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Varimax factor rotations, while popular among practitioners in psychology and statistics since being introduced by Kaiser (1958) , have historically been viewed with skepticism and suspicion by some theoreticians and mathematical statisticians. Now, work by Rohe & Zeng (2023) provides new, fundamental insight: varimax rotations provably perform statistical estimation in certain classes of latent variable models when paired with spectral-based matrix truncations for dimensionality reduction. We build on this new-found understanding of varimax rotations by developing further connections to network analysis and spectral methods rooted in entrywise matrix perturbation analysis. Concretely, this paper establishes the asymptotic multivariate normality of vectors in varimax-transformed Euclidean point clouds that represent low-dimensional node embeddings in certain latent space random graph models. We address related concepts including network sparsity, data denoising and the role of matrix rank in latent variable parameterizations. Collectively, these findings, at the confluence of classical and contemporary multivariate analysis, reinforce methodology and inference procedures grounded in matrix factorization-based techniques. Numerical examples illustrate our findings and supplement our discussion. [ABSTRACT FROM AUTHOR]

Singular Spectrum Analysis (SSA) and its Multivariate extension (mSSA) are powerful tools for decomposing time series into ‘skeleton’ signals and residual noise. To address the issue of eigenvector mixing, Groth and Ghil (2011) introduced the varimax mSSA algorithm. Despite its widespread use, the detailed capabilities of varimax mSSA for handling noisy and incomplete time series have not been fully explored. In this study, we present a simple, yet effective imputation algorithm based on varimax mSSA, and conduct a comprehensive evaluation of its ability to extract dynamic signals with clearly physical interpretations from data with varying Noise levels and missing rates. Our findings show that varimax mSSA significantly reduces eigenvector mixing and improves the interpretability of reconstructed components. Analysis of both simulated and real-world GNSS time series demonstrates that varimax mSSA can accurately reconstruct the skeleton signal. Impressively, even under challenging conditions of 30% Noise and 50% data missing, the ‘skeleton’ signal extracted exhibits remarkable accuracy and consistency, achieving a normalized root-mean-square-error of 0.0884 and a correlation coefficient of 0.9883. This evidence highlights varimax mSSA’s effectiveness as a robust method for imputation and signal extraction in multivariate time series analysis.

In this study, the principal component analysis-multivariate adaptive regression splines (PCA-MARS) technique was applied to efficiently predict the surface area in zeolites. Before building the MARS model, the data matrix obtained from infrared spectroscopy was subjected to robust principal component analysis (rPCA) and six principal component (PC) scores with the explained validation variance 97.983% were used as inputs to the MARS algorithm. The training set (72 × 6) was used to develop the rPCA-MARS model, and the efficiency of the proposed method was evaluated in terms of coefficient of determination (R²), R² estimated by generalized cross-validation (R²GCV), root mean square error of calibration (RMSEC), root mean square error of prediction (RMSEP), and mean absolute error (MAE). R², RMSEC, RMSEP, MAE, and R²GCV in the piecewise-linear rPCA-MARS model were 0.9976, 1.4166, 1.8370, 1.0120, and 0.9955, respectively. We proposed also to use varimax (Var) rotated of the significant principal components as input to the MARS algorithm (R² = 0.9964, RMSEC = 1.4214, RMSEP = 1.9031, MAE = 1.0511, and R²GCV = 0.9951). Upon viewing the PCA-Var-MARS results, we concluded that the obtained results are comparable with rPCAMARS results. In this study, principal component regression (PCR), partial least squares regression (PLSR), and support vector machine regression (SVMR) methods were also used for the quantitative determination of the surface area of zeolites. The RMSEP for PCR, PLSR, and SVMR was 11.5636, 8.7111, and 7.2426, respectively. Based on the results obtained, the MARS model is more reliable than commonly used regression models. It can be concluded that the rPCA-MARS method is an appropriate method for analyzing spectral data to determine the textural properties of zeolite. [ABSTRACT FROM AUTHOR]

