Robust Factor Analysis Research Articles

Aykırı değer varlığında sağlam konum ve ölçek kestiricilerinin faktör analizinde kullanımı

Factor analysis, one of those multivariate methods, is used for data reduction, determining the relationships between variables, and also as a classification method. The researchers frequently face with the observations that might have bad affects on the results while analysing data sets with many variables. Those kind of observations are called outliers. Outliers, usually evaluated as erroneous observations, may reflect important information about the data set, but on the other hand may cause misspecification of the model, biased parameter estimates, and may lead incorrect analysis results. The aim of this study is to use factor analysis method which will not make biased parameter estimations of the outliers. For this aim, among the robust local and scale parameter estimators which reduce the affects of outliers, fast minimum covariance determinant estimators are choosen and an application is performed. As a result, robust factor analysis estimation results are obtained which are mostly fitted to the data by reducing the affect of the outliers, with higher explained variability and with explained variables which are gathered on more significant factors.

Phase Transitions and Sample Complexity in Bayes-Optimal Matrix Factorization

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix calibration, sparse principal component analysis, blind source separation, low rank matrix completion, robust principal component analysis or factor analysis. It is also important in machine learning: unsupervised representation learning can often be studied through matrix factorization. We use the tools of statistical mechanics - the cavity and replica methods - to analyze the achievability and computational tractability of the inference problems in the setting of Bayes-optimal inference, which amounts to assuming that the two matrices have random independent elements generated from some known distribution, and this information is available to the inference algorithm. In this setting, we compute the minimal mean-squared-error achievable in principle in any computational time, and the error that can be achieved by an efficient approximate message passing algorithm. The computation is based on the asymptotic state-evolution analysis of the algorithm. The performance that our analysis predicts, both in terms of the achieved mean-squared-error, and in terms of sample complexity, is extremely promising and motivating for a further development of the algorithm.

Discriminating sediment archives and sedimentary processes in the arid endorheic Ejina Basin, NW China using a robust geochemical approach

Geochemical characteristics have been intensively used to assign sediment properties to paleoclimate and provenance. Nonetheless, in particular concerning the arid context, bulk geochemistry of different sediment archives and corresponding process interpretations are hitherto elusive. The Ejina Basin, with its suite of different sediment archives, is known as one of the main sources for the loess accumulation on the Chinese Loess Plateau. In order to understand mechanisms along this supra-regional sediment cascade, it is crucial to decipher the archive characteristics and formation processes. To address these issues, five profiles in different geomorphological contexts were selected. Analyses of X-ray fluorescence and diffraction, grain size, optically stimulated luminescence and radiocarbon dating were performed. Robust factor analysis was applied to reduce the attribute space to the process space of sedimentation history. Five sediment archives from three lithologic units exhibit geochemical characteristics as follows: (i) aeolian sands have high contents of Zr and Hf, whereas only Hf can be regarded as a valuable indicator to discriminate the coarse sand proportion; (ii) sandy loess has high Ca and Sr contents which both exhibit broad correlations with the medium to coarse silt proportions; (iii) lacustrine clays have high contents of felsic, ferromagnesian and mica source elements e.g., K, Fe, Ti, V, and Ni; (iv) fluvial sands have high contents of Mg, Cl and Na which may be enriched in evaporite minerals; (v) alluvial gravels have high contents of Cr which may originate from nearby Cr-rich bedrock. Temporal variations can be illustrated by four robust factors: weathering intensity, silicate-bearing mineral abundance, saline/alkaline magnitude and quasi-constant aeolian input. In summary, the bulk-composition of the late Quaternary sediments in this arid context is governed by the nature of the source terrain, weak chemical weathering, authigenic minerals, aeolian sand input, whereas pedogenesis and diagenesis exert only limited influences. Hence, this study demonstrates a practical geochemical strategy supplemented by grain size and mineralogical data, to discriminate sediment archives and thereafter enhance our ability to offer more intriguing information about the sedimentary processes in the arid central Asia.

