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.

A State-Migration Particle Swarm Optimizer for Adaptive Latent Factor Analysis of High-Dimensional and Incomplete Data

High-dimensional and incomplete(HDI) matrices are primarily generated in all kinds of big-data-related practical applications. A latent factor analysis(LFA) model is capable of conducting efficient representation learning to an HDI matrix,whose hyper-parameter adaptation can be implemented through a particle swarm optimizer(PSO) to meet scalable requirements.However, conventional PSO is limited by its premature issues,which leads to the accuracy loss of a resultant LFA model. To address this thorny issue, this study merges the information of each particle's state migration into its evolution process following the principle of a generalized momentum method for improving its search ability, thereby building a state-migration particle swarm optimizer(SPSO), whose theoretical convergence is rigorously proved in this study. It is then incorporated into an LFA model for implementing efficient hyper-parameter adaptation without accuracy loss. Experiments on six HDI matrices indicate that an SPSO-incorporated LFA model outperforms state-of-the-art LFA models in terms of prediction accuracy for missing data of an HDI matrix with competitive computational efficiency.Hence, SPSO's use ensures efficient and reliable hyper-parameter adaptation in an LFA model, thus ensuring practicality and accurate representation learning for HDI matrices.

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.

Enhancing Clothing Fit for Asian Women through Digital Transformation and Statistical Analysis

This study focuses on designing a solution to the perennial issue of clothing fit in Fashion Industry using tools offered by digital technology and statistical analysis, in particular, the data gathered on Asian women (Bangladeshi and Chinese). The study reveals that managing information can significantly enhance the capability of the industry to cater to the needs of its consumers and increase diversity. It centers on the effectiveness of turning dressmaking patterns into digital ones, thus transecting from traditional cutting and stitching to remote techniques. This entails the requirement to have correct self-measures and probable errors, which can arise in the process. Thus, with the help of regression analysis, the study identifies, which measurements are incorrect and influence the fit of the clothes, and, therefore, digital pattern creation is more accurate. Altogether, it can be observed how digitalization and statistical methods are crucial to transforming the way clothes are created to approach an ideal standard of measurements that fulfill every customer’s needs to make operational and efficient the clothing sector.

Customized Optimization for Vehicle Acoustic Statistical Energy Analysis

Statistical Energy Analysis(SEA) is one of the conventional tools for predicting vehicle high-frequency acoustic responses.This study proposes a new method that can provide customized optimization solutions to meet NVH targets based on the specific needs of different project teams during the initial project stages.This approach innovatively integrates dynamic optimization,Radial Basis Function(RBF),and Fuzzy Design Variables Genetic Algorithm(FDVGA) into the optimization process of Statistical Energy Analysis(SEA),and also takes vehicle sheet metal into account in the optimization of sound packages.In the implementation process,a correlation model is established through Python scripts to link material density with acoustic parameters,weight,and cost.By combining Optimus and VaOne software,an optimization design workflow is constructed and the optimization design process is successfully executed.Under various constraints related to acoustic performance,weight and cost,a globally optimal design is achieved.This technology has been effectively applied in the field of Battery Electric Vehicle(BEV).

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.

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.