Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

Exploratory factor analysis in validation studies : Uses and recommendations

Resumen tomado de la publicaci??n

The use of a multiple criteria decision analysis to evaluate the effectiveness of landscape and habitat enhancement mechanisms: an example from the South Downs

A range of funding schemes and policy instruments exist to effect enhancement of the landscapes and habitats of the UK. While a number of assessments of these mechanisms have been conducted, little research has been undertaken to compare both quantitatively and qualitatively their relative effectiveness across a range of criteria. It is argued that few tools are available for such a multi-faceted evaluation of effectiveness. A form of Multiple Criteria Decision Analysis (MCDA) is justified and utilized as a framework in which to evaluate the effectiveness of nine mechanisms in relation to the protection of existing areas of chalk grassland and the creation of new areas in the South Downs of England. These include established schemes, such as the Countryside Stewardship and Environmentally Sensitive Area Schemes, along with other less common mechanisms, for example, land purchase and tender schemes. The steps involved in applying an MCDA to evaluate such mechanisms are identified and the process is described. Quantitative results from the comparison of the effectiveness of different mechanisms are presented, although the broader aim of the paper is that of demonstrating the performance of MCDA as a tool for measuring the effectiveness of mechanisms aimed at landscape and habitat enhancement.

Exploratory factor analysis of the Brazilian OHIP for edentulous subjects

P>The use of seven domains for the Oral Health Impact Profile (OHIP)-EDENT was not supported for its Brazilian version, making data interpretation in clinical settings difficult. Thus, the aim of this study was to assess patients` responses for the translated OHIP-EDENT in a group of edentulous subjects and to develop factor scales for application in future studies. Data from 103 conventional and implant-retained complete denture wearers (36 men, mean age of 69 center dot 1 +/- 10 center dot 3 years) were assessed using the Brazilian version of the OHIP-EDENT. Oral health-related quality of life domains were identified by factor analysis using principal component analysis as the extraction method, followed by varimax rotation. Factor analysis identified four factors that accounted for 63% of the 19 items total variance, named masticatory discomfort and disability (four items), psychological discomfort and disability (five items), social disability (five items) and oral pain and discomfort (five items). Four factors/domains of the Brazilian OHIP-EDENT version represent patient-important aspects of oral health-related quality of life.

Multiple-criteria decision analysis for integrated catchment management

Implementation of integrated catchment management (ICM) is hampered by the lack of a conceptual framework for explaining how landowners select farming systems for their properties. Benefit–cost analysis (a procedure that estimates the costs and benefits of alternative actions or policies) has limitations in this regard, which might be overcome by using multiple-criteria decision analysis (MCDA). MCDA evaluates and ranks alternatives based on a landowner's preferences (weights) for multiple-criteria and the values of those criteria. A MCDA approach to ICM is superior to benefit–cost analysis which focuses only on the monetary benefits and costs, because it: 1) recognizes that human activities within a catchment are motivated by multiple and often competing criteria and/or constraints; 2) does not require monetary valuation of criteria; 3) allows trade-offs between criteria to be measured and evaluated; 4) explicitly considers how the spatial configuration of farming systems in a catchment influences the values of criteria; 5) is comprehensive, knowledge-based, and stakeholder oriented which greatly increases the likelihood of resolving catchment problems; and 6) allows consideration of the fairness and sustainability of land and water resource management decisions. A MCDA based on an additive, multiple-criteria utility function containing five economic and environmental criteria was used to score and rank five farming systems. The rankings were based on the average criteria weights for a sample of 20 farmers in a US catchment. The most profitable farming system was the lowest-ranked farming system. Three possible reasons for this result are evaluated. First, the MCDA method might cause respondents to express socially acceptable attitudes towards environmental criteria even when they are not important from a personal viewpoint. Second, the MCDA method could inflate the ranks of less profitable farming systems for the simple reason that it allows the respondent to assign non-zero weights to non-economic criteria. Third, the MCDA might provide a better framework for evaluating a landowner's selection of farming systems than the profit maximization model.

Factor analysis of partners' commitment to risk management in public-private partnership projects

Purpose – The purpose of this paper is to investigate and uncover key determinants that could explain partners' commitment to risk management in public-private partnership projects so that partners' risk management commitment is taken into the consideration of optimal risk allocation strategies.

Design/methodology/approach – Based on an extensive literature review and an examination of the purchasing power parity (PPP) market, an industry-wide questionnaire survey was conducted to collect the data for a confirmatory factor analysis. Necessary statistical tests are conducted to ensure the validity of the analysis results.

Findings – The factor analysis results show that the procedure of confirmatory factor analysis is statistically appropriate and satisfactory. As a result, partners' organizational commitment to risk management in public-private partnerships can now be determined by a set of components, namely general attitude to a risk, perceived one's own ability to manage a risk, and the perceived reward for bearing a risk.

Practical implications – It is recommended, based on the empirical results shown in this paper, that, in addition to partners' risk management capability, decision-makers, both from public and private sectors, should also seriously consider partners' risk management commitment. Both factors influence the formation of optimal risk allocation strategies, either by their individual or interacting effects. Future research may therefore explore how to form optimal risk allocation strategies by integrating organizational capability and commitment, the determinants and measurement of which have been established in this study.

Originality/value – This paper makes an original contribution to the general body of knowledge on risk allocation in large-scale infrastructure projects in Australia adopting the procurement method of public-private partnership. In particular, this paper has innovatively established a measurement model of organisational commitment to risk management, which is crucial to determining optimal risk allocation strategies and in turn achieving project success. The score coefficients of all obtained components can be used to construct components by linear combination so that commitment to risk management can be measured. Previous research has barely focused on this topic.

Underdetermined blind source separation by parallel factor analysis in time-frequency domain

This paper presents a new time-frequency approach to the underdetermined blind source separation using the parallel factor decomposition of third-order tensors. Without any constraint on the number of active sources at an auto-term time-frequency point, this approach can directly separate the sources as long as the uniqueness condition of parallel factor decomposition is satisfied. Compared with the existing two-stage methods where the mixing matrix should be estimated at first and then used to recover the sources, our approach yields better source separation performance in the presence of noise. Moreover, the mixing matrix can be estimated at the same time of the source separation process. Numerical simulations are presented to show the superior performance of the proposed approach to some of the existing two-stage blind source separation methods that use the time-frequency representation as well.

Confirmatory factor analysis of the Beck Depression inventory in obese individuals seeking surgery

Background : The Beck Depression Inventory (BDI) is frequently employed as measure of depression in studies of obesity. The aim of the study was to assess the factorial structure of the BDI in obese patients prior to bariatric surgery.

Methods : Confirmatory factor analysis was conducted on the current published factor analyses of the BDI. Three published models were initially analysed with two additional modified models subsequently included. A sample of 285 patients presenting for Lap-Band® surgery was used.

Results : The published bariatric model by Munoz et al. was not an adequate fit to the data. The general model by Shafer et al. was a good fit to the data but had substantial limitations. The weight loss item did not significantly load on any factor in either model. A modified Shafer model and a proposed model were tested, and both were found to be a good fit to the data with minimal differences between the two. A proposed model, in which two items, weight loss and appetite, were omitted, was suggested to be the better model with good reliability.

Conclusions : The previously published factor analysis in bariatric candidates by Munoz et al. was a poor fit to the data, and use of this factor structure should be seriously reconsidered within the obese population. The hypothesised model was the best fit to the data. The findings of the study suggest that the existing published models are not adequate for investigating depression in obese patients seeking surgery.