Hydrographic conditions driving sardine and anchovy populations in a land-locked sea

The aim of this paper is to establish a relationship between long-term variability in sardine and anchovy populations in the Adriatic Sea and ocean dynamics and processes that occur over interannual and decadal timescales in the Adriatic-Ionian basin. Basis for such analysis are annual time series of sardine and anchovy landings and recruits at age 0 and annual time series of environmental parameters observed at a representative Adriatic station between 1975 and 2010. Pearson correlations and robust Dynamic Factor Analysis (DFA) were applied to quantify the connections between fisheries and environmental parameters. Variations and trends in fisheries series were best explained by changes in near-bottom temperature and salinity, being an appropriate proxy for tracking changes in water masses' dynamics and hydrographic conditions in the basin. It seems that a prolonged period of decreasing sardine population was characterized by low oxygen availability and environmental conditions in the deep Adriatic waters, triggered by an extraordinary basin-wide event called the Eastern Mediterranean Transient. A collapse in anchovy population has been observed after an exceptional cooling event followed by dense water formation.

Bayesian factor analysis with uncertain functional constraints about factor loadings

Factor analysis with uncertain functional constraints about factor loading matrix is considered from a Bayesian viewpoint, in which the uncertain prior information is incorporated in the analysis. We propose a hierarchical screened scale mixture of normal factor ( HSMF ) model for flexible inference of the constrained factor loadings, factor scores, and specific variances as well as the covariance matrix of the factors. The proposed model makes provisions for robust factor analysis with uncertainty about the functional constraints. A number of inferential aspects of the proposed model are investigated in order to render the proposed analysis optimal. These include the closure properties of a class of rectangle-screened scale mixture of multivariate normal ( R S M N ) distributions which is useful for statistical inference of the HSMF model, eliciting the prior and posterior evolutions of the uncertainly constrained factor loadings, and providing the efficient Bayesian estimation procedure by using the MCMC methods. Empirical analysis for Bayesian factor models with synthetic data and real data applications is given to illustrate the usefulness of the proposed model.

Investigating Critical Success Factors in Implementing ITIL Framework

Nowadays, many organizations adopt Information Technology Service Management (ITSM) best practices to enhance their IT service related processes. Although many organizations have adopted ITSM frameworks such as Information Technology Infrastructure Library (ITIL), not all have been successful. Keeping this in mind, this paper seeks to identify Critical Success Factors (CSFs) that impact on successful implementation of ITSM frameworks with a focus on ITIL in Iranian organizations as a case of a developing country. Hence, based on a mixed method, at first, with the semi-structured interviews and literature review, 22 success factors were identified. Following that, a questionnaire was developed and sent out to domain experts. Next, robust Exploratory Factor Analysis (EFA) was run for analyzing data and establishing construct validity which finally classified critical success factors into five groups named as “organizational”, “human resources”, “project management”, “managerial” and “process”. The findings of this study have provided a very useful reference for IT standardization scholars and practitioners to identify the important issues of ITSM frameworks implementation projects in their research and practice.

A robust factor analysis model using the restricted skew- $$t$$ t distribution

Factor analysis is a classical data-reduction technique that seeks a potentially lower number of unobserved variables that can account for the correlations among the observed variables. This paper presents an extension of the factor analysis model, called the skew-\(t\) factor analysis model, constructed by assuming a restricted version of the multivariate skew-\(t\) distribution for the latent factors and a symmetric \(t\)-distribution for the unobservable errors jointly. The proposed model shows robustness to violations of normality assumptions of the underlying latent factors and provides flexibility in capturing extra skewness as well as heavier tails of the observed data. A computationally feasible expectation conditional maximization algorithm is developed for computing maximum likelihood estimates of model parameters. The usefulness of the proposed methodology is illustrated using both simulated and real data.

The Use of Robust Factor Analysis of Compositional Geochemical Data for the Recognition of the Target Area in Khusf 1:100000 Sheet, South Khorasan, Iran

The closed nature of geochemical data has been proven in many studies. Compositional data have special properties that mean that standard statistical methods cannot be used to analyse them. These data imply a particular geometry called Aitchison geometry in the simplex space. For analysis, the dataset must first be opened by the various transformations provided. One of the most popular of the applied transformations is the log-ratio transform. The main purpose of this research is to identify the anomalous area in the Khusf 1:100000 sheet which is located in the western part of Birjand, South Khorasan province. To achieve the goal, a dataset of 652 stream sediments geochemically analysed for 20 elements was collected. In practice, the geochemical data were first opened by CLR transformation and then the range correlation coefficient (RCC) ratio was calculated and mapped. In consequence, the robust factor analysis for compositional data was used to separate the elements, mostly in the high-value regions obtained by the method of RCC. Finally, the priority of anomalies was specified using weighted catchment analysis. The above procedures led to the recognition of some anomaly zones for elements of Cu, Bi, Sb, Ni and Cr in the study area. Such results can be useful for designing an appropriate exploratory plan for semi-detailed and detailed exploration steps.

