Should partial least squares be used for analysing psychological constructs?

This paper critically examines an analytical tool - partial least squares regression, or P LS - that is increasingly being used in the academic business literature to validate measures of psychological constructs, and to test hypotheses based on these. The paper provides a contextual and historical review of the resurgence of P LS, and explores several of the claims made by its developers and supporters when it was first promoted in the 1980s, and, more recently, when it reappeared in the information systems literature. Many claims appear plausible but rest on non-mainstream uses of terms and concepts taken from the psychometric field. The paper also canvasses why P LS is a poor analytical tool for research that involves psychological constructs.

Partial least squares and principal components analysis of wine vintage by high performance liquid chromatography with chemiluminescence detection

HPLC with acidic potassium permanganate chemiluminescence detection was employed to analyse 17 Cabernet Sauvignon wines across a range of vintages (1971–2003). Partial least squares regression analysis and principal components analysis was used in order to investigate the relationship between wine composition and vintage. Tartaric acid, vanillic acid, catechin, sinapic acid, ethyl gallate, myricetin, procyanadin B and resveratrol were found to be important components in terms of differences between the vintages.

Rapid determination of protein contents in microencapsulated fish oil supplements by ATR-FTIR spectroscopy and partial least square regression (PLSR) analysis

Following the recent success in quantitative analysis of essential fatty acid compositions in a commercial microencapsulated fish oil (?EFO) supplement, we extended the application of portable attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopic technique and partial least square regression (PLSR) analysis for rapid determination of total protein contents-the other major component in most commercial ?EFO powders. In contrast to the traditional chromatographic methodology used in a routine amino acid analysis (AAA), the ATR-FTIR spectra of the ?EFO powder can be acquired directly from its original powder form with no requirement of any sample preparation, making the technique exceptionally fast, noninvasive, and environmentally friendly as well as being cost effective and hence eminently suitable for routine use by industry. By optimizing the spectral region of interest and number of latent factors through the developed PLSR strategy, a good linear calibration model was produced as indicated by an excellent value of coefficient of determination R2 = 0.9975, using standard ?EFO powders with total protein contents in the range of 140-450 mg/g. The prediction of the protein contents acquired from an independent validation set through the optimized PLSR model was highly accurate as evidenced through (1) a good linear fitting (R2 = 0.9759) in the plot of predicted versus reference values, which were obtained from a standard AAA method, (2) lowest root mean square error of prediction (11.64 mg/g), and (3) high residual predictive deviation (6.83) ranked in very good level of predictive quality indicating high robustness and good predictive performance of the achieved PLSR calibration model. The study therefore demonstrated the potential application of the portable ATR-FTIR technique when used together with PLSR analysis for rapid online monitoring of the two major components (i.e., oil and protein contents) in finished ?EFO powders in the actual manufacturing setting.

ICT Interventions for Schoolgirls Do Matter! Understanding the Factors Influencing ICT Career Intentions through Partial Least Squares Analysis.

Intervention programs aimed at promoting study and work opportunities in the Information and Communications Technology (ICT) field to schoolgirls (Interventions) have been encouraged to combat a decline in the interest among girls to study ICT at school. The goal of our study is to investigate the influence of Interventions on schoolgirls’ intentions to choose a career in the ICT field by analysing the  comprehensive survey data (n = 3577), collected during four interventions in Australia, using the Partial Least Squares method. Our study is also aimed at identifying other factors influencing ICT career intentions. We found that the attitude towards interventions has an indirect influence on ICT career intentions by affecting interest in ICT. Our results also challenge several existing theoretical studies by showing that factors that had previously been suggested as influencers were found to have little or no impact in this study, these being same-sex education and computer usage.

