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.

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.

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.

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.

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.

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.

Analysis of factors influencing the Henry Hub natural gas price based on factor analysis

Henry Hub as an important transaction hub for natural gas sets the gas price standard in the USA. In this paper, the factors influencing Henry Hub natural gas prices are analyzed, and the major factors determining the price levels in the period between January 1997 and December 2016 are studied. It is found that economic conditions, total energy demand, US dollar exchange rate and gas consumption are the major factors. The mechanism of each factor influencing the Henry Hub natural gas price is also explored in the paper.

Modeling Indicator Systems for Evaluating Environmental Sustainable Development Based on Factor Analysis

Indicator systems of environmental sustainable development in the Poyang Lake Basin are established from 51 elementary indexes by factor analysis, which is composed of four steps such as the factor model, the parameter estimation, the factor rotation and the factor score. Under the condition that the cumulative proportion is greater than 85%, 5 explicit factors of environmental sustainable development as well as its factor score by region are carried out. The result indicates some impact factors to the basin environmental in descending sort order are volume of water, volume of waste gas discharge,volume of solid wasters.the degree to comprehensive utilization of waste gas, waste water and solid wastes, the emission volume of waste gas, waste water and solid wastes. It is helpful and important to provide decision support for constituting sustainable development strategies and evaluate the sustainable development status of each city.

Wave Energy Estimation by Using A Statistical Analysis and Wave Buoy Data near the Southern Caspian Sea

Statistical analysis was done on simultaneous wave and wind using data recorded by discus-shape wave buoy. The area is located in the southern Caspian Sea near the Anzali Port. Recorded wave data were obtained through directional spectrum wave analysis. Recorded wind direction and wind speed were obtained through the related time series as well. For 12-month measurements（May 25 2007-2008）, statistical calculations were done to specify the value of nonlinear auto-correlation of wave and wind using the probability distribution function of wave characteristics and statistical analysis in various time periods. The paper also presents and analyzes the amount of wave energy for the area mentioned on the basis of available database. Analyses showed a suitable comparison between the amounts of wave energy in different seasons. As a result, the best period for the largest amount of wave energy was known. Results showed that in the research period, the mean wave and wind auto correlation were about three hours. Among the probability distribution functions, i.e Weibull, Normal, Lognormal and Rayleigh, ＂Weibull＂ had the best consistency with experimental distribution function shown in different diagrams for each season. Results also showed that the mean wave energy in the research period was about 49.88 k W/m and the maximum density of wave energy was found in February and March, 2010.

Application of Factor Analysis in Sensory Evaluation of Tobacco Raw Materials

[ Objective] This study aimed to analyze the main sensory quality indexes of reconstituted tobacco materials. [ Method ] The factor analysis was per- formed to analyze sensory quality of reconstituted tobacco raw materials. [ Result] The results showed that the contribution rate was 87. 791% and four factors were obtained via factor analysis. The factor loading of factor 1 （ aroma quality, aroma amount, offensive odor, after-taste） was relatively large. Factor 2 was the exterior factor. Factor 3 was momentum factor. Factor 4 was the concentration factor. The comprehensive scores of samples from different regions demonstrated a descending order of Hubei, Yuxi, Chuxiong, Honghe, Dali, Kunming, Hunan, Henan, Fujian, Qujing, Baoshan, Guizhou, Zhaotong, Chongqing, Puer, Wenshan, Guang- dong, and Jiangxi. [ Conclusion] The factor analysis results provided a theoretical basis for subsequent sensory evaluation of reconstituted tobacco.

基于SPSS的城市区域地下水变异Factor Analysis过程

对需要大量运算的统计问题,运用SPSS软件可以快速得到演算结果,从而彻底消除重复而单调的过程,研究人员可更多地专注于统计模型的建立。作者建立了城市建设引发城市区域的地下水缓慢变异的模型,调用SPSS的Factor Analysis过程,对城市区域地下水场变异起重要的组分进行提取,以起重要作用的K、Na、Ca、Mg、Fe、Mn组分最少组合来作为评价地下水变异的指标体系。对南宁市区地下水中特征点进行初步定量分析表明,城市区域地下水年变异水平是城市的建设与发展作用的结果,随时间增长变异水平呈增长之势。从历史背景下研究城市区域地下水缓慢变异程度及趋势,对城市地下水演化规律的认识有重要的指导意义。

Source Apportionment of Ambient PM_(10) in the Urban Area of Longyan City,China:a Comparative Study Based on Chemical Mass Balance Model and Factor Analysis Method