A Robust Factor Analysis Model for Dichotomous Data

AbstractFactor analysis is widely used in psychology, sociology and economics, as an analytically tractable method of reducing the dimensionality of the data in multivariate statistical analysis. The classical factor analysis model in which the unobserved factor scores and errors are assumed to follow the normal distributions is often criticized because of its lack of robustness. This paper introduces a new robust factor analysis model for dichotomous data by using robust distributions such as multivariatet-distribution. After comparing the fitting results of the normal factor analysis model and the robust factor analysis model for dichotomous data, it can been seen that the robust factor analysis model can get more accurate analysis results in some cases, which indicates this model expands the application range and practical value of the factor analysis model.

Exploratory data analysis and C–A fractal model applied in mapping multi-element soil anomalies for drilling: A case study from the Sari Gunay epithermal gold deposit, NW Iran

This contribution investigates potential best practice in statistical treatment of exploration geochemistry data for drill target definition, using data from the Sari Gunay epithermal gold deposit, northwest Iran. Primarily, a robust factor analysis was applied to the soil geochemical data to identify anomalies related to outcropping and weak surface expression of hidden gold mineralizations. Investigation of outcropping mineralization indicates that the invisible gold mostly occurs in arsenian pyrite, accompanied by antimony and mercury sulfides. Therefore, a favorable principal factor with strong association of Au, As, Sb, Hg, Tl and S elements, related to epithermal mineralization, was selected for analysis. Then, the boxplot and median+2MAD (median absolute deviation) techniques of the exploratory data analysis (EDA) and also concentration–area (C–A) fractal model were applied to the favorable factor loading to set the threshold values for defining multi-element soil geochemical anomalies for drilling. The median+2MAD and C–A fractal models successfully identified the known outcropping gold mineralization at the Sari Gunay and Agh Dagh hills. In contrast, the boxplot method only identified the strong outcropping gold mineralization at the Sari Gunay hill, but failed to map the weaker mineralization at the Agh Dagh hill due to the usage of higher threshold values. In addition, the C–A fractal analysis identified a few second-class, weaker multi-element soil anomalies, mostly related to subsurface gold mineralization. The identified soil geochemical anomalies were compared with the in situ economic gold concentration in channel rock samples, mostly below the soil cover, and the outcropping host lithologies for validation. The results indicated the EDA approaches failed to map weak surface expression of gold mineralization and only mapped strong geochemical anomalies, useful only for reconnaissance drilling stages. The C–A fractal analysis is capable of mapping multi-class geochemical anomalies, some of which were associated with the weak surface expression of hidden gold mineralization, and is therefore useful in defining targets at both the reconnaissance and systematic drilling stages. The identified geochemical anomalies by C–A fractal analysis were also useful to characterize the favorable lithologies (e.g. quartz–tourmaline breccias, intrusive fragmental rocks including diatreme and dacite/trachyte porphyry) and hydrothermal alterations (e.g. quartz-sericite, K-feldspar and silicification) hosting gold mineralization at Sari Gunay.

An Investigation of BI Implementation Critical Success Factors in Iranian Context

Nowadays, many organizations take Business Intelligence (BI) systems to improve their decision-making processes. Although many organizations have adopted BI systems, not all of these implementations have been successful. This paper seeks to identify critical success factors (CSFs) that impact on successful implementation of BI systems in organizations. So, at first, through literature review, 26 CSFs were identified. Following that, a questionnaire was developed and then filled out by domain experts who had at least three years of experience in BI implementation projects in Iran. Robust Exploratory Factor Analysis (EFA) was run for data analysis, which finally classified 26 CSFs into four distinct groups termed as “organizational”, “human”, “project management”, and “technical”. The results of this study provide a very useful reference for scholars and managers to identify the relevant issues of BI projects in Iran.