A primer on phylogenetic generalised least squares

Phylogenetic generalised least squares (PGLS) is one of the most commonly employed phylogenetic comparative methods. The technique, a modification of generalised least squares, uses knowledge of phylogenetic relationships to produce an estimate of expected covariance in cross-species data. Closely related species are assumed to have more similar traits because of their shared ancestry and hence produce more similar residuals from the least squares regression line. By taking into account the expected covariance structure of these residuals, modified slope and intercept estimates are generated that can account for interspecific autocorrelation due to phylogeny. Here, we provide a basic conceptual background to PGLS, for those unfamiliar with the approach. We describe the requirements for a PGLS analysis and highlight the packages that can be used to implement the method. We show how phylogeny is used to calculate the expected covariance structure in the data and how this is applied to the generalised least squares regression equation. We demonstrate how PGLS can incorporate information about phylogenetic signal, the extent to which closely related species truly are similar, and how it controls for this signal appropriately, thereby negating concerns about unnecessarily ‘correcting’ for phylogeny. In addition to discussing the appropriate way to present the results of PGLS analyses, we highlight some common misconceptions about the approach and commonly encountered problems with the method. These include misunderstandings about what phylogenetic signal refers to in the context of PGLS (residuals errors, not the traits themselves), and issues associated with unknown or uncertain phylogeny.

Development and evaluation of a raman flow cell for monitoring continuous flow reactions

We show how in-line Raman spectroscopy can be used to monitor both reactant and product concentrations for a heterogeneously catalysed Suzuki cross reaction operating in continuous flow. The flow system consisted of an HPLC pump to drive a homogeneous mixture of the reactants (4-bromobenzonitrile, phenylboronic acid, and potassium carbonate) through an oven heated (80°C) palladium catalyst immobilised on a silica monolith. A custom built PTFE in-line flow cell with a quartz window enabled the coupling of an Ocean Optics Raman spectrometer probe to monitor both the reactants and product (4-cyanobiphenyl). Calibration was based on obtaining multivariate spectral data in the range 1530 cm–1 and 1640 cm–1 and using partial least-squares regression (PLSR) to obtain a calibration model which was validated using gas chromatography–mass spectrometry (GCMS) analysis. In-line Raman monitoring of the reactant and product concentrations enable (i) determination of reaction kinetic information such as the empirical rate law and associated rate constant and (ii) optimisation of either the product conversion (61 % at 0.02 mL min–1 generating 17 g h–1) or product yield (14 % at 0.24 mL min–1 generating 53 g h–1).

FTIR microspectroscopy for rapid screening and monitoring of polyunsaturated fatty acid production in commercially valuable marine yeasts and protists

The increase in polyunsaturated fatty acid (PUFA) consumption has prompted research into alternative resources other than fish oil. In this study, a new approach based on focal-plane-array Fourier transform infrared (FPA-FTIR) microspectroscopy and multivariate data analysis was developed for the characterisation of some marine microorganisms. Cell and lipid compositions in lipid-rich marine yeasts collected from the Australian coast were characterised in comparison to a commercially available PUFA-producing marine fungoid protist, thraustochytrid. Multivariate classification methods provided good discriminative accuracy evidenced from (i) separation of the yeasts from thraustochytrids and distinct spectral clusters among the yeasts that conformed well to their biological identities, and (ii) correct classification of yeasts from a totally independent set using cross-validation testing. The findings further indicated additional capability of the developed FPA-FTIR methodology, when combined with partial least squares regression (PLSR) analysis, for rapid monitoring of lipid production in one of the yeasts during the growth period, which was achieved at a high accuracy compared to the results obtained from the traditional lipid analysis based on gas chromatography. The developed FTIR-based approach when coupled to programmable withdrawal devices and a cytocentrifugation module would have strong potential as a novel online monitoring technology suited for bioprocessing applications and large-scale production.

Neither fixed nor random: weighted least squares meta-regression

Our study revisits and challenges two core conventional meta-regression estimators: the prevalent use of‘mixed-effects’ or random-effects meta-regression analysis and the correction of standard errors that defines fixed-effects meta-regression analysis (FE-MRA). We show how and explain why an unrestricted weighted least squares MRA (WLS-MRA) estimator is superior to conventional random-effects (or mixed-effects) meta-regression when there is publication (or small-sample) bias that is as good as FE-MRA in all cases and better than fixed effects in most practical applications. Simulations and statistical theory show that WLS-MRA provides satisfactory estimates of meta-regression coefficients that are practically equivalent to mixed effects or random effects when there is no publication bias. When there is publication selection bias, WLS-MRA always has smaller bias than mixed effects or random effects. In practical applications, an unrestricted WLS meta-regression is likely to give practically equivalent or superior estimates to fixed-effects, random-effects, and mixed-effects meta-regression approaches. However, random-effects meta-regression remains viable and perhaps somewhat preferable if selection for statistical significance (publication bias) can be ruled out and when random, additive normal heterogeneity is known to directly affect the ‘true’ regression coefficient.