Mixed data arise when observations are described by a mixture of numerical and categorical variables. The R package PCAmixdata extends to this type of data standard multivariate analysis methods which allow description, exploration and visualization of the data. The key techniques/methods included in the package are principal component analysis for mixed data (PCAmix), varimax-like orthogonal rotation for PCAmix, and multiple factor analysis for mixed multi-table data. This paper proposes a unified math-ematical presentation of the different methods with common notations, as well as providing a summarised presentation of the three algorithms, with details to help the user understand graphical and numerical outputs of the corresponding R functions. This then allows the user to easily provide relevant interpretations of the results obtained. The three main methods are illustrated on a real dataset composed of four data tables characterizing living conditions in different municipalities in the Gironde region of southwest France. [ABSTRACT FROM AUTHOR]

Nuha Alnaami,1 Ali Al Haqwi,2 Emad Masuadi2 1Department of Clinical Skills, Alfaisal University, Riyadh, Middle Region, Kingdom of Saudi Arabia; 2Department of Medical Education, King Saud Bin Abdulaziz University for Health Sciences, Riyadh, Middle Region, Kingdom of Saudi ArabiaCorrespondence: Nuha AlnaamiAlfaisal University, P.O. Box 50927, Riyadh 11533, Kingdom of Saudi ArabiaTel +966 11 215 7777Fax +966 11 215 7611Email nalnaami@alfaisal.eduIntroduction: The Clinical Learning Evaluation Questionnaire (CLEQ) is a multidimensional, reliable instrument designed to measure the effectiveness of the clinical learning environment for undergraduate medical students. This study seeks to measure and examine the underlying construct along with the latent variables by conducting a confirmatory factor analysis, using structural equation modeling (SEM) so that the instrument can be utilized as an evaluation tool for the continuous improvement of educational environments and curricula.Methods: A cross-sectional study was carried out on 185 third- and fourth-year medical students. A confirmatory factor analysis was conducted, beginning with principal component analysis for standardized factor loadings, using varimax rotation in SPSS to explore the underlying construct of items. The constructs to which each item was tied were determined, and then the data were run through AMOS to assess construct validity through item reduction based on the modification indices, and estimates were made of the standardized residual covariance of each item in order to determine the best model fit.Results: A total of 185 students completed the CLEQ Inventory. The original six-factor structure of the CLEQ did not achieve model fit (X2=1587.475, RMSEA=0.092, RMR=0.146, GFI=0.651, AGFI=0.601, CFI=0.728, NFI=0.626). However, the suggested four-factor model of CLEQ displayed good model fit with the improvement of values (X2=86.184, RMSEA=0.052, RMR=0.062, GFI=0.903, AGFI=0.865, CFI=0.951, NFI=0.871). Internal consistency analysis showed that Cronbach’s alpha values of the original six-factor model ranged from 0.68 to 0.88, while four-factor model ranged from 0.72 to 0.87.Conclusion: This study did not support the proposed six-factor structure of the CLEQ tool. However, the four-factor CLEQ structure demonstrated an adequate degree of good fit and was found to be as reliable as the original structure. Further research on the predictive validity of CLEQ is required as well as a comparison of the psychometric properties across different institutions and countries.Keywords: principal component analysis, varimax rotation, construct validity, clinical education, undergraduate medical students

