R-Factor Analysis of Data Based on Population Models Comprising R- and Q-Factors Leads to Biased Loading Estimates

Effects of performing an R-factor analysis of observed variables based on population models comprising R- and Q-factors were investigated. Although R-factor analysis of data based on a population model comprising R- and Q-factors is possible, this may lead to model error. Accordingly, loading estimates resulting from R-factor analysis of sample data drawn from a population based on a combination of R- and Q-factors will be biased. It was shown in a simulation study that a large amount of Q-factor variance induces an increase in the variation of R-factor loading estimates beyond the chance level. Tests of the multivariate kurtosis of observed variables are proposed as an indicator of possible Q-factor variance in observed variables as a prerequisite for R-factor analysis.

3D Modeling and Determination of Factors Responsible for Zinc-Lead Mineralization in the Mehdiabad Deposit,Central Iran,based on Statistical Analysis of Geochemical Data

Although the Mehdiabad zinc-lead deposit is one of the most well-known deposits in the central Iran structural zone,the genesis of the deposit remains controversial.The host rock of the ore is a dolomitic limestone of the Lower Cretaceous Taft Formation.In the two main orebodies of the deposit,which includes the Black Hill and East Ridge ore zones,the oxide and sulfide ores are observed at the surface and at depth,respectively.The elements Zn,Fe,Mn and Mg are more abundant in the East Ridge ore zone(in both sulfide and oxide ores),with Ba,Pb,Ag and Cu being more abundant in the Black Hill oxide ore.Based on the distribution of elements and their correlation with each other in these ore zones,the elements are divided into three general groups,that of terrigenous elements,chemically-deposited elements and oreforming(hydrothermally deposited)elements,a division that is supported by the results of factor analyses.The spatial distribution of elements is jointly affected by contact with host rocks,the boundary of oxide-sulfide ores and fault zones.The main factors governing the distribution of elements are the mechanical transfer of detrital sediments,chemical sedimentation,transfer by hydrothermal fluids,oxidation and surface dissolution,all of which affected the spatial distribution of elements.The ore-forming elements are mostly affected by hydrothermal fluids and oxidation.This study not only provides additional information about the genesis of the Mehdiabad deposit,but also could assist in the exploitation of ore and further exploration purposes.The results of this study can aid in the exploration and exploitation of the Mehdiabad deposit and similar deposits in the region.

Dealing with Multicollinearity in Factor Analysis: The Problem, Detections, and Solutions

Multicollinearity in factor analysis has negative effects, including unreliable factor structure, inconsistent loadings, inflated standard errors, reduced discriminant validity, and difficulties in interpreting factors. It also leads to reduced stability, hindered factor replication, misinterpretation of factor importance, increased parameter estimation instability, reduced power to detect the true factor structure, compromised model fit indices, and biased factor loadings. Multicollinearity introduces uncertainty, complexity, and limited generalizability, hampering factor analysis. To address multicollinearity, researchers can examine the correlation matrix to identify variables with high correlation coefficients. The Variance Inflation Factor (VIF) measures the inflation of regression coefficients due to multicollinearity. Tolerance, the reciprocal of VIF, indicates the proportion of variance in a predictor variable not shared with others. Eigenvalues help assess multicollinearity, with values greater than 1 suggesting the retention of factors. Principal Component Analysis (PCA) reduces dimensionality and identifies highly correlated variables. Other diagnostic measures include the condition number and Cook’s distance. Researchers can center or standardize data, perform variable filtering, use PCA instead of factor analysis, employ factor scores, merge correlated variables, or apply clustering techniques for the solution of the multicollinearity problem. Further research is needed to explore different types of multicollinearity, assess method effectiveness, and investigate the relationship with other factor analysis issues.

Analysis of inhomogeneity of solidified microstructure of continuous casting copper tubular billet based on factor analysis

The horizontal continuous casting process,the initial step in TP2 copper tubular processing,directly determines the microstructure and properties of copper tubular.However,the process parameters of the continuous casting characterize time variation,multiple disturbances and strong coupling.As a consequence,their influence on a casting billet is difficult to be determined.Due to the above issues,the common factor and special factor analysis of the factor analysis model were used in this study,and the casting experiment and billet metallographic experiment were carried out to diagnose and analyze the reason of the microstructure inhomogeneity.The multiple process parameters were studied and classified using common factor analysis,2 the cast billets with abnormal microstructures were identified by GT^(2) statistics,and the most important factors affecting the microstructural homogeneity were found by special factor analysis.The calculated and experimental results show that the principal parameters influencing the inhomogeneity of solidified microstructure are the primary inlet water pressure and the primary outlet water temperature.According to the consequence of the above investigation,the inhomogeneity of the copper billet microstructure can be effectively improved when the process parameters are controlled and adjusted.

