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.

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.

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.

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.

Measuring speed consistency for freeway diverge areas using factor analysis

Although either absolute speed or speed difference can be considered as a measure for speed consistency, few researches consider both in practice. The factor analysis method was introduced to extract an optimal number of factors from numerous original measures. The freeway diverging zone was divided into four elements, namely the upstream, the diverge area, the downstream and the exit ramp. Operating speeds together with individual vehicle speeds were collected at each element with radar guns. Following the factor analysis procedure, two factors, which explain 96.722% of the variance in the original data, were retained from the initial seven speed measures. According to the loadings after Varimax rotation, the two factors are clearly classified into two categories. The first category is named "speed scale" reflecting the absolute speed, and the other one is named "speed dispersion" interpreting speed discreteness. Then, the weighted score of speed consistency for each diverge area is given in terms of linear combination of the two retained factors. To facilitate the level classification of speed consistency, the weighted scores are normalized in the range of (0, 1.0). The criterion for speed consistency classification is given as 0≤F N <0.30, good consistency; 0.30≤F N <0.60, fair consistency; 0.60≤ F N ≤1.00, poor consistency. The validation by comparing with previously developed measures shows that the proposed measure is acceptable in evaluating speed consistency.

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.

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.

Evaluation and classification of residential greenbelt quality based on factor analysis & clustering analysis:An example of Xinxiang City,China

Five factors expressing greenbelt quality and one factor expressing quantity were adopted for evaluation of the residential greenbelt, and the AHP （Analytical Hierarchy Process） method was used to determine the value of factors. Thirty residential areas were selected as the samples. Two principal components were extracted and their expression was constructed by method of factor anlysis, therefore, quality evaluation of residential greenbelt was obtained. The accuracy of the function and implement quality classification toward the residential greenbelts in Xinxiang City were validated by clustering analysis method. The results showed that the greenbelt quality of fourteen residential areas was higher than the average level, of which eleven were newly-built residential areas. The 30 residential areas were classified into three types according to their greenbelt features and their formation by clustering analysis method. Finally rational proposal basing on aforesaid evaluating results was proposed for construction and renewal of residential greenbelt, upon which directive basis was provided for construction and renewal of residential greenbelt.

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.

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。

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.

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.

Factor Analysis on Air Quality of Key Environmental Protection Cities

Statistical analysis was performed on 678 data of 6 key indices on air pollution in 113 key cities on basis of China Statistical Yearbook in 2015.Besides,factor analysis was then performed with SPSS17.0 to make overall assessment on air quality in different cities.The results showed that air pollution is quite severe in varying degrees in different cities and the research is expected to provide references for air pollution control in key environment protection cities.

Factor Analysis on Quantity of Discharged Pollutants in Wastewater in Major Cities

The research performed statistical analysis on 186 data concerning the amount of discharged industrial wastewater, the amount of oxygen demand of industrial wastewater, the amount of ammonia and nitrogen discharged from industries, the amount of urban discharged domestic sewage, the amount of daily life chemical oxygen demand, and the amount of domestic ammonia and nitrogen to explore source of pollutants from wastewater and guarantee urban water quality.Factor analysis was then performed with SPSS according to discharge quantity of pollutants. The results should that the major pollutants are from domestic sewage it is expected scientific suggestions be proposed on water quality in our country.