Background: COVID-19 protective behaviors are key interventions advised by the World Health Organization (WHO) to prevent COVID-19 transmission. However, achieving compliance with this advice is often challenging, particularly among socially vulnerable groups., Objective: We developed a social vulnerability index (SVI) to predict individuals' propensity to adhere to the WHO advice on protective behaviors against COVID-19 and identify changes in social vulnerability as Omicron evolved in African countries between January 2022 and August 2022 and Asia Pacific countries between August 2021 and June 2022., Methods: In African countries, baseline data were collected from 14 countries (n=15,375) during the first Omicron wave, and follow-up data were collected from 7 countries (n=7179) after the wave. In Asia Pacific countries, baseline data were collected from 14 countries (n=12,866) before the first Omicron wave, and follow-up data were collected from 9 countries (n=8737) after the wave. Countries' socioeconomic and health profiles were retrieved from relevant databases. To construct the SVI for each of the 4 data sets, variables associated with COVID-19 protective behaviors were included in a factor analysis using polychoric correlation with varimax rotation. Influential factors were adjusted for cardinality, summed, and min-max normalized from 0 to 1 (most to least vulnerable). Scores for compliance with the WHO advice were calculated using individuals' self-reported protective behaviors against COVID-19. Multiple linear regression analyses were used to assess the associations between the SVI and scores for compliance to WHO advice to validate the index., Results: In Africa, factors contributing to social vulnerability included literacy and media use, trust in health care workers and government, and country income and infrastructure. In Asia Pacific, social vulnerability was determined by literacy, country income and infrastructure, and population density. The index was associated with compliance with the WHO advice in both time points in African countries but only during the follow-up period in Asia Pacific countries. At baseline, the index values in African countries ranged from 0.00 to 0.31 in 13 countries, with 1 country having an index value of 1.00. The index values in Asia Pacific countries ranged from 0.00 to 0.23 in 12 countries, with 2 countries having index values of 0.79 and 1.00. During the follow-up phase, the index values decreased in 6 of 7 African countries and the 2 most vulnerable Asia Pacific countries. The index values of the least vulnerable countries remained unchanged in both regions., Conclusions: In both regions, significant inequalities in social vulnerability to compliance with WHO advice were observed at baseline, and the gaps became larger after the first Omicron wave. Understanding the dimensions that influence social vulnerability to protective behaviors against COVID-19 may underpin targeted interventions to enhance compliance with WHO recommendations and mitigate the impact of future pandemics among vulnerable groups., (©Suladda Pongutta, Viroj Tangcharoensathien, Kathy Leung, Heidi J Larson, Leesa Lin. Originally published in JMIR Public Health and Surveillance (https://publichealth.jmir.org), 13.08.2024.)

The new economy and the knowledge-based society brought significant changes in all the areas of our daily lives. Also, the COVID-19 pandemic and the COVID-19 crisis implicated tremendous transformations in all the domains, on the one hand, threatening the balance of our society and, on the other hand, challenging the dynamic of the new economy development and the rhythm of the societal modernization. In these delicate times, the all-important relationship between ethics, leadership, teamwork, effective communication, productivity, and performance is brought to the attention, in particular, due to its benefits for our society, taking into consideration the pivotal advancement that a well governed relationship of this type could provide to the knowledge-based economy. The present research describes the implication of ethics in leadership, teamwork, effective communication, and productivity, which includes the application of ethical values as university graduates assume the role of each of the mentioned dimensions of study in the organizations. The absence of research that relates ethics to these four elements simultaneously was noticed. This information is essential to know how these dimensions influence the organizational level. The sample that included 410 university graduates was applied in Baja California, Mexico, and the industrial nucleus of great relevance, bordering California in the United States of America. The data was obtained using a questionnaire. A reliability and validity analysis of the measurement instrument was carried out in terms of the ethical values associated with the dimensions mentioned using the exploratory factor analysis by the principal components method. Qualitative items were also analyzed using the constant comparison method. The results obtained in this research provide a greater perspective and practical knowledge and support of usefulness and practical reality to businesspeople and employees, leaders and university graduates; and also extensive to students, teachers, and human beings in general, in order to be better prepared to give and apply solutions with their consequent ethical and productive achievements desired by all. Additionally, this current research has the purpose to raise the will to understand, at a higher level and at a more in-depth degree of knowledge, the relationship between ethics, leadership, teamwork, effective communication, productivity, and performance, in the attempt to foster a creative and innovative business environment, based on a robust and sustainable business administration and business competencies, capable to position at higher ranks the strengths, opportunities, aspirations and outcomes that today's new economy is due to offer and diminish the dangerous effects of the COVID-19 pandemic and the COVID-19 crisis in all the domains. [ABSTRACT FROM AUTHOR]