Using Factor Analysis to Determine the Factors Impacting Learning Python for Non-Technical Business Analytics Graduate Students

This pioneering research represents a unique and singular study conducted within the United States, with a specific focus on non-technical graduate students pursuing degrees in business analytics. The primary impetus behind this study stems from the escalating demand for data-driven professionals, the diverse academic backgrounds of students, the imperative for adaptable pedagogical methods, the ever-evolving landscape of curriculum designs, and the overarching commitment to fostering educational equity. To investigate these multifaceted dynamics, we employed a data collection method that included the distribution of an online survey on platforms such as LinkedIn. Our survey reached and engaged 74 graduate students actively pursuing degrees in Business Analytics within the United States. This comprehensive research is the first and only one of its kind conducted in this context, and it serves as a vanguard exploration into the challenges and influences that shape the learning journey of Python among non-technical graduate Business Analytics students. The analytical insights derived from this research underscore the pivotal role of hands-on learning strategies, exemplified by practice exercises and assignments. Moreover, the study highlights the positive and constructive influence of collaboration and peer support in the process of learning Python. These invaluable findings significantly augment the existing body of knowledge in the field of business analytics. Furthermore, they offer an essential resource for educators and institutions seeking to optimize the educational experiences of non-technical students as they acquire essential Python skills.

GREY RELATIONAL ANALYSIS: A NEW STATISTICAL METHOD OF MULTIFACTORIAL ANALYSIS IN MEDICINE

The concept, fundamental theory, analytical steps and formulae of grey relational analysis (GRA)-a new statistical method or multifactorial analysis in the field of medicine were introduced. GRA of grouping sequence that is applied to medical study was built by the authors. An example was given to demonstrate it. The superiority of GRA was recounted briefly.

Improved statistical fluctuation analysis for two decoy-states phase-matching quantum key distribution

Phase-matching quantum key distribution is a promising scheme for remote quantum key distribution,breaking through the traditional linear key-rate bound.In practical applications,finite data size can cause significant system performance to deteriorate when data size is below 1010.In this work,an improved statistical fluctuation analysis method is applied for the first time to two decoy-states phase-matching quantum key distribution,offering a new insight and potential solutions for improving the key generation rate and the maximum transmission distance while maintaining security.Moreover,we also compare the influence of the proposed improved statistical fluctuation analysis method on system performance with those of the Gaussian approximation and Chernoff-Hoeffding boundary methods on system performance.The simulation results show that the proposed scheme significantly improves the key generation rate and maximum transmission distance in comparison with the Chernoff-Hoeffding approach,and approach the results obtained when the Gaussian approximation is employed.At the same time,the proposed scheme retains the same security level as the Chernoff-Hoeffding method,and is even more secure than the Gaussian approximation.

Influencing factor analysis of interception probability and classification-regression neural network based estimation

The interception probability of a single missile is the basis for combat plan design and weapon performance evaluation,while its influencing factors are complex and mutually coupled.Existing calculation methods have very limited analysis of the influence mechanism of influencing factors,and none of them has analyzed the influence of the guidance law.This paper considers the influencing factors of both the interceptor and the target more comprehensively.Interceptor parameters include speed,guidance law,guidance error,fuze error,and fragment killing ability,while target performance includes speed,maneuverability,and vulnerability.In this paper,an interception model is established,Monte Carlo simulation is carried out,and the influence mechanism of each factor is analyzed based on the model and simulation results.Finally,this paper proposes a classification-regression neural network to quickly estimate the interception probability based on the value of influencing factors.The proposed method reduces the interference of invalid interception data to valid data,so its prediction accuracy is significantly better than that of pure regression neural networks.