In order to identify the day and night pollution sources of PM10 in ambient air in Longyan City,the authors analyzed the elemental composition of respirable particulate matters in the day and night ambient air samples and various pollution sources which were collected in January 2010 in Longyan with inductivity coupled plasma-mass spectrometry（ICP-MS）.Then chemical mass balance（CMB） model and factor analysis（FA） method were applied to comparatively study the inorganic components in the sources and receptor samples.The results of factor analysis show that the major sources were road dust,waste incineration and mixed sources which contained automobile exhaust,soil dust/secondary dust and coal dust during the daytime in Longyan City,China.There are two major sources of pollution which are soil dust and mixture sources of automobile exhaust and secondary dust during the night in Longyan.The results of CMB show that the major sources are secondary dust,automobile exhaust and road dust during the daytime in Longyan.The major sources are secondary dust,soil dust and automobile exhaust during the night in Longyan.The results of the two methods are similar to each other and the results will guide us to plan to control the PM10 pollution sources in Longyan.

Quantum Biophysics of the Atmosphere: Factor Analysis of the Annual Dynamics of Maximum, Minimum and Average Temperatures from 1879 to 2017 to Hadley English Temperature Center (Hadcet)

Factor analysis of annual dynamics from 1879 to 2017 was carried out by the method of identification of stable regularities:maximum,minimum and average air temperature of Central England according to HadCET.The sample capacity was 139 rows.In factor analysis,time is excluded,and it acts only as a system-forming factor that ensures the relationship between the three parameters of climate and weather.Therefore,the ade­quacy of the dynamics models is taken into account in the diagonal cells of the correlation matrix.In addition to time,different lists of objects are possible in factor analysis.The coefficient of correlation variation,that is,a measure of the functional relationship between the parameters of the system(annual weather at the weather station in Central England)is 0.8230 for trends,0.8603 taking into account the annual dynamics of the four-membered model obtained from the computational capabilities of the software environment CurveExpert-1.40,and 0.9578 for the full up to the error of measurement wavelet analysis of the dynamics of the values of three factors.In all three methods of factor analysis,the meteorolog­ical parameter«average Annual temperature»was in the first place as the influencing variable,the«Maximum temperature»was in the second place,and the«Minimum temperature»was in the third place.As the dependent measure in these areas there are three kinds of temperature.The comparison shows that among the binary relations between the three temperatures,the average temperature on the maximum air temperature in the surface layer of the atmosphere has the greatest influence on the correlation coefficient 0.9765.At the same time,all six equations refer to strong connections,so there is a high quantum certainty between the three types of temperature.But when predicting the most meaningful essence showed the maximum temperature.

Simultaneous Spectrophotometric Determination of Four Components including Acetaminophen by Taget Factor Analysis

UV Spectrophotometric Target Factor Analysis （TFA） was used for the simultaneous determination of four components （acetaminophen, guuaifenesin, caffeine, Chlorphenamine maleate） in cough syrup. The computer Frogram of TFA is based on VC＋＋ language. The difficulty of overlapping of absorption spectra of four compounds was overcome by this procedure. The experimental results show that the average recovery of each component is all in the range from 98.9% to 106.8% and each component obtains satisfactory results without any pre-separation.

Discrimination of marine algal taxonomic groups based on fluorescence excitation emission matrix, parallel factor analysis and CHEMTAX

An in vivo three-dimensional fluorescence method for the determination of algae community structure was developed by parallel factor analysis （PARAFAC） and CHEMTAX. The PARAFAC model was applied to fluo-rescence excitation-emission matrix （EEM） of 60 algae species belonging to five divisions and 11 fluorescent components were identified according to the residual sum of squares and specificity of the composition profiles of fluorescent. By the 11 fluorescent components, the algae species at different growth stages were classified correctly at the division level using Bayesian discriminant analysis （BDA）. Then the reference fluo-rescent component ratio matrix was constructed for CHEMTAX, and the EEM-PARAFAC-CHEMTAX method was developed to differentiate algae taxonomic groups. The correct discrimination ratios （CDRs） when the fluorometric method was used for single-species samples were 100% at the division level, except for Bacil-lariophyta with a CDR of 95.6%. The CDRs for the mixtures were above 94.0% for the dominant algae species and above 87.0% for the subdominant algae species. However, the CDRs of the subdominant algae species were too low to be unreliable when the relative abundance estimated was less than 15.0%. The fluorometric method was tested using the samples from the Jiaozhou Bay and the mesocosm experiments in the Xiaomai Island Bay in August 2007. The discrimination results of the dominant algae groups agreed with microscopy cell counts, as well as the subdominant algae groups of which the estimated relative abundance was above 15.0%. This technique would be of great aid when low-cost and rapid analysis is needed for samples in a large batch. The fluorometric technique has the ability to correctly identify dominant species with proper abundance both in vivo and in situ.