Robust factor analysis in the presence of normality violations, missing data, and outliers: Empirical questions and possible solutions

Robust factor analysis in the presence of normality violations, missing data, and outliers: Empirical questions and possible solutions

Robust Factor Analysis and Its Applications in the CSI 100 Index

We apply the object-oriented robust factor analysis R package robustfa to the 28 financial indicators of the 100 listed companies in China’s Chinese Securities Index (CSI) 100 index in the first quarter of 2013. First of all, according to the size of the data, we automatically choose a robust estimator, the robust Ogk estimator. By the Mahalanobis distances which are computed by the robust Ogk estimator, greater than the critical value, we find a total of 47 abnormal points. This paper discovers that the results of the sample correlation matrix, the rotated factor loading matrix, the contribution of the factors to the original variables, the contribution rate, the cumulative contribution rate, the screeplot of the eigenvalues of the sample correlation matrix, the scatter plot of the first two factor scores, factor scores, and the sorted scores according to factor scores etc. computed by the classical estimator and the robust Ogk estimator are quite different. Finally, we condense the 28 financial indicators to 5 factors by combining the principal component analysis method and the robust Ogk estimator: Provident fund market value factor, profit factor, market value profit rate factor, value per share factor, and asset liability factor. Finally, we sort the 5 factor scores from high to low of each factor, and also get some special stocks according to the factor scores. The robust factor analysis results provide a good basis for investors to choose the stocks.

A statistical basis for harmonization of thyroid stimulating hormone immunoassays using a robust factor analysis model

Between-method equivalence ideally is achieved by calibration against an SI-traceable reference measurement procedure. For measurement of thyroid stimulating hormone (TSH), it is unlikely to accomplish this goal in mid-term. Therefore, we investigated a statistical alternative based on a factor analysis (FA) model. The FA model was applied to TSH results for 94 samples generated by 14 immunoassays (concentration range: 0.0005-78 mIU/L). The dataset did not fulfill the assumption of a homogeneous sample from an elliptically symmetric distribution, and, therefore, required standardization prior to application of the FA model. As outliers and missing values also occurred, the key quantities of the FA model had to be estimated with a method that can handle these complications. We selected a robust alternating regressions (RAR) method, which replaces in the minimization criterion of the fitting process the squared differences between results xij and model fit x^ij ${\hat x_{ij}}$ by a weighted absolute difference. The weights are adaptively determined in successive regressions, which down weighs the outliers. The weights for missing values are set to zero. The quality of the estimated targets was reflected by their central position in the distributions, and description of the relationship between results and targets by a simple two-parameter regression equation with high correlation coefficients and low SDs of the percentage-residuals. Mathematical recalibration eliminated the method differences and improved the between-method CV from 11% to 6%. RAR applied to a multimethod comparison dataset hampered by outliers and missing values, is fit to the purpose of harmonization.

Validation of the Croatian and Lebanese Revised Illness Perception Questionnaires for Healthy People (IPQ-RH)

The absence of Croatian- and Arabic-language measures to assess illness representations has contributed to lack of research among Croatian and Lebanese populations. Utilising the robust confirmatory factor analysis (CFA) approach, this study aimed to validate Croatian and Arabic versions of the Revised Illness Perception Questionnaire for Healthy People (IPQ-RH) in the breast and cervical cancer contexts, and compared these illness perceptions among Croatian and Lebanese women living in Australia. Forward and back-translated versions of the IPQ-RH were administered in Croatian to Croatian-born (n = 238), and Arabic to Lebanese-born (n = 240) women. The IPQ-RH illness perceptions were assessed for each cancer type, and the Negative Affect (NA) subscale of the Positive and Negative Affect Schedule (PANAS) assessed discriminant validity. The CFA method demonstrated acceptable models across the Croatian and Lebanese IPQ-RH measures. The internal reliabilities for the IPQ-RH subscales were adequate and the subscales had low correlations with the NA subscale of the PANAS, indicating that the IPQ-RH measures are largely distinguishable from negative affective dispositions. These findings demonstrate that the Croatian and Lebanese IPQ-RH breast and cervical cancer measures have a factor structure similar to the originally developed IPQ-RH scale and provide further support for the theoretically developed illness representations.

