Multivariate Procedures Research Articles

Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage

This paper is concerned with the positive definiteness (PDness) problem in covariance matrix estimation. For high-dimensional data, many regularized estimators have been proposed under structural assumptions on the true covariance matrix, including sparsity. They were shown to be asymptotically consistent and rate-optimal in estimating the true covariance matrix and its structure. However, many of them do not take into account the PDness of the estimator and produce a non-PD estimate. To achieve PDness, researchers considered additional regularizations (or constraints) on eigenvalues, which make both the asymptotic analysis and computation much harder. In this paper, we propose a simple modification of the regularized covariance matrix estimator to make it PD while preserving the support. We revisit the idea of linear shrinkage and propose to take a convex combination between the first-stage estimator (the regularized covariance matrix without PDness) and a given form of diagonal matrix. The proposed modification, which we call the FSPD (Fixed Support and Positive Definiteness) estimator, is shown to preserve the asymptotic properties of the first-stage estimator if the shrinkage parameters are carefully selected. It has a closed form expression and its computation is optimization-free, unlike existing PD sparse estimators. In addition, the FSPD is generic in the sense that it can be applied to any non-PD matrix, including the precision matrix. The FSPD estimator is numerically compared with other sparse PD estimators to understand its finite-sample properties as well as its computational gain. It is also applied to two multivariate procedures relying on the covariance matrix estimator – the linear minimax classification problem and the Markowitz portfolio optimization problem – and is shown to improve substantially the performance of both procedures.

Study-related mental health symptoms and their correlates among allied health professions students.

Allied health professions (AHP) students are subject to critical levels of study-related stressors including mental health symptoms (MHS) and musculoskeletal pain. Few studies recruited AHP students of multiple academic majors simultaneously. This study investigated and compared the prevalence of MHS severity and their associated factors among students of nine AHP majors. A cross-sectional design was used with a sample of nine AHP academic majors (n = 838). Participants completed a validated self-administered questionnaire that included demographics and life style, the Depression Anxiety Stress Scale (DASS 21), and the Nordic Musculoskeletal Questionnaire. MHS scores were statistically compared between males and females and between majors. A general linear model (GLM) multivariate procedure was used to assess the statistical associations between MHS and their correlates. Mild to extremely severe MHS levels were found in 62.2% of the participants for depression, 65.3% for anxiety, and 54.2% for stress. Compared to males, females showed significantly higher levels of stress (p < 0.01) and depression (p = 0.018). MHS were statistically associated with gender, physical health, diet quality, study difficulty, satisfaction with academic major, academic major and musculoskeletal pain. University GPA demonstrated negative significant correlations with MHS. MHS in AHP students are prevalent and should be accounted for by AHP educators. More studies are encouraged to assess actual mechanisms causing MHS among AHP students, and effective treatment programs are needed.

Blood Pressure Estimation Using Electrocardiogram and Photoplethysmogram

An increasing number of people are suffering from cardiac diseases, diabetes, high or low blood pressure, and many more. There are many devices available in the commercial market to measure heart rate, blood pressure, and temperature of the human body. Old fashioned blood pressure meters are cuff based and inconvenient for daily monitoring. The aim of this project is to design a platform to optimally estimate blood pressure using electrocardiogram (ECG), photoplethysmogram (PPG), Pulse Transit Time (PTT), wavelet transform and artificial neural network (ANN). This kind of blood pressure assessment may not be satisfactorily correct because the regulation of blood pressure inside the human body is complex, multivariate biological procedure. Predefined data is used to get ECG and PPG. 70% data is used for training and 30% data is used for testing in ANN to get accuracy of the system.

