements and on a real data set. The obtained results suggest that the proposed methodology can be used for constructing satisfactory regression models in terms of their trimmed root mean squared errors.     

Multivariate linear regression with missing values

This contribution presents and discusses an efficient algorithm for multivariate linear regression analysis of data sets with missing values. The algorithm is based on the insight that multivariate linear regression can be formulated as a set of individual univariate linear regressions. All available information is used and the calculations are explicit. The only restriction is that the independent variable matrix has to be non-singular. There is no need for imputation of interpolated or otherwise guessed values which require subsequent iterative refinement.     

A simple program for weighted linear regression applied to activation analysis data processing

A simple ALGOL program for activation analysis data handling is presented The program, although designed in principle for processing single-channel spectrometry data, may also be used for multichannel spectrometry, on condition that the peak area is computed separately. The calculations of instrumental error and standard deviation are carried out. The outliers are tested, and the regression line diagram with the related observations are plotted by the program.     

Partitioned partial least squares regression with application to a batch fermentation process

The performance of Partial Least Squares regression (PLS) in predicting the output with multivariate cross‐ and autocorrelated data is studied. With many correlated predictors of varying importance PLS does not always predict well and we propose a modified algorithm, Partitioned Partial Least Squares (PPLS). In PPLS the predictors are partitioned into smaller subgroups and the important subgroups with high prediction power are identified. Finally, regular PLS analysis using only those subgroups is performed. The proposed Partitioned PLS (PPLS) algorithm is used in the analysis of data from a real pharmaceutical batch fermentation process for which the process variables follow certain profiles during a specific fermentation period. We observed that PPLS leads to a more accurate prediction of the yield of the fermentation process and an easier interpretation, since fewer predictors are used in the final PLS prediction. In the application important issues such as alignment of the profiles from one batch to another and standardization of the predictors are also addressed. For instance, in PPLS noise magnification due to standardization does not seem to create problems as it might in regular PLS. Finally, PPLS is compared to several recently proposed functional PLS and PCR methods and a genetic algorithm for variable selection. More specifically for a couple of publicly available data sets with near infrared spectra it is shown that overall PPLS has lower cross‐validated error than PLS, PCR and the functional modifications hereof, and is similar in performance to a more complex genetic algorithm. Copyright © 2011 John Wiley & Sons, Ltd.     

A nonlinear regression model applied to kinetic multi-component analysis of esters with a SAW-impedance sensor

A kinetic nonlinear regression model for multi-component assay of esters was proposed based on their different alkaline-catalysed hydrolysis rate. The reaction rate was determined by monitoring the conductance change in solution with a liquid-purpose surface acoustic wave impedance sensor(SAW). The model was tested theoretically and experimentally with the mixture of methyl acetate and n-propyl acetate. The experimental detection limit of methyl acetate and n-propyl acetate (within 10 min) was 0.5 umol/L and 1.0 umol/L respectively and the recovery of the sensor system ranged from 93% to 106% (n=6).     

Water oxidation intermediates applied to catalysis: benzyl alcohol oxidation

Four distinct intermediates, Ru(IV)═O(2+), Ru(IV)(OH)(3+), Ru(V)═O(3+), and Ru(V)(OO)(3+), formed by oxidation of the catalyst [Ru(Mebimpy)(4,4'-((HO)(2)OPCH(2))(2)bpy)(OH(2))](2+) [Mebimpy = 2,6-bis(1-methylbenzimidazol-2-yl) and 4,4'-((HO)(2)OPCH(2))(2)bpy = 4,4'-bismethylenephosphonato-2,2'-bipyridine] on nanoITO (1-PO(3)H(2)) have been identified and utilized for electrocatalytic benzyl alcohol oxidation. Significant catalytic rate enhancements are observed for Ru(V)(OO)(3+) (~3000) and Ru(IV)(OH)(3+) (~2000) compared to Ru(IV)═O(2+). The appearance of an intermediate for Ru(IV)═O(2+) as the oxidant supports an O-atom insertion mechanism, and H/D kinetic isotope effects support net hydride-transfer oxidations for Ru(IV)(OH)(3+) and Ru(V)(OO)(3+). These results illustrate the importance of multiple reactive intermediates under catalytic water oxidation conditions and possible control of electrocatalytic reactivity on modified electrode surfaces.     