Geogenic and agricultural controls on the geochemical composition of European agricultural soils

Purpose: Concern about the environmental impact of agriculture caused by intensification is growing as large amounts of nutrients and contaminants are introduced into the environment. The aim of this paper is to identify the geogenic and agricultural controls on the elemental composition of European, grazing and agricultural soils. Materials and methods: Robust factor analysis was applied to data series for Al, B, Ca, Cd, Co, Cu, Fe, K, Mg, Mn, Na, Ni, P, S, Se, Sr, U, Zn (ICP-MS) and SiO2, K2O, Na2O, Fe2O3, Al2O3 (XRF) based on the European GEMAS dataset. In addition, the following general soil properties were included: clay content, pH, chemical index of alteration (CIA), loss on ignition (LOI), cation exchange capacity (CEC), total organic carbon (TOC) and total carbon and total sulfur. Furthermore, this dataset was coupled to a dataset containing information of historic P2O5 fertilization across Europe. Also, a mass balance was carried out for Cd, Cu and Zn to determine if concentrations of these elements found in the soils have their origin in historic P2O5 fertilization. Results and discussion: Seven geogenic factors and one agricultural factor were found of which four prominent ones (all geogenic): chemical weathering, reactive iron-aluminum oxide minerals, clay minerals and carbonate minerals. Results for grazing and agricultural soils were near identical, which further proofs the prominence of geogenic controls on the elemental composition. When the cumulative amount of P2O5 fertilization was considered, no extra agriculture-related factors became visible. The mass balance confirms these observations. Conclusions: Overall, the geological controls are more important for the soil chemistry in agricultural and grazing land soils than the anthropogenic controls. © 2013 Springer-Verlag Berlin Heidelberg.

Robust confirmatory factor analysis based on the forward search algorithm

A key concept of the forward search algorithm in confirmatory factor analysis is ordering of the data on the basis of observational residuals. These residuals are computed under the proposed model and measure the discrepancy between the observed and predicted response for each unit of the sample. Regression-type factor scores are used to estimate model predictions. Informative forward plots are created for indexing influential observations and to show the dynamics of the estimates throughout the search. The detailed influence of each observation on the model parameters and fit indices is analyzed and a robust model inference is achieved. Real and simulated data sets with known contamination schemes are used to demonstrate the performance of the forward search algorithm.

Bayesian Robust PCA of Incomplete Data

We present a probabilistic model for robust factor analysis and principal component analysis in which the observation noise is modeled by Student-t distributions in order to reduce the negative effect of outliers. The Student-t distributions are modeled independently for each data dimensions, which is different from previous works using multivariate Student-t distributions. We compare methods using the proposed noise distribution, the multivariate Student-t and the Laplace distribution. Intractability of evaluating the posterior probability density is solved by using variational Bayesian approximation methods. We demonstrate that the assumed noise model can yield accurate reconstructions because corrupted elements of a bad quality sample can be reconstructed using the other elements of the same data vector. Experiments on an artificial dataset and a weather dataset show that the dimensional independency and the flexibility of the proposed Student-t noise model can make it superior in some applications.

Identification and classification of ERP critical failure factors in Iranian industries

Implementation of Enterprise Resource Planning systems (ERPs) is a complex and costly process, which usually results in serious failures. The majority of previous studies and research projects have been conducted in identifying ERP Critical Success Factors (CSFs) rather than Critical Failure Factors (CFFs). On the other hand, most studies have been devoted to developed countries, while in developing countries, many companies have moved towards using such systems. The majority of IT/IS management standards and guidelines have been developed by technologically-leading countries. But developing countries, which mostly confront with especial challenges, have a different condition from the implicit assumptions of leading countries. Iran is one of these countries that many of its ERP implementation projects led to failure. There is no comprehensive study that identifies ERP CFFs in Iranian industries. The main purpose of this study is to identify such factors and classify them to help other industries, consultants and implementers to prevent failures in the implementation of ERP projects. So, at first, with the semi structured interviews and literature reviews, 47 failure factors were identified. After that a questionnaire developed and sent to ERP project team members in Iranian industries that failed in their ERP projects. Robust Exploratory Factor Analysis (EFA) has been used for data analysis, which finally classified critical failure factors in seven groups named as vendor and consultant, human resources, managerial, project management, processes, organizational and technical. The results of this study have provided a very useful reference for scholars and managers to identify the relevant issues of ERP projects failure in developing countries.

Exploratory factor analysis revisited: How robust methods support the detection of hidden multivariate data structures in IS research

Exploratory factor analysis is commonly used in IS research to detect multivariate data structures. Frequently, the method is blindly applied without checking if the data fulfill the requirements of the method. We investigated the influence of sample size, data transformation, factor extraction method, rotation, and number of factors on the outcome. We compared classical exploratory factor analysis with a robust counterpart which is less influenced by data outliers and data heterogeneities. Our analyses revealed that robust exploratory factor analysis is more stable than the classical method.