Monotone approximation of aggregation operators using least squares splines

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

Least squares splines with free knots: global optimization approach

Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting angle method of deterministic global optimisation, which allows one to solve a wide class of optimisation problems on a simplex. The results of the cutting angle method are subsequently improved by local discrete gradient method. The resulting algorithm is sufficiently fast and guarantees that the global minimum has been reached. The results of numerical experiments are presented.

Neither fixed nor random: weighted least squares meta-analysis

This study challenges two core conventional meta-analysis methods: fixed effect and random effects. We show how and explain why an unrestricted weighted least squares estimator is superior to conventional random-effects meta-analysis when there is publication (or small-sample) bias and better than a fixed-effect weighted average if there is heterogeneity. Statistical theory and simulations of effect sizes, log odds ratios and regression coefficients demonstrate that this unrestricted weighted least squares estimator provides satisfactory estimates and confidence intervals that are comparable to random effects when there is no publication (or small-sample) bias and identical to fixed-effect meta-analysis when there is no heterogeneity. When there is publication selection bias, the unrestricted weighted least squares approach dominates random effects; when there is excess heterogeneity, it is clearly superior to fixed-effect meta-analysis. In practical applications, an unrestricted weighted least squares weighted average will often provide superior estimates to both conventional fixed and random effects.

Shape preserving approximation using least squares splines

Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.

Immobilized artificial membrane chromatography : quantitative structure-retention relationships of structurally diverse drugs

The chromatographic capacity factors (log k‘) for 32 structurally diverse drugs were determined by high performance liquid chromatography (HPLC) on a stationary phase composed of phospholipids, the so-called immobilized artificial membrane (IAM). In addition, quantitative structure-retention relationships (QSRR) were developed in order to explain the dependence of retention on the chemical structure of the neutral, acidic, and basic drugs considered in this study. The obtained retention data were modeled by means of multiple regression analysis (MLR) and partial least squares (PLS) techniques. The structures of the compounds under study were characterized by means of calculated physicochemical properties and several nonempirical descriptors. For the carboxylic compounds included in the analysis, the obtained results suggest that the IAM-retention is governed by hydrophobicity factors followed by electronic effects due to polarizability in second place. Further, from the analysis of the results obtained of two developed quantitative structure-permeability studies for 20 miscellaneous carboxylic compounds, it may be concluded that the balance between polarizability and hydrophobic effects is not the same toward IAM phases and biological membranes. These results suggest that the IAM phases could not be a suitable model in assessing the acid-membrane interactions. However, it is not possible to generalize this observation, and further work in this area needs to be done to obtain a full understanding of the partitioning of carboxylic compounds in biological membranes. For the non-carboxylic compounds included in the analysis, this work shows that the hydrophobic factors are of prime importance for the IAM-retention of these compounds, while the specific polar interactions, such as electron pair donor−acceptor interactions and electrostatic interactions, are also involved, but they are not dominant.

Optimal hedge ration with moving least squares - an empirical study using Indian single stock futures data

The use of commodity, currency and stock index futures to hedge risky exposures in the underlying assets is well documented in financial literature. However single stock futures are a relatively new addition to the family of futures and as such, academic research on its use as a hedging tool is relatively thin. In this study we have explored the efficacy of two different methodological approaches that may be applied when hedging a long position in the underlying stock with a single stock future. We use daily trading data covering years 2002 to 2007 from the Indian market, where single stock futures have been really thriving in terms of volume of trade, to extract the optimal hedge ratios using both static OLS as well as 30-day, 60-day and 90-day moving least squares. The method of moving least squares has been in use by market practitioners for some time primarily as a trend analysis and charting tool. Our results indicate that the moving least squares approach outperforms the static OLS in terms of the hedging efficiency, which has been measured by the root mean square hedging error.