Simplex-centroid design and Derringer’s desirability function approach for simultaneous separation of phenolic compounds from Mimosa scabrella Bentham honeydew honeys by HPLC/DAD

Honeydew honeys have been under-evaluated about their major phenolic compounds, especially Mimosa scabrella Bentham (bracatinga) honeydew honey. In this work, a fast and robust chromatographic method was optimized for simultaneous separation and quantification by HPLC/DAD of 18 phenolic compounds detected in bracatinga honeydew honey. A simplex-centroid design, central composite rotatable design and response surface-desirability function simultaneous optimization of Derringer and Suich were used, evaluating the mobile phase composition, flow rate and oven temperature to separate all the peaks. These multivariate procedures were efficient in determining the optimal separation conditions, using peak pair resolutions and run time as responses. The 18 peaks were separated in 25 min and the mobile phase gradient started with 1.6% MeOH, 3.3% ACN, 1.0% THF and 94.1% formic acid 0.1% changing to 10.0% MeOH, 33.3% ACN, 6.0% THF and 50.7% formic acid 0.1%, oven temperature of 33 °C and flow rate of 0.73 mL min−1. The method was validated according to Eurachem guidelines and considered accurate and robust. It was applied to 18 bracatinga honeydew honey samples in which 9 phenolic compounds were identified and quantified.

Monitoring daily routine performance in quantitative NMR (qNMR) spectroscopy: Is the system suitability test necessary?

Nuclear magnetic resonance spectrometry (NMR) finds numerous applications in pharmacy, cosmetic, and food control as well as in developing tools for "big data" analysis. However, there remains a need for automated tools to assess instrument system suitability in real time for each particular routine sample. An automated procedure has been introduced to monitor a number of characteristics (resolution, symmetry, and half width) in real time after the measurement of two samples distributed by the vendor (0.3% CHCl3 in acetone-d6 with tetramethylsilane and 2mM sucrose in H2 O-D2 O). The results over 11months were discussed in terms of average values, standard deviations, and spectrometer variability. Moreover, multivariate statistical procedure was implemented to evaluate metrics generated from three NMR spectrometers. Performance of three NMR spectrometers (500MHz with BBO Prodigy Cryoprobe, 500MHz with BBFOPLUS SmartProbe, and 600MHz with BBO Cryoprobe) differed significantly. The developed routine was also applied to calculate the performance characteristics during routine quantitative NMR experiments. The procedure was evaluated for NMR spectra of 659 active pharmaceutical ingredients dissolved in CDCl3 , DMSO, and CH3 OD. This test is more preferable than the routine procedure using standard solutions because the performance is estimated separately for each matrix at the specific time point of measurements. Our automated routine is the ideal tool for any NMR laboratory. In full automation, the NMR data are validated directly for each sample, making unnecessary daily measurements of standard solutions and manual evaluation to their NMR spectra.

Mapping service quality in electricity distribution: An exploratory study of Brazil

The paper provides a diagnostic of service quality in electricity distribution in Brazil. Considering indicators related to customer complaints, average time for solving problems, and consumer satisfaction, there are some signs of deterioration over time. To address the multidimensional character of service quality, various well-established multivariate statistical analysis procedures are applied. A cluster analysis suggests that firms cluster into a small number of groups that are not directly related to the geographic region or firm size. A dynamic factor analysis for each firm provides mixed evidence, but in nearly 43% of the cases, important common patterns of indicators are found within firms. A canonical correlation analysis indicates a weak association between direct service quality and overall perceived satisfaction. The nature of firm heterogeneity can potentially provide guidance on how to incorporate service quality adjustments in the price-cap rule.

Theoretical and Applied Aspects of Automating Multivariate Analysis Procedures

This paper addresses some important theoretical and applied aspects of modern computer science that are associated with analytical processing of scientific, technical, and economic information. The main trends in using automated non-parametric procedures for logical and mathematical processing of arrays (flows) of digital data are discussed. Some methodological aspects of developing new technological approaches and algorithms for analytical post-processing that allow one to design a wide range of multi-step procedures for assessment and multivariate analysis of scientific, technical, and economic data based on polygram estimation of functionals are considered. It is shown that the procedures and algorithms based on these methods of non-parametric statistics and multivariate data analysis can be useful in various applications, including the development of analytical technologies for big data.

Mean\u2013variance and mean\u2013semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.