A correct preoperative diagnosis is essential for the treatment and prognosis of necrotic glioblastoma and brain abscess, but the differentiation between them remains challenging. We constructed a diagnostic prediction model with good performance and enhanced clinical applicability based on data from 86 patients with necrotic glioblastoma and 32 patients with brain abscess that were diagnosed between January 2012 and January 2020. The diagnostic values of three regions of interest based on contrast-enhanced T1 weighted images (including whole tumor, brain-tumor interface, and an amalgamation of both regions) were compared using Logistics Regression and Random Forest. Feature reduction based on the optimal regions of interest was performed using principal component analysis with varimax rotation. The performance of the classifiers was assessed by receiver operator curves. Finally, clinical predictors were utilized to detect the diagnostic power. The mean area under curve (AUC) values of the whole tumor model was significantly higher than other two models obtained from Brain-Tumor Interface (BTI) and combine regions both in training (AUC mean = 0.850) and test/validation set (AUC mean = 0.896) calculated by Logistics Regression and in the testing set (AUC mean = 0.876) calculated by Random Forest. Among these three diagnostic prediction models, the combined model provided superior discrimination performance and yielded an AUC of 0.993, 0.907, and 0.974 in training, testing, and combined datasets, respectively. Compared with the brain-tumor interface and the combined regions, features obtained from the whole tumor showed the best differential value. The radiomic features combined with the peritumoral edema/tumor volume ratio provided the prediction model with the greatest diagnostic performance. [ABSTRACT FROM AUTHOR]

Morphometric analyses on the immature stages of Anisops breddini Kirkaldy (Hemiptera: Notonectidae) was done by collecting insects from the field. Measurements of 36 characters of nymphal instars I--V were taken based on ten individuals of each developmental stage. Morphometric measurements of vertex (V), synthlipsis (S) and head length (HL) in instars I-V revealed a uniform pattern of development. Twenty nine morphometric ratios were analyzed by using one-way analysis of variance (ANOVA), principal component analysis (PCA) and varimax rotation to identify the important morphometric ratios for characterization of instars I-V. The variations in each morphometric ratio among the developmental stages were found statistically significant. ANOVA and PCA have revealed that ratios of synthlipsis to vertex (S/V), synthlipsis to head width (S/HW) and length of rostrum segment four to rostrum length (R4L/RL) are useful morphometric ratios for description and separation of instars I-V. However, instar I can be easily distinguished from rest by the absence of wing pad. [ABSTRACT FROM AUTHOR]

In this study, morphotectonic analysis was performed to investigate the influence of tectonic activity on drainage network in Qorve-Dehgolan basin, located in Sanandaj - Sirjan Zone (SSZ). Eight watersheds were delineated using burnt DEM and eleven morphotectonic indices including stream length gradient index (SL); drainage basin asymmetry (Af); hypsometric curve (HC); hypsometric integral (HI); roughness (R); elongation ratio (Re); mountain front sinuosity (Smf); basin shape (Bs); curvature of surface (C), basin slope (Sb) and river sinuosity index (K) were calculated. The higher altitude watersheds specifically showed various anomalies in the calculated indices. These indices when subjected to factor analysis (using Varimax rotation) resulted in extraction of "steepness factor" and "asymmetric factor" as two principal factors influencing the drainage network. The integrated analysis revealed that steepness factor, indicating ongoing tectonism, plays a significant role in the hydrology of higher altitude watersheds, whereas asymmetric factor is more dominant in lower altitude watersheds. [ABSTRACT FROM AUTHOR]