Integration between Genomic and Computational Statistical Surveys for the Screening of SNP Genetic Variants in Inflammatory Bowel Disease (IBD) Pediatric Patients*

Inflammatory bowel diseases (IBD) are complex multifactorial disorders that include Crohn’s disease (CD) and ulcerative colitis (UC). Considering that IBD is a genetic and multifactorial disease, we screened for the distribution dynamism of IBD pathogenic genetic variants (single nucleotide polymorphisms;SNPs) and risk factors in four (4) IBD pediatric patients, by integrating both clinical exome sequencing and computational statistical approaches, aiming to categorize IBD patients in CD and UC phenotype. To this end, we first aligned genomic read sequences of these IBD patients to hg19 human genome by using bowtie 2 package. Next, we performed genetic variant calling analysis in terms of single nucleotide polymorphism (SNP) for genes covered by at least 20 read genomic sequences. Finally, we checked for biological and genomic functions of genes exhibiting statistically significant genetic variant (SNPs) by introducing Fitcon genomic parameter. Findings showed Fitcon parameter as normalizing IBD patient’s population variability, as well as inducing a relative good clustering between IBD patients in terms of CD and UC phenotypes. Genomic analysis revealed a random distribution of risk factors and as well pathogenic SNPs genetic variants in the four IBD patient’s genome, claiming to be involved in: i) Metabolic disorders, ii) Autoimmune deficiencies;iii) Crohn’s disease pathways. Integration of genomic and computational statistical analysis supported a relative genetic variability regarding IBD patient population by processing IBD pathogenic SNP genetic variants as opposite to IBD risk factor variants. Interestingly, findings clearly allowed categorizing IBD patients in CD and UC phenotypes by applying Fitcon parameter in selecting IBD pathogenic genetic variants. Considering as a whole, the study suggested the efficiency of integrating clinical exome sequencing and computational statistical tools as a right approach in discriminating IBD phenotypes as well as improving inflammatory bowel disease (IBD) molecular diagnostic process.

Using factor analysis on the comprehensive evaluation of oil pollution in the Haihe river basin

Selecting six indexs of pH, DO, COD, BOD5, ammonia nitrogen and petroleum hydrocarbons in Haihe River Basin of four seasons in 2012 - 2013 for factor analysis, appling Water Quality Pollution Index （API） to evaluate DO, COD, BOD5 and ammonia nitrogen, aims for systematic evluation to water quality of Haihe River Basin The results showed that two stations of B J1 and HB2 were the 1V type of water, others were the V type; Water Quality Pollution Index （API） was 1.44, which illustrated Haihe River Basin in the state of contamination that the degree of pollution exceeded the standard of functional areas. Factor Analysis explained that between COD, DO and NH3-N were significant difference （P〈0.05）; principal component analysis showed that, in addition to pH and BOD5, the other indicators were above 0.70; the contribution rate of COD, DO, NH3-N and TPH were higher, petroleum hydrocarbons was 100%, it can be considered that the waters type of pollution was organic pollution, and petroleum hydrocarbon contamination was more prominent.

Factor Analysis Based on the Level of Urban Facilities in Different Regions

With the rapid growth of economy in China, people＇s living standard has been generally improved, and people＇s requirements on the quality and quantity of infrastructures like transportation convenience, city greening have become higher and higher, which requires the government to attach importance to these livelihood is- sues. Based on the China Statistical Yearbook, 6 target factors of 31 provinces and cities in China were conducted with factor analysis, and the conditions of the infras- tructures in the 31 provinces and cities were judged and evaluated through the ex- traction of common factors and the calculation of these common factors, and corre- sponding suggestions were proposed with the aim to improve the infrastructures in China.

Comparison of Several Statistical Analysis Models for Genotypic Stability of Saccharum officinarum

[Objective] The study aimed to compare several statistical analysis models for estimating the sugarcane （Saccharum spp.） genotypic stability. [Method] The data of sugarcane regional trials in Guangdong, in 2009 was analyzed by three models respectively： Finlay and Wilkinson model： the additive main effects and multiplicative interaction （AMMI） model and linear regression-principal components analysis （LR- PCA） model, so as to compare the models. [Result] The Finlay and Wilkinson model was easier, but the analysis of the other two models was more comprehensive, and there was a bit difference between the additive main effects and multiplicative inter- action （AMMI） model and linear regression-principal components analysis （LR-PCA） model. [Conclusion] In practice, while the proper statistical method was usually con- sidered according to the different data, it should be also considered that the same data should be analyzed with different statistical methods in order to get a more reasonable result by comparison.