Divergence and genetic parameters between coffea sp. genotypes based in foliar morpho-anatomical traits

Knowing the genetic variability of a population is essential for guiding its preservation and maintenance, in addition to increasing the efficiency of genetic breeding programs. On this basis, the objective of this work was to estimate the genetic parameters, and to study genetic divergence in a coffee plants population constituted by 30 genotypes of Coffea canephora and 4 of C. arabica, by means of univariate and multivariate statistical procedures based on easy to obtain leaf morpho-anatomic characteristics (stomata number; index, density, area index, polar diameter, equatorial diameter, and functionality, as well as leaf area, dry weight, and specific dry weight). The materials were arranged in a randomized-blocks experimental design with four replicates. Significant differences were detected by the F-test (p < 0.01) between genotypes of Coffea sp. and for all morphological characters evaluated. This highlighted the heterogeneity of the genetic constitution of the evaluated population, which is quite relevant for the genetic divergence analysis and for breeding purposes, having the potential to identify superior genotypes. The tests of Scott-Knott allowed to detect variability between genotypes for all evaluated leaf morpho-anatomical characteristics, distributing genotypes in up to five groups. The clusters formed by Tocher’s optimization and the UPGMA hierarchical method were concordant, grouping the genotypes in ten and seven groups, respectively, showing similarities in the clusters. Three of the four clustered genotypes of C. arabica constituted an exclusive group for this species, in both methods. The characteristics with higher contribution to such distribution were stomata density (37.1%), number (17.3%), and index (12.1%), which together were responsible for 66.5% of the genetic diversity between the studied genotypes.

Bioluminescent-like squamation in the galeomorph shark Apristurus ampliceps (Chondrichthyes: Elasmobranchii)

Galeomorph sharks constitute the most taxonomically and ecologically diverse superorder of living selachians. Despite comprising several typically deep-water taxa, no bioluminescent species have been reported in this group so far. Interestingly, the study of shark squamation has been revealed in recent years to be a good proxy for inferring some ecological aspects of poorly known species. In particular, the high morphological specificity of the dermal denticles and the squamation patterns of all currently-known bioluminescent sharks could constitute a potential tool for predicting bioluminescence in both fossil and living taxa. Following this idea, we provide the first evidence supporting the possible existence of bioluminescence among galeomorph sharks by means of the quantitative study of Apristurus ampliceps squamation pattern. Classical morphometric analysis and multivariate statistical procedures have allowed us to determine that A. ampliceps squamation, composed mainly of bristle-shaped dermal denticles, is highly convergent with that of the bioluminescent shark Etmopterus spinax. The ecology of A. ampliceps, being a species that exclusively inhabits aphotic waters, is in agreement with such a morphofunctional interpretation, but finding photophores is imperative to confirm this prediction.

Antegrade versus Retrograde Single Balloon Enteroscopy - Which Is Better?

Introduction: There are 2 major approaches of single balloon enteroscopy- through mouth or ante-grade approach (AG), or through anus or retrograde (RG)approach. Aim of this study was to assess the differences in performance and complications of both these approaches. Methods: A retrospective cohort study was conducted using a registry of consecutive cases of single balloon enteroscopy at the Cleveland Clinic over 8 years from January 1, 2008- December 31,2016. Electronic medical records were utilized to collect variables including patient demographic, status of antiplatelet agents (at time of procedure), and coexisting comorbid diseases (cardiovascular, renal, and hepatic). Data on endoscopic findings, intervention (if received) was also obtained. Performance of procedures was assessed on the basis of scope time (in minutes), extent reached and need for repeat procedures within 30 days. Numerical values were assigned based on the depth of scope insertion to assess extent reached: 1 = unable to reach small bowel, 2 = proximal jejunum for ante-grade and distal ileum for retro-grade, 3 = mid jejunum for ante-grade and mid ileum for retro-grade, and 4 = distal jejunum for ante-grade and proximal ileum for retro-grade studies. Results: Of 510 patients who underwent SBE, 124 386 (75.7%) patients underwent AG procedures. At baseline patients in both groups were similar, except for older age (68.5 for RG vs 71 for AG, p=0.043) and higher antiplatelet use (34.7% for RG vs 42.5% for AG, p=0.042) in AG group. Deeper scope insertion depth (depth level 3 for AG vs 1 for RG, p < 0.001) and lesser scope time (37.4 mins in AG vs 48.9 mins in RG, p<0.001) was observed with AG procedures. On multivariate analysis AG procedures were found to have 118 higher odds (95% CI 60.5-229.9, p <0.001) of having a deeper scope insertion than RG, and RG procedures had 11.9 higher odds (95% CI 6.7-17, p <0.001) of longer scope time compared to AG. No difference in the rates of adverse outcomes including, bleeding, perforation, aspiration and change in level of care were noted between the two modalities. (Table 1&2)2793_A Figure 1 No Caption available.Conclusion: AG approach is less time consuming and more likely to have a deeper extent of insertion compared to RG approach, with similar rates of complications. Unless the lesion of interest is in close proximity to the ileo-cecal valve, it may be more prudent to proceed with AG approach rather than RG approach.2793_B Figure 2 No Caption available.