Classification of data with missing elements and outliers

Missing elements and outliers can often occur in experimental data. The presence of outliers makes the evaluation of any least squares model parameters difficult, while the missing values influence the adequate identification of outliers. Therefore, approaches that can handle incomplete data containing outliers are highly valued. In this paper, we present the expectation-maximization robust soft independent modeling of class analogy approach (EM-S-SIMCA) based on the recently introduced spherical SIMCA method. Several important issues like the possibility of choosing the complexity of the model with the leverage correction procedure, the selection of training and test sets using methods of uniform design for incomplete data and prediction of new samples containing missing elements are discussed. The results of a comparison study showed that EM-S-SIMCA outperforms the classic expectation-maximization SIMCA method. The performance of the method was illustrated on simulated and real data sets and led to satisfactory results.     

Comparison of robust regression methods based on least-median and adaptive kalman filtering approaches applied to linear calibration data

Five algorithms for data analysis are evaluated for their abilities to discriminate against outliers in small data sets (4–10 points). These methods included least-squares regression, the least absolute -deviation method, the least median of squares method, and two techniques based on an adaptive Kalman filter. For data sets consisting of 4–9 points with one outlier, the average errors in the estimation of the slope were found to be 18.9 % by least-squares, 17.7% by the least absolute deviation method, 0.5% by the least median of squares algorithm, 9.1% by an adaptive Kalman filter algorithm, and 0.9% by a zero-lag adaptive Kalman filter algorithm. Based on these results, the conclusion is that the zero-lag adaptive Kalman filter and the least median of squares approaches are best suited for the detection of outliers in small calibration data sets.     

A nonlinear regression model applied to kinetic studies of ester hydrolysis with a surface acoustic wave sensor

A non-linear regression model was derived for the simultaneous determination of the rate constant in alkaline hydrolysis of esters and the initial concentration of esters based on the linear relationship between the frequency response of the surface acoustic wave sensor system and the conductivity of the solution. The model was tested theoretically and experimentally with the methyl-, ethyl-, and n-propyl-acetate systems. The corresponding rate constants estimated at 25 degrees C are 0.147, 0.103 and 0.0671 respectively.     

用于环己烷氧化混合产物的分析方法

针对环己烷空气液相氧化混合产物的不同特性，采用了不同的测定方法：环己基过氧化氢采用间接碘量法定量；酸和酯采用酸碱滴定法定量；环己醇和环己酮等有机物采用气相色谱法，但进样前先加入三苯基膦以避免环己基过氧化氢的干扰。该方法回收率为96．62％～101．69％，相对标准偏差为1．12％～5．09％。     

Electrocatalytic and photocatalytic water oxidation to dioxygen based on metal complexes

The construction of an artificial photosynthetic device requires detailed understanding of the catalytic aspects of photo- or photoelectro-driven water oxidation. This has been attracting much interest as one of the promising clean energy-providing systems for the future. This review mainly covers progress on electrocatalytic and photocatalytic systems for water oxidation in the last decade. It includes conventional iridium oxide colloid catalysts and the new electrodeposited cobalt-phosphate catalyst films for water oxidation.     

Degradation of the herbicide isoproturon by a photocatalytic process

In this study, the adsorption and photocatalytic degradation of isoproturon (one of the most widely used herbicides in agriculture) was investigated in an annular photoreactor packed with a TiO₂ photocatalyst. The results highlighted that the monolayer Langmuir adsorption isotherm model was well obeyed. The isoproturon adsorption equilibrium constant was determined experimentally. The codegradation of isoproturon and of other copollutants such as salicylic acid and phenol occurred, demonstrating that within the catalyst, the same type of sites can be involved in the adsorption of the two pollutants. The heat of adsorption fell in the range of 20 to 50 °C and was found to be ∼43 kJ/mol. As expected, the adsorption constant K_a decreased with increasing the fluid flow due to the temperature rise. The kinetics of the photocatalytic degradation of isoproturon revealed a first-order reaction for initial concentrations between 3 and 43 ppm. In our experimental conditions, no by-products were detected and total disappearance of isoproturon was observed.     

SAW enzyme sensor applied to the determination of enzyme kinetic constants with the aid of a non-linear regression algorithm

A general program SAWBEH is proposed for the kinetic data evaluation of enzyme-catalysed hydrolysis by using the frequency shift response of an SAW sensor device. The Marquardt-Fletcher algorithm was employed as the minimum basis. The program was validated theoretically and compared with normal linear analysis methods by using synthetic data added with noise at different levels. The standard deviations of results obtained by the latter are about 100 times those obtained by the former. The system trypsin/benzoyl-L-arginine ethyl ester (BAEE) as a test model was studied at pH 7.6–7.8 and 32 °C. The Michaelis constant was estimated to be 6.34 × 10^–5 M.     