Application of Integration of Spatial Statistical Analysis with GIS to Regional Economic Analysis

This paper summarizes a few spatial statistical analysis methods for to measuring spatial autocorrelation and spatial association, discusses the criteria for the identification of spatial association by the use of global Moran Coefficient, Local Moran and Local Geary. Furthermore, a user-friendly statistical module, combining spatial statistical analysis methods with GIS visual techniques, is developed in Arcview using Avenue. An example is also given to show the usefulness of this module in identifying and quantifying the underlying spatial association patterns between economic units.

Multivariate Statistical Process Monitoring of an Industrial Polypropylene Catalyzer Reactor with Component Analysis and Kernel Density Estimation

Abstract Data-driven tools, such as principal component analysis （PCA） and independent component analysis （ICA） have been applied to different benchmarks as process monitoring methods. The difference between the two methods is that the components of PCA are still dependent while ICA has no orthogonality constraint and its latentvariables are independent. Process monitoring with PCA often supposes that process data or principal components is Gaussian distribution. However, this kind of constraint cannot be satisfied by several practical processes. To ex-tend the use of PCA, a nonparametric method is added to PCA to overcome the difficulty, and kernel density estimation （KDE） is rather a good choice. Though ICA is based on non-Gaussian distribution intormation, .KDE can help in the close monitoring of the data. Methods, such as PCA, ICA, PCA.with .KDE（KPCA）, and ICA with KDE,（KICA）, are demonstrated and. compared by applying them to a practical industnal Spheripol craft polypropylene catalyzer reactor instead of a laboratory emulator.

Construction of Inorganic Elemental Fingerprint and Multivariate Statistical Analysis of Marine Traditional Chinese Medicine Meretricis concha from Rushan Bay

Meretricis concha is a kind of marine traditional Chinese medicine(TCM), and has been commonly used for the treatment of asthma and scald burns. In order to investigate the relationship between the inorganic elemental fingerprint and the geographical origin identification of Meretricis concha, the elemental contents of M. concha from five sampling points in Rushan Bay have been determined by means of inductively coupled plasma optical emission spectrometry(ICP-OES). Based on the contents of 14 inorganic elements(Al, As, Cd, Co, Cr, Cu, Fe, Hg, Mn, Mo, Ni, Pb, Se, and Zn), the inorganic elemental fingerprint which well reflects the elemental characteristics was constructed. All the data from the five sampling points were discriminated with accuracy through hierarchical cluster analysis(HCA) and principle component analysis(PCA), indicating that a four-factor model which could explain approximately 80% of the detection data was established, and the elements Al, As, Cd, Cu, Ni and Pb could be viewed as the characteristic elements. This investigation suggests that the inorganic elemental fingerprint combined with multivariate statistical analysis is a promising method for verifying the geographical origin of M. concha, and this strategy should be valuable for the authenticity discrimination of some marine TCM.

Factor analysis identifies subgroups of constipation

AIM:To determine whether distinct symptom groupings exist in a constipated population and whether such grouping might correlate with quantifiable pathophysiological measures of colonic dysfunction.METHODS:One hundred and ninety-one patients presenting to a Gastroenterology clinic with constipation and 32 constipated patients responding to a newspaper advertisement completed a 53-item,wide-ranging selfreport questionnaire.One hundred of these patients had colonic transit measured scintigraphically.Factor analysis determined whether constipation-related symptoms grouped into distinct aspects of symptomatology.Cluster analysis was used to determine whether indi-vidual patients naturally group into distinct subtypes.RESULTS:Cluster analysis yielded a 4 cluster solution with the presence or absence of pain and laxative unresponsiveness providing the main descriptors.Amongst all clusters there was a considerable proportion of patients with demonstrable delayed colon transit,irritable bowel syndrome positive criteria and regular stool frequency.The majority of patients with these characteristics also reported regular laxative use.CONCLUSION:Factor analysis identified four constipation subgroups,based on severity and laxative unresponsiveness,in a constipated population.However,clear stratification into clinically identifiable groups remains imprecise.

Factor analysis of earthquake-induced geological disasters of the M7.0 Lushan earthquake in China

The seismic intensities, lithologic characteristics and terrain features from a 3000 km2-region near the epicenter of the Lushan earthquake are used to analyze earthquake-induced geological disaster. The preliminary results indicate that secondary effects of the earthquake will affect specific areas, including those with glutenite and carbonate bedrock, a seismic intensity of IX, slopes between 40° and 50°, elevations of less than 2500 m, slope change rates between 20° and 30°, slope curvatures from - 1 to -0.5 and 0. 5 to 1, and relief between 50 and 100 m. Regions with susceptibility indices greater than 0.71 are prone to landslides and collapses. The secondary features are mainly distributed on both sides of the ridges that extend from Baosheng to Shuangshi and from Baosheng to Longxing. Other features are scattered on both sides of the ridges that extend from Qishuping to Baosheng and from Masangping to Lingguan. The distribution of the earthquake-related features trends in the NE direction, and the area that was most affected by the Lushan earthquake covers approximately 52.4 km^2.