Direct use of peak ground motion parameters for the estimation of inelastic displacement ratio of SDOF systems subjected to repeated far fault ground motions

This study is aimed at developing statistical equations to estimate the inelastic displacement ratio of singledegree- of-freedom systems subjected to far fault repeated earthquakes. In the study, peak ground motion parameters are used to define the scatter of the original data. The ratio of peak ground acceleration to peak ground velocity, and peak ground velocity of the ground motion records and structural parameters such as period of vibration and lateral strength ratio are used in the proposed equations. For the development of the equations, nonlinear time history analyses of single-degree-offreedom systems are conducted. Then, the results are used in a multivariate regression procedure. The equations are verified by comparing the estimated results with the calculated results. The average error and coefficient of variation of the proposed equations are presented. The analyses results revealed that the direct use of peak ground motion parameters for the estimation of inelastic displacement ratio significantly reduced the scatter in the original data and yielded accurate results. From the comparative results it is also observed that results obtained using equations specific to peak ground velocity or peak ground acceleration to peak ground velocity ratio are similar.

MHC IIB Genetic Diversity and its Association With Humoral Immune Responses in Commercial Turkey

Background: Major histocompatibility complex (MHC) is one of the best characterized genetic regions controlling immune responses against vaccines. Identifying the association between MHC haplotypes and improved immune responses would be useful in genetic breeding strategies in animals. OBJECTIVES: MHC class II B genetic diversity and its association with humoral immune responses against Newcastle vaccine (NDV) were evaluated in commercial turkey poults (meleagris gallopavo). METHODS: A total of 92 turkey poults were vaccinated with live VG/GA strain of Newcastle disease vaccine at age of 10 and 20 days. Serum NDV specific IgY was assessed by indirect enzyme linked immunosorbent assay (ELISA) and MHC II B polymorphism was determined using high resolution melting curve (HRM) technique and DNA sequencing method. Effects of alleles on humoral immune responses were evaluated by multivariate regression analysis and GLM procedures. RESULTS: A total of 8 HRM profiles and 10 alleles were identified in this population. B1-1*3, B1-1*4 and B1-1*5 alleles were significantly associated with lower antibody responses against vaccine in commercial turkey poults. CONCLUSIONS: Three alleles reported in this study were associated with reduced immune responses against NDV vaccine in turkey population. Due to such negative associations, molecular breeding programs based on specific genetic markers should be implemented with great caution.

Analytical Development of a Four-Axis Magnetic Multimedia Control Element

Magnetic position and orientation detection systems have been penetrating the market in the last years due to their excellent properties. Specifically, the development of the cost effective 3-D Hall sensor brings new possibilities for consumer applications. In this paper, we propose a new magnetic design of a four-axis multimedia control element, which requires only a single magnet and a single 3-D Hall sensor. The development is based on an analytical model, which enables an efficient multivariate geometric optimization procedure. Optimal parameters are evaluated and discussed with respect to magnetic state separation up to several millitesla using a reasonable set of discrete rotational and tilt states. Experiments to prove the concept are presented.