This work presents a confirmatory factor analysis (CFA) considering the version of the scale of attitudes elaborated by Elena Auzmendi in 1992, adapted from Spanish, being translated into Portuguese considering the students' attitudes towards probability teaching. After confirming the attitudes of 492 students who took a mandatory subject in 2019 focused on probabilistic content in a bachelor of science and technology course at a federal university in the state of São Paulo, Brazil, we related different variables (gender; age; if they worked; marital status; if they received any type of scholarship; if they carried out complementary activities in their education; if they have parental support to carry out their studies; if they have a computer and internet at home) and general aspects in relation to academic performance. The results obtained by the factor analysis, using the method of factorisation of the main axis and Varimax rotation, confirm a solution of 4 (four) factors with an explained variance of 58.419%. The internal consistency assessed by Cronbach's alpha coefficient is 0.926, indicating an adequate discrimination capacity of the items. Some of the results indicate that students have negative connotations regarding satisfaction in dealing with issues related to probability, but have positive aspects related to its usefulness for the job market. We also highlight that the students' attitudes present statistically significant differences in relation to gender, age, if they work and if they took the subject in the ideal period proposed by the curricular structure. [ABSTRACT FROM AUTHOR]

Introduction: Poor air quality in the heavily polluted cities like Tehran is often the main city problem that influences people health and comfort. The main goals of this study are summarized as: 1) Seasonal pollutants mean variations during 2005, meteorological conditions effects on pollutant concentration; 2) Meteorological conditions case study and pollution spatial distribution for three determining synoptic patterns (MET1, MET4, MET5); 3) Further analysis of the episode from 30th November to 13th December 2005 (MET4); 4) Episode analysis from 30th November to 13th December 2005 (MET4) and 5) Episode analysis from 12th-22th of September 2005 (MET5). These are systematic weather patterns that usually affect the air pollution levels in Tehran. Materials and methods: Concentration changes of CO, PM10, SO2 and O3, as the relationship between the air pollution extreme events and atmospheric conditions in Tehran have been investigated. The hourly air pollution data from 11 representative monitoring sites were used. To understand the relationship between local meteorological synoptic patterns and air pollution, the principal component analysis (PCA) method has been applied to meteorological data. Then for minimizing the data complication the varimax rotations (VR) was used and five synoptic perspectives weather patterns have resulted for highly polluted periods. Results: Pollutants correlation investigation of the five patterns showed that air quality was highly dependent on middle tropospheric high geopotential ridge development, local southerly wind with strong static stability. Conclusion: The most polluted periods were associated with a weak pressure gradient, a weak wind, severe air descent, and radiation inversion.

Cucumber (Cucumis sativus L.) seed is imported to Iran. A breeding program is needed locally to select elite lines. Factor analysis is a useful tool for investigating variable relationships for complex factors because it allows investigation of concepts that are not easily measured directly by collapsing a large number of variables into a few interpretable underlying factors. Forty genotypes, representing hybrids of commercial cucumber, cv. Negeen, and lines B10 and B12, developed locally, were used in the experiment at Rasht, Iran. Factor analysis, based on principal component analysis and varimax rotation, indicated the factors yield, major yield contributing factors, fruit quality, fruit firmness, and vegetative factors accounted for 66.5% of total variation. Genotypes positioned near the commercial cultivar in scatter diagrams were acceptable because they had high yield, and major yield contributing factors, and good fruit quality. If gynociouse and parthenocarpic lines are not available germplasm can be selected from progenies of commercial hybrids and local lines with a simple factor analysis. [ABSTRACT FROM AUTHOR]

The study of electroencephalographic (EEG) activity during sleep in the spider monkey has provided new insights into primitive arboreal sleep physiology and behavior in anthropoids. Nevertheless, studies conducted to date have maintained the frequency ranges of the EEG bands commonly used with humans. The aim of the present work was to determine the EEG broad bands that characterize sleep and wakefulness in the spider monkey using principal component analysis (PCA). The EEG activity was recorded from the occipital, central, and frontal EEG derivations of six young‐adult male spider monkeys housed in a laboratory setting. To determine which frequencies covaried and which were orthogonally independent during sleep and wakefulness, the power EEG spectra and interhemispheric and intrahemispheric EEG correlations from 1 to 30 Hz were subjected to PCA. Findings show that the EEG bands detection differed from those reported previously in both spider monkeys and humans, and that the 1–3 and 2–13 Hz frequency ranges concur with the oscillatory activity elucidated by cellular recordings of subcortical regions. Results show that applying PCA to the EEG spectrum during sleep and wakefulness in the spider monkey led to the identification of frequencies that covaried with, and were orthogonally independent of, other frequencies in each behavioral vigilance state. The new EEG bands differ from those used previously with both spider monkeys and humans. The 1–3 and 2–13 Hz frequency ranges are in accordance with the oscillatory activity elucidated by cellular recordings of subcortical regions in other mammals. [ABSTRACT FROM AUTHOR]