Coupled membrane process applied to fruit juice concentration

A coupled membrane process of membrane distillation and osmotic evaporation, where the solutions were thermostated separately at different temperatures, was developed. Enhanced water flux was obtained since the total driving force of the coupled process was higher than the sum of the driving forces of single processes. Apple, raspberry, sour cherry, red, and black currant juices were concentrated by the novel, mild technique. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Peptide retention prediction applied to proteomic data analysis

A retention prediction model was developed for peptides separated in reversed-phase chromatography. The model was utilized to identify and exclude the false positive (FP) peptide identifications obtained via database search. The selected database included human proteins, as well as decoy sequences of random proteins. The FP peptide detection rate was defined either as number of retention time outliers, or random decoy sequence identifications. The FP rate for various MASCOT scores was calculated. The peptides identified in one-dimensional (1D) and two-dimensional (2D) liquid chromatography/mass spectrometry (LC/MS) experiments were validated by prediction models. Multi-dimensional LC was based on two orthogonal reversed-phase chromatography modes; prediction models were successfully applied for data filtering in both separation dimensions.     

Polynomial multivariate least‐squares regression for modeling nonlinear data applied to in‐depth characterization of chromatographic resolution

Well‐established, linear multivariate calibration methods such as multivariate least‐squares regression (MLR), principal component regression (PCR), or partial least squares (PLS) have two limitations: (i) measured data must be linearly related to the response variables and (ii) predictor variables x_{n = 1, …, N} cannot be coupled to each other. For evaluation of nonlinear data, however, these restrictions need to be overcome and thus polynomial multivariate least‐squares regression (PMLR or “response surfaces”) has been introduced here. PMLR is based on multivariate least squares but incorporates all combinations of predictor variables up to a user‐selected polynomial order (e.g., including u or v = 0). Because of the inclusion of such coupled terms and their powers, PMLR models are better adapted to model nonlinear data and can help to enhance the prediction step's accuracy and precision. PMLR has been based on MLR because it facilitates—unlike PCR or PLS—a physical and chemical interpretation of the predictors. Hence, the origins and the relevance of nonlinear and/or coupled predictors can be investigated. The details of the PMLR algorithm and its implementation are presented along with a method for model optimization utilizing gradients of response surfaces. Newly developed PMLR models up to quintic order have been applied to predict a chromatograph's peak resolution as a function of six‐instrument parameters. It has been demonstrated that PMLR is better capable than MLR and PCR to describe these nonlinear and coupled instrument parameters. In addition, the novel software tool has been utilized for model optimization to determine instrument parameters, which result in the best chromatographic resolution. Copyright © 2011 John Wiley & Sons, Ltd.     

Parallel factor analysis combined with PLS regression applied to the on-line monitoring of Pichia pastoris cultures

Various key variables (biomass, substrate and product) of bioprocesses should be monitored in order to retrieve useful information on the system, with the biomass (the cell density) the principal target. Although several analytical methods have been adapted and used to monitor the evolution of cell density evolution in cultures, a general method for performing this determination has not yet been established, as each technique has its own advantages and drawbacks. In the present work, noninduced glycerol batch cultures (for which biomass and substrate are the key variables) were monitored using multiwavelength fluorescence spectroscopy. The data gathered were modelled via PARAFAC-PLS chemometric methodologies, resulting in important qualitative and quantitative information about the behaviours of different biogenic fluorophors in batch cultures of the yeast Pichia pastoris. This information was used to predict the target process variables in such cultures; this permitted the applicability of this combined technique to bioprocess monitoring to be assessed.     

D-MORPH regression: application to modeling with unknown parameters more than observation data

Diffeomorphic modulation under observable response preserving homotopy (D-MORPH) is a model exploration method, originally developed for differential equations. We extend D-MORPH to regression treatment of a model described as a linear superposition of basis functions with unknown parameters being the expansion coefficients. The goal of D-MORPH regression is to improve prediction accuracy without sacrificing fitting accuracy. When there are more unknown parameters than observation data, the corresponding linear algebraic equation system is generally consistent, and has an infinite number of solutions exactly fitting the data. In this case, the solutions given by standard regression techniques can significantly deviate from the true system structure, and consequently provide large prediction errors for the model. D-MORPH regression is a practical systematic means to search over system structure within the infinite number of possible solutions while preserving fitting accuracy. An explicit expression is provided by D-MORPH regression relating the data to the expansion coefficients in the linear model. The expansion coefficients obtained by D-MORPH regression are particular linear combinations of those obtained by least-squares regression. The resultant prediction accuracy provided by D-MORPH regression is shown to be significantly improved in several model illustrations.