Spatial decision‐support tools to guide restoration and seed‐sourcing in the Desert Southwest

AbstractAltered disturbance regimes and shifting climates have increased the need for large‐scale restoration treatments across the western United States. Seed‐sourcing remains a considerable challenge for revegetation efforts, particularly on public lands where policy favors the use of native, locally sourced plant material to avoid maladaptation. An important area of emphasis for public agencies has been the development of spatial tools to guide selection of genetically appropriate seed. When genetic information is not available, current seed transfer guidelines stipulate use of climate‐based or provisional seed transfer zones, which serve as a proxy for local adaptation by representing climate gradients to which plants are commonly adapted. Despite this guidance, little emphasis has been placed on identifying best practices for deriving provisional seed zones or on incorporating predictions from future climate. We describe a flexible, multivariate procedure for deriving such zones that incorporates a broad range of climatic characteristics while accounting for covariation among climate variables. With this approach, we derive provisional seed zones for four regions in the Desert Southwest (the Mojave Desert, Sonoran Desert, Colorado Plateau, and Southern Great Basin). To facilitate future‐resilient restoration designs, we project each zone into its relative position in the future climate based on near‐term, RCP4.5 and RCP8.5 emissions scenarios. Although provisional seed zones are useful in a variety of contexts, there are also situations in which site‐specific guidance is preferable. To meet this need, we implement Climate Distance Mapper, an interactive decision‐support tool designed to help practitioners match seed sources with restoration sites through an accessible online interface. The application allows users to rank the suitability of seed sources anywhere on the landscape based on multivariate climate distances. Users can perform calculations for either the current or future climates. Additionally, tools are available to guide sample effort in regional‐scale seed collections or to partition the landscape into climate clusters representing suitable planting sites for different seed sources. Our tools and analytic procedures represent a flexible and reproducible framework for advancing native plant development programs in the Desert Southwest and beyond.

Permutation based testing on covariance separability.

Separability is an attractive feature of covariance matrices or matrix variate data, which can improve and simplify many multivariate procedures. Due to its importance, testing separability has attracted much attention in the past. The procedures in the literature are of two types, likelihood ratio test (LRT) and Rao's score test (RST). Both are based on the normality assumption or the large-sample asymptotic properties of the test statistics. In this paper, we develop a new approach that is very different from existing ones. We propose to reformulate the null hypothesis (the separability of a covariance matrix of interest) into many sub-hypotheses (the separability of the sub-matrices of the covariance matrix), which are testable using a permutation based procedure.We then combine the testing results of sub-hypotheses using the Bonferroni and two-stage additive procedures. Our permutation based procedures are inherently distribution free; thus it is robust to non-normality of the data. In addition, unlike the LRT, they are applicable to situations when the sample size is smaller than the number of unknown parameters in the covariance matrix. Our numerical study and data examples show the advantages of our procedures over the existing LRT and RST.

Exploiting green sorbents in rotating-disk sorptive extraction for the determination of parabens by high-performance liquid chromatography with tandem electrospray ionization triple quadrupole mass spectrometry.

In this study, the viability of applying cork and montmorillonite clay modified with ionic liquid as biosorbents in the rotating-disk sorptive extraction technique was investigated. Specifically, this was aimed at the determination of methyl paraben, ethyl paraben, propyl paraben, and isobutyl paraben, with separation/determination by high-performance liquid chromatography coupled with mass spectrometry. The optimization of the method for both biosorbents was performed using multivariate procedures. The extraction efficiencies for the target compounds in aqueous matrices were compared to those obtained using the commercial sorbent Octadecil Silano-C18. The optimum extraction conditions for both natural sorbents were the use of an ammonia solution (pH 10) as desorption solvent and an extraction time of 30min. The proposed methods show limits of quantification of 0.8μg/L for cork, 3.0μg/L for montmorillonite clay and 6.0μg/L for Octadecil Silano-C18. The relative recoveries from river water and tap water samples ranged from 80.3 to 118.7% and 80.0 to 119.9% for cork and montmorillonite clay modified with ionic liquid, respectively. Relative standard deviations were obtained for intra- and interday precisions of <15% and <19% for cork and <19% and <17% for montmorillonite clay modified with ionic liquid.