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OBJECTIVES: The study was designed to construct a valid and reliable social comparison scale for women with infertility (SCS-WI) in Pakistan. METHODS: A mixed-method approach with purposive sampling techniques was used to construct the scale. Study duration was 13 months and was set in private and government hospitals and clinics of major cities of four provinces of Pakistan. Factor structure of 37 item with primary infertility was explored through exploratory factor analysis (EFA) on a sample of 215 women with primary infertility with age range from 20-45(Mage= 31.03; SD= 6.18) years. The obtained factor structure of Social Comparison Scale for Women with Infertility (32 items) was further confirmed through confirmatory factor analysis (CFA) on a sample of 210 women with primary infertility whose ages ranged between 20 years and 45 years (Mage =32.42, SD=5.49). RESULTS: Principal component analysis (PCA) with Varimax rotation method yielded three factors (viz., social distress, emotional burden and personal incapacities) and accounted for 63.37% variance and all 32 items of the scale were retained. The CFA supported the measurement structure of SCS-WI retained after EFA. The Cronbach’s alpha coefficient for the scale was 0.95 (alphas range from .85-.90 for subscales) with sound convergent and divergent validity (r = 0.37, p = 0.05) (r = -0.70, p

OBJECTIVE: The study was designed to construct a valid and reliable social comparison scale for women with infertility (SCS-WI) in Pakistan. METHODS: A mixed-method approach with purposive sampling techniques was used to construct the scale. Study duration was 13 months and was set in private and government hospitals and clinics of major cities of four provinces of Pakistan. Factor structure of 37 item with primary infertility was explored through exploratory factor analysis (EFA) on a sample of 215 women with primary infertility with age range from 20-45(Mage= 31.03; SD= 6.18) years. The obtained factor structure of Social Comparison Scale for Women with Infertility (32 items) was further confirmed through CFA on a sample of 210 women with primary infertility whose ages ranged between 20 years and 45 years (Mage =32.42, SD=5.49). RESULTS: Principal component analysis (PCA) with Varimax rotation method yielded three factors (viz., social distress, emotional burden and personal incapacities) and accounted for 63.37% variance and all 32 items of the scale were retained. The CFA supported the measurement structure of SCS-WI retained after EFA. The Cronbach's alpha coefficient for the scale was 0.95 (alphas range from .85-.90 for subscales) with sound convergent and divergent validity (r = 0.37, p = 0.05) (r = -0.70, p<0.001) respectively. Test re-test reliability was (r = 0.93, p < 0.001). CONCLUSION: Social comparison scale for women with infertility is a valid scale with good items homogeneity, internal consistency and a revelatory pattern of validity. [ABSTRACT FROM AUTHOR]

This paper attempts to develop a few measures or scales of entrepreneurial motives of women, given the socio-cultural factors in developing economies. Within the push–pull theory of entrepreneurial motivation, we use exploratory factor analysis with an orthogonal varimax rotation technique to examine entrepreneurial motivation, integrating it with socio-cultural beliefs. We identify five entrepreneurial motives—self-dependence, preserving handloom culture, providing monetary support, formal job environment, and work-flexibility. Within socially constructed gender roles, generic desires of women are crucial for entrepreneurial behavior. Contrary to existing findings, we found that women with a higher desire to provide monetary support to their family were found to be less likely to become micro-entrepreneurs, which can be accounted for their poor economic conditions, a significant risk-averse attitude, and credit constraints. The scales constructed could be used across cultures, especially in developing economies. Their replication should provide an understanding of why women micro-entrepreneurs tend to be concentrated in specific sectors, resulting in gender segregation. Given the context specific measurement items, scholars interested in studying socio-cultural attributes in entrepreneurial motivation can further develop and validate the multi-item constructs that distinguish women's motivations for specific activities. [ABSTRACT FROM AUTHOR]