Rutting influencing factors and prediction model for asphalt pavements based on the factor analysis method

To clarify the importance of various influencing factors on asphalt pavement rutting deformation and determine a screening method of model indicators,the data of the RIOHTrack full-scale track were examined using the factor analysis method(FAM).Taking the standard test pavement structure of RIOHTrack as an example,four rutting influencing factors from different aspects were determined through statistical analysis.Furthermore,the common influencing factors among the rutting influencing factors were studied based on FAM.Results show that the common factor can well characterize accumulative ESALs,center-point deflection,and temperature,besides humidity,which indicates that these three influencing factors can have an important impact on rutting.Moreover,an empirical rutting prediction model was established based on the selected influencing factors,which proved to exhibit high prediction accuracy.These analysis results demonstrate that the FAM is an effective screening method for rutting prediction model indicators,which provides a reference for the selection of independent model indicators in other rutting prediction model research when used in other areas and is of great significance for the prediction and control of rutting distress.

Solar term peak of onset and death in 1 597 patients with acute ischemic stroke Circular statistical analysis

BACKGROUND： Previously, time data were analyzed by using constituent ratio or relative ratio; however, circular statistical analysis could exactly provide average peak phase of diseases. OBJECTIVE： To investigate the correlation of solar term peak with onset and death of acute ischemic stroke. DESIGN： Retrospective case analysis. SETTINGS： Emergency Department of Foshan Municipal Hospital of Traditional Chinese Medicine; Department of Science and Education, the Second People＇s Hospital of Foshan. PARTICIPANTS： A total of 1 597 patients with acute ischemic stroke were selected from Emergency Room, Department of Neurology, Foshan Municipal Hospital of Traditional Chinese Medicine from 1994 to 2002. There were 875 males and 722 females, and their ages ranged from 33 to 97 years. All cases met the diagnostic criteria of acute cerebral infarction modified by the Second National Cerebrovascular Disease Academic Meeting; meanwhile, they were diagnosed with CT/MRI test. Patients and their relatives provided the confirmed consent. METHODS： Solar term of onset was retrospectively analyzed in 1 597 patients with acute ischemic stroke; among them, solar term of death in 90 cases were analyzed by using circular statistical analysis to calculate peak phase of onset and death of acute ischemic stroke and investigate the correlation of solar term with onset and death of acute ischemic stroke. MAIN OUTCOME MEASURES： Onset and death time of patients with acute ischemic stroke. RESULTS： Solar term of onset in 1 597 patients, especially solar term of death in 90 patients, was not concentrated （P 〉 0.05）, and specific peak phase was not found out. Acute ischemic stroke low attacked from vernal equinox to summer begins, but death caused by acute ischemic stroke high attacked from grain buds to autumn begins. CONCLUSION： Patients with acute ischemic stroke do not have specific solar term peak of onset and death.

Potential hydraulic connectivity of coal mine aquifers based on statistical analysis of hydrogeochemistry

Mining activities interfere with the natural groundwater chemical environment,which may lead to hydrogeochemical changes of aquifers and mine water inrush disasters.This study analyzed the hydrochemical compositions of 80 water samples in three aquifers and developed a water source identification model to explore the control factors and potential hydraulic connection of groundwater chemistry in a coal mine.The results showed that the hydrochemical types of the three aquifers were different.The main hydrochemical compositions of the loose-layer,coal-bearing,and limestone aquifers were HCO_(3)·Cl-Na,SO_(4)·HCO_(3)-Na,and SO_(4)-Na·Ca,respectively.The correlation,Unmix,and factor an-alyses showed that the hydrochemical composition of groundwater was controlled by the dissolution of soluble minerals(such as calcite,dolomite,gypsum,and halite)and the weathering of silicate minerals.The factor score plot combined with Q-mode cluster analysis demon-strated no remarkable hydraulic connection among the three aquifers in the study area.The water source identification model effectively identified the source of inrush water.Moreover,the mixing ratio model rationally quantified the contributions of the three aquifers to inrush water.