Short communication: Multivariate outlier detection for routine Nordic dairy cattle genetic evaluation in the Nordic Holstein and Red population

It is of practical importance to ensure the data quality from a milk-recording system before use for genetic evaluation. A procedure was developed for detection of multivariate outliers based on an approximation for Mahalanobis distance and was implemented in the Nordic Holstein and Red population. The general target of this procedure is based on the Nordic Cattle Genetic Evaluation yield model, which is a 9-trait model for milk, protein, and fat in the first 3 lactations. The procedure is based on the phenotypic correlation structure as a function of days in milk (DIM) and on computation of trait means and standard deviations within a production year, lactation, and DIM. For each record in the data, a Mahalanobis distance value was computed based on the trait mean and the covariance matrix for the actual production year, lactation, and DIM. A set of cutoff values, ranging from 10 to 100 with steps of 10, for discarding multivariate outliers was investigated. Prediction accuracy was calculated as the Pearson correlations between estimated breeding values predicted by full data set and estimated breeding values predicted by reduced data set for cows without records in the reduced data set and with 1 or more records deleted due to the editing rules on Mahalanobis distance. The results showed that, averaged over all scenarios, gains of 0.005 to 0.048 on prediction accuracy have been obtained by deleting the multivariate outliers. The improvements were more profound for progeny of young bulls compared with progeny of proven bulls. It is easy to implement this multivariate outlier-detection procedure in the routine genetic evaluation for different dairy cattle breeds; however, an optimal cutoff value for Mahalanobis distance needs to be defined to achieve an acceptable compromise between genetic evaluation accuracy and data deletion.

Central Composite Design-Desirability Function Approach for Optimum Ultrasound-Assisted Extraction of Daidzein and Genistein from Soybean and Their Antimycotoxigenic Potential

Soybean isoflavones have been underestimated about their possible antifungal or antimycotoxigenic potential. In the present investigation, chemometric approaches were used such as the fractioned experimental design, the central composite rotatable design, and the Derringer’s desirability function to optimize a method to extract the isoflavones daidzein and genistein by ultrasound-assisted extraction. The optimized method was validated and applied to ten soybeans. The possible antimycotoxigenic abilities of isoflavones were evaluated by the inhibition of hydrolytic and oxidative enzymes. The multivariate procedures were efficient to determine the optimal extraction conditions, using daidzein and genistein concentration as responses. The best conditions were extraction time, 30 min; frequency, 55 kHz (36 kJ mL−1); hydrolysis time, 20 min; and hydrolysis temperature, 168 °C. The method was validated according to Eurachem guidelines and considered reproducible. The daidzein concentration was higher than genistein in soybeans. Low concentrations of aglycones were capable to inhibit fungal α-amylase (0.1 μg mL−1), highlighting genistein. Daidzein and genistein were able to inhibit oxidative processes in two strands, inhibition of oxidative enzyme and free radical propagation. These properties indicate that these isoflavones are able to contribute to avoid stress situations that could promote fungal contamination and manifestation of their mycotoxigenic potential.

How ethical leadership stimulates academics’ retention in universities

PurposeThe purpose of this paper is to investigate the relationship between ethical leadership and academics’ retention in universities. It draws on the conservation of resources theory to deepen the understanding of a process underlying this relationship whereby academics are more likely to stay in universities through the practice of ethical leadership. Specifically, it advances academics’ job-related affective well-being as a potential mediating mechanism, fostered by ethical leadership, which lowers their intention to leave.Design/methodology/approachThis study is conducted through a cross-sectional survey of 303 academics in Australian universities. Univariate, bivariate and multivariate analysis procedures are deployed to analyse academics’ data. The research hypotheses are tested through a bootstrapped regression analysis of academics’ perceived ethical leadership, affective well-being and intention to leave.FindingsThe findings lend support to the hypothesised relations, indicating a significant role of ethical leadership on enhanced intentions of academics to stay in universities by directly conserving their job-related affective well-being.Research limitations/implicationsThis paper contributes to knowledge of the relationship between ethical leadership and academics’ retention by identifying job-related affective well-being as an underlying mechanism in the university sector.Practical implicationsThis paper has practical implications for higher educational institutes seeking to retain their academic staff. Its findings show that the practice of ethical leadership in universities matters, because it lowers academics’ intentions to leave by nurturing their well-being at work.Originality/valueThis is the first study to examine the impact of ethical leadership on academics’ well-being and intentions to leave in the context of universities in Australia. It is one of the first studies to explore the mediating role of affective well-being in the ethical leadership and leadership and intention to leave relationship.