Aiming to improve the fault detection ability of FD-KNN in the nonlinear and multimodal process, this paper proposed a K-nearest neighbors fault detection method based on varimax rotation (Rot-KNN). Firstly, it implemented varimax rotation in observed data set to obtain an orthogonal space. Next, it implemented FD-KNN in the new orthogonal space to detect faults. At last, it proposed a fault diagnosis strategy based on contribution chart. A nonlinear simulation example and the Tennessee Eastman (TE) processes of a typical nonlinear industrial process prove that the method is effective for the latent variable fault diagnosis. The experimental results indicate that the proposed method outperforms the PGA, FD-KNN and PC-KNN. [ABSTRACT FROM AUTHOR]

Gradient projection rotation (GPR) is an openly available and promising tool for factor and component rotation. We compare GPR toward the Varimax criterion in principal component analysis to the built-in Varimax procedure in SPSS. In a simulation study, we tested whether GPR-Varimax yielded multiple local solutions by creating population simple structure with a single optimum and with two optima, a global and a local one (double-optimum condition). The other conditions comprised the number of components (k = 3, 6, 9, and 12), the number of variables per component (m/k = 4, 6, and 8), the number of iterations per rotation (i = 25 and 250), and whether loadings were Kaiser normalized before rotation or not. GPR-Varimax was conducted with unrotated and multiple (q = 1, 10, 50, and 100) random start loadings. We found equal results for GPR-Varimax and SPSS-Varimax in most conditions. The few very small differences in favor of SPSS-Varimax were eliminated when Kaiser-normalized loadings and 250 iterations per rotation were used. Selecting the best solution out of multiple random starts in GPR-Varimax increased proximity to population components in the double-optimum condition with Kaiser normalized loadings, for which GPR-Varimax recovered population structure better than SPSS-Varimax. We also included an empirical example and found that GPR-Varimax and SPSS-Varimax yielded highly similar solutions for orthogonal simple structure in a real data set. We suggest that GPR-Varimax can be used as an alternative to Varimax rotation in SPSS. Users of GPR-Varimax should allow for at least 250 iterations, normalize loadings before rotation, and select the best solution from at least 10 random starts to ensure optimal results. [ABSTRACT FROM AUTHOR]

Highlights • The mineral composition of mustard leaves depends on the cooking method employed. • The cooking using microwave oven decreases the mineral content of mustard leaves. • The mustard leaves have a mineral composition recommended as supplement food. • The mustard leaves have a high content of potassium, calcium, magnesium, and phosphor. • To reduce the potassium content cooking using a microwave oven is the most appropriate. Abstract This work evaluated the influence of the cooking methods (cooked in a water bath, in a stove, and in a microwave oven) on the mineral composition of mustard leaves (Sinapis alba). So, raw and cooked samples were digested and afterward the elements calcium, magnesium, potassium, sodium, iron, zinc, phosphor, barium and sulfur were determined using inductively coupled plasma optical emission spectrometry (ICP OES). The experimental work involved a set of five samples from different locations, processed in triplicates. The results were evaluated employing Principal Component Analysis (PCA), Hierarchical Cluster Analysis (HCA) and Linear Discriminate Analysis (LDA). All techniques showed that the mineral content of the raw and cooked samples in a water bath is different from the samples cooked in stove and microwave oven. Especially for potassium, whose content is strictly controlled for chronic renal patients, this study showed that cooking using microwave oven has the greatest efficiency for reduction. [ABSTRACT FROM AUTHOR]

Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of the matrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches.