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 istheny = 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 analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon 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 thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing modelsbetween end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework.We present here a possible solution based on factor analysis of compositions illustrated with a case study.We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables thatlay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hiddencomponents, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members.We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained totalvariance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphicalrepresentation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysisof diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, exceptfertilisers due to the heterogeneity of their composition.This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations areintrinsic to the relative nature of compositional data

Exploratory Factor Analysis of the contents and styles of irrational thoughts assessed by "The Attitudes and Beliefs Inventory"

The factor structure of a back translated Spanish version (Lega, Caballo and Ellis, 2002) of the Attitudes and Beliefs Inventory (ABI) (Burgess, 1990) is analyzed in a sample of 250 university students.The Spanish version of the ABI is a 48-items self-report inventory using a 5-point Likert scale that assesses rational and irrational attitudes and beliefs. 24-items cover two dimensions of irrationality: a) areas of content (3 subscales), and b) styles of thinking (4 subscales).An Exploratory Factor Analysis (Parallel Analysis with Unweighted Least Squares method and Promin rotation) was performed with the FACTOR 9.20 software (Lorenzo-Seva and Ferrando, 2013).The results reproduced the main four styles of irrational thinking in relation with the three specific contents of irrational beliefs. However, two factors showed a complex configuration with important cross-loadings of different items in content and style. More analyses are needed to review the specific content and style of such items.

Confirmatory factor analysis of an integrated model of psycopathology assessed with MMPI-2-RF and the MCMI-III

We presented an integrated hierarchical model of psychopathology that more accurately captures empirical patterns of comorbidity between clinical syndromes and personality disorders.In order to verify the structural validity of the model proposed, this study aimed to analyze the convergence between the Restructured Clinical (RC) scales and Personality scales (PSY-5) of the MMPI-2-RF and the Clinical Syndrome and Personality Disorder scales of the MCMI-III.The MMPI-2-RF and MCMI-III were administered to a clinical sample of 377 outpatients (167 men and 210 women).The structural hypothesiswas assessed by using a Confirmatory Factor Analytic design with four common superordinate factors. An independent-cluster-basis solution was proposed based on maximum likelihood estimation and the application of several fit indices.The fit of the proposed model can be considered as good and more so if we take into account its complexity.

Exploratory Factor Analysis of the contents and styles of irrational thoughts assessed by "The Attitudes and Beliefs Inventory"

The factor structure of a back translated Spanish version (Lega, Caballo and Ellis, 2002) of the Attitudes and Beliefs Inventory (ABI) (Burgess, 1990) is analyzed in a sample of 250 university students.The Spanish version of the ABI is a 48-items self-report inventory using a 5-point Likert scale that assesses rational and irrational attitudes and beliefs. 24-items cover two dimensions of irrationality: a) areas of content (3 subscales), and b) styles of thinking (4 subscales).An Exploratory Factor Analysis (Parallel Analysis with Unweighted Least Squares method and Promin rotation) was performed with the FACTOR 9.20 software (Lorenzo-Seva and Ferrando, 2013).The results reproduced the main four styles of irrational thinking in relation with the three specific contents of irrational beliefs. However, two factors showed a complex configuration with important cross-loadings of different items in content and style. More analyses are needed to review the specific content and style of such items.

Identification-commitment inventory (ICI-Model): confirmatory factor analysis and construct validity

The aim of this study is to confirm the factorial structure of the Identification-Commitment Inventory (ICI) developed within the frame of the Human System Audit (HSA) (Quijano et al. in Revist Psicol Soc Apl 10(2):27-61, 2000; Pap Psicól Revist Col Of Psicó 29:92-106, 2008). Commitment and identification are understood by the HSA at an individual level as part of the quality of human processes and resources in an organization; and therefore as antecedents of important organizational outcomes, such as personnel turnover intentions, organizational citizenship behavior, etc. (Meyer et al. in J Org Behav 27:665-683, 2006). The theoretical integrative model which underlies ICI Quijano et al. (2000) was tested in a sample (N = 625) of workers in a Spanish public hospital. Confirmatory factor analysis through structural equation modeling was performed. Elliptical least square solution was chosen as estimator procedure on account of non-normal distribution of the variables. The results confirm the goodness of fit of an integrative model, which underlies the relation between Commitment and Identification, although each one is operatively different.

Confirmatory factor analysis of an inventory of perception of insecurity and fear of crime

This paper focuses on the study of the factorial structure of an inventory to estimate the subjective perception of insecurity and fear of crime. Made from the review of the literature on the subject and the results obtained in previous works, this factor structure shows that this attitude towards insecurity and fear of crime is identified through a number of latent factors which are schematically summarized in (a) personal safety, (b) the perception of personal and social control, (c) the presence of threatening people or situations, (d) the processes of identity and space appropriation, (e) satisfaction with the environment, and (f) the environmental and the use of space. Such factors are relevant dimensions to analyze the phenomenon. Method: A sample of 571 participants in a neighborhood of Barcelona was evaluated with the proposed inventory, which yielded data from the distributions of all the items provided. The administration was conducted by researchers specially trained for it and the results were analyzed by using standard procedures in the confirmatory factor analysis (CFA) from the hypothesized theoretical structure. The analysis was performed by decatypes according to the different response scales prepared in the inventory and their ordinal nature, and by estimating the polychoric correlation coefficients. The results show an acceptable fit of the proposed model, an appropriate behavior of the residuals and statistically significant estimates of the factor loadings. This would indicate the goodness of the proposed factor structure.

Dual activation of pathways regulated by steroid receptors and peptide growth factors in primary prostate cancer revealed by Factor Analysis of microarray data

Background: We use an approach based on Factor Analysis to analyze datasets generated for transcriptional profiling. The method groups samples into biologically relevant categories, and enables the identification of genes and pathways most significantly associated to each phenotypic group, while allowing for the participation of a given gene in more than one cluster. Genes assigned to each cluster are used for the detection of pathways predominantly activated in that cluster by finding statistically significant associated GO terms. We tested the approach with a published dataset of microarray experiments in yeast. Upon validation with the yeast dataset, we applied the technique to a prostate cancer dataset. Results: Two major pathways are shown to be activated in organ-confined, non-metastatic prostate cancer: those regulated by the androgen receptor and by receptor tyrosine kinases. A number of gene markers (HER3, IQGAP2 and POR1) highlighted by the software and related to the later pathway have been validated experimentally a posteriori on independent samples. Conclusion: Using a new microarray analysis tool followed by a posteriori experimental validation of the results, we have confirmed several putative markers of malignancy associated with peptide growth factor signalling in prostate cancer and revealed others, most notably ERRB3 (HER3). Our study suggest that, in primary prostate cancer, HER3, together or not with HER4, rather than in receptor complexes involving HER2, could play an important role in the biology of these tumors. These results provide new evidence for the role of receptor tyrosine kinases in the establishment and progression of prostate cancer.

Quantitative analysis of image factors in a cultural heritage tourist destination

The tourism consumer’s purchase decision process is, to a great extent, conditioned by the image the tourist has of the different destinations that make up his or her choice set. In a highly competitive international tourist market, those responsible for destinations’ promotion and development policies seek differentiation strategies so that they may position the destinations in the most suitable market segments for their product in order to improve their attractiveness to visitors and increase or consolidate the economic benefits that tourism activity generates in their territory. To this end, the main objective we set ourselves in this paper is the empirical analysis of the factors that determine the image formation of Tarragona city as a cultural heritage destination. Without a doubt, UNESCO’s declaration of Tarragona’s artistic and monumental legacies as World Heritage site in the year 2000 meant important international recognition of the quality of the cultural and patrimonial elements offered by the city to the visitors who choose it as a tourist destination. It also represents a strategic opportunity to boost the city’s promotion of tourism and its consolidation as a unique destination given its cultural and patrimonial characteristics. Our work is based on the use of structured and unstructured techniques to identify the factors that determine Tarragona’s tourist destination image and that have a decisive influence on visitors’ process of choice of destination. In addition to being able to ascertain Tarragona’s global tourist image, we consider that the heterogeneity of its visitors requires a more detailed study that enables us to segment visitor typology. We consider that the information provided by these results may prove of great interest to those responsible for local tourism policy, both when designing products and when promoting the destination.

Soil quality assessment through a multi-approach analysis in soils of abandoned terraced land in NE Spain

The abandonment of agricultural land in mountainous areas has been an outstanding problem along the last century and has captured the attention of scientists, technicians and administrations, for the dramatic consequences sometimes occurred due to soil instability, steep slopes, rainfall regimes and wildfires. Hidromorfological and pedological alterations causing exceptional floods and accelerated erosion processes has therefore been studied, identifying the cause in the loss of landscape heterogeneity. Through the disappearance of agricultural works and drainage maintenance, slope stability has resulted severely affected. The mechanization of agriculture has caused the displacement of vines, olives and corks trees cultivation in terraced areas along the Mediterranean catchment towards more economically suitable areas. On the one hand, land use and management changes have implicated sociological changes as well, transforming areas inhabited by agricultural communities into deserted areas where the colonization of disorganized spontaneous vegetation has buried a valuable rural patrimony. On the other hand, lacking of planning and management of the abandoned areas has produced badlands and infertile soils due to wildfire and high erosion rates strongly degrading the whole ecosystems. In other cases, after land abandonment a process of soil regeneration has been recorded. Investigations have been conducted in a part of NE Spain where extended areas of terraced soils previously cultivated have been abandoned in the last century. The selected environments were semi-abandoned vineyards, semi-abandoned olive groves, abandoned stands of cork trees, abandoned stands of pine trees, scrubland of Cistaceaea, scrubland of Ericaceaea, and pasture. The research work was focused on the study of most relevant physical, chemical and biological soil properties, as well as runoff and erosion under soils with different plant cover to establish the abandonment effect on soil quality, due to the peculiarity and vulnerability of these soils with a much reduced depth. The period of observation was carried out from autumn 2009 to autumn 2010. The sediment concentration of soil erosion under vines was recorded as 34.52 g/l while under pasture it was 4.66 g/l. In addition, the soil under vines showed the least amount of organic matter, which was 12 times lower than all other soil environments. The carbon dioxide (CO2) and total glomalin (TG) ratio to soil organic carbon (SOC) in this soil was 0.11 and 0.31 respectively. However, the soil under pasture contained a higher amount of organic matter and showed that the CO2 and TG ratio to SOC was 0.02 and 0.11 respectively indicating that the soil under pasture better preserves the soil carbon pool. A similar trend was found in the intermediate soils in the sequence of land use change and abandonment. Soil structural stability increased in the two soil fractions investigated (0.25-2.00 mm, 2.0-5.6 mm) especially in those soils that did not undergo periodical perturbations like wildfires. Soil quality indexes were obtained by using relevant physical and chemical soil parameters. Factor analysis carried out to study the relationship between all soil parameters allowed to related variables and environments and identify those areas that better contribute to soil quality towards others that may need more attention to avoid further degradation processes

Análisis morfométrico de la extremidad anterior en Carnivora

Durante los cuatro años de disfrute de la beca (2006 – 2009) se ha consolidado una base de datos de medidas osteológicas del esqueleto apendicular de numerosas especies del O. Carnivora. Concretamente, se han medido 364 individuos de 126 especies. Los ejemplares pertenecían a las colecciones del Phyletisches Museum (Jena, Alemania), el Museum für Naturkunde (Berlín, Alemania), el Museu de Ciències Naturals de la Ciutadella (Barcelona, España), el Múseum National d'Histoire Naturelle (París, Francia), y el Museo Nacional de Ciencias Naturales (Madrid, España). Asimismo, con estos datos se han estado preparando tres artículos sobre la morfología de ciertos elementos del esqueleto apendicular en carnívoros, dos de los cuales se encuentran actualmente en estado de revisión para su publicación científica. Dos de ellos, "Scapula, habitat and locomotion in Carnivora" y "Size and shape in the carnivore scapula", relacionan la morfología escapular con factores como el tamaño del animal, el tipo de locomoción que presenta y el hábitat en el que se encuentra; el primero mediante metodología multivariante (análisis funcional) y el segundo bajo las nuevas técnicas de morfometría geométrica. El tercer artículo, "Scaling and mechanics in the carnivore calcaneus: A comparison of natural and artificial selection", evalúa el efecto de diferentes tipos de selección, natural frente a artificial, sobre la morfología del calcáneo y su influencia en la biomecánica de este hueso. Finalmente, también se ha desarrollado un estudio experimental sobre la búsqueda de estabilidad durante la locomoción arbórea, cuyos resultados han dado lugar al artículo "The search for stability on narrow supports: An experimental study in cats and dogs", que también se halla bajo revisión actualmente.

La transició a la societat xarxa a Catalunya. Informe final de recerca (volum I)

Aquest estudi analitza les pràctiques diàries, els valors socials i les actituds de la població catalana en el procés de transició cap a la societat xarxa. Analitza el comportament de les persones a Internet i fora d'Internet, investigant el paper específic dels usos d'Internet a l'hora d'influenciar pràctiques i actituds. Es basa en les respostes a una enquesta de 3.005 individus, una mostra representativa de la població catalana el 2002. L'enquesta es va fer entre el febrer i el maig del 2002, i es basava en entrevistes cara a cara a partir d'un qüestionari de 179 preguntes. Es van utilitzar fonts secundàries per a situar els resultats catalans, particularment sobre els usos d'Internet, en el context global. L'anàlisi es va completar el 2007 incorporant-hi noves dades secundàries. L'estudi va cobrir pràctiques socials de treball, comunicació, sociabilitat, usos d'espai i temps, usos d'Internet, identitat cultural, pràctica política, associacionisme i formació de projectes d'autonomia. Es van construir diversos models estadístics per a proporcionar una anàlisi causal de cada una d'aquestes àrees d'estudi. El descobriment més significatiu fa referència a la relació entre els usos d'Internet i la construcció d'autonomia per part d'actors socials. Fent servir anàlisis factorial, l'estudi va definir cinc índexs d'autonomia que eren estadísticament independents: autonomia personal, autonomia professional, autonomia comunicativa, autonomia corporal i autonomia sociopolítica. Cada un d'aquests índexs d'autonomia independents estan fortament associats amb la freqüència i la intensitat de l'ús d'Internet, i les relacions observades es mantenen quan es controlen per variables sociodemogràfiques. A partir d'aquest estudi es pot afirmar que Internet és una plataforma important per a la construcció d'autonomia en la societat xarxa. En general, la societat catalana sembla que canviï de manera similar a altres societats en transició, amb l'èmfasi afegit del paper del territori i la família a l'hora d'enfortir les relacions socials, amb la contribució positiva d'Internet a un dens patró d'interacció social.

La transición en la sociedad red en Catalunya. Informe final de investigación (volumen II)

Aquest estudi analitza les pràctiques diàries, els valors socials i les actituds de la població catalana en el procés de transició cap a la societat xarxa. Analitza el comportament de les persones a Internet i fora d'Internet, investigant el paper específic dels usos d'Internet a l'hora d'influenciar pràctiques i actituds. Es basa en les respostes a una enquesta de 3.005 individus, una mostra representativa de la població catalana el 2002. L'enquesta es va fer entre el febrer i el maig del 2002, i es basava en entrevistes cara a cara a partir d'un qüestionari de 179 preguntes. Es van utilitzar fonts secundàries per a situar els resultats catalans, particularment sobre els usos d'Internet, en el context global. L'anàlisi es va completar el 2007 incorporant-hi noves dades secundàries. L'estudi va cobrir pràctiques socials de treball, comunicació, sociabilitat, usos d'espai i temps, usos d'Internet, identitat cultural, pràctica política, associacionisme i formació de projectes d'autonomia. Es van construir diversos models estadístics per a proporcionar una anàlisi causal de cada una d'aquestes àrees d'estudi. El descobriment més significatiu fa referència a la relació entre els usos d'Internet i la construcció d'autonomia per part d'actors socials. Fent servir anàlisis factorial, l'estudi va definir cinc índexs d'autonomia que eren estadísticament independents: autonomia personal, autonomia professional, autonomia comunicativa, autonomia corporal i autonomia sociopolítica. Cada un d'aquests índexs d'autonomia independents estan fortament associats amb la freqüència i la intensitat de l'ús d'Internet, i les relacions observades es mantenen quan es controlen per variables sociodemogràfiques. A partir d'aquest estudi es pot afirmar que Internet és una plataforma important per a la construcció d'autonomia en la societat xarxa. En general, la societat catalana sembla que canviï de manera similar a altres societats en transició, amb l'èmfasi afegit del paper del territori i la família a l'hora d'enfortir les relacions socials, amb la contribució positiva d'Internet a un dens patró d'interacció social.

La transición en la sociedad red en Catalunya. Informe final de investigación (volumen I)

Aquest estudi analitza les pràctiques diàries, els valors socials i les actituds de la població catalana en el procés de transició cap a la societat xarxa. Analitza el comportament de les persones a Internet i fora d'Internet, investigant el paper específic dels usos d'Internet a l'hora d'influenciar pràctiques i actituds. Es basa en les respostes a una enquesta de 3.005 individus, una mostra representativa de la població catalana el 2002. L'enquesta es va fer entre el febrer i el maig del 2002, i es basava en entrevistes cara a cara a partir d'un qüestionari de 179 preguntes. Es van utilitzar fonts secundàries per a situar els resultats catalans, particularment sobre els usos d'Internet, en el context global. L'anàlisi es va completar el 2007 incorporant-hi noves dades secundàries. L'estudi va cobrir pràctiques socials de treball, comunicació, sociabilitat, usos d'espai i temps, usos d'Internet, identitat cultural, pràctica política, associacionisme i formació de projectes d'autonomia. Es van construir diversos models estadístics per a proporcionar una anàlisi causal de cada una d'aquestes àrees d'estudi. El descobriment més significatiu fa referència a la relació entre els usos d'Internet i la construcció d'autonomia per part d'actors socials. Fent servir anàlisis factorial, l'estudi va definir cinc índexs d'autonomia que eren estadísticament independents: autonomia personal, autonomia professional, autonomia comunicativa, autonomia corporal i autonomia sociopolítica. Cada un d'aquests índexs d'autonomia independents estan fortament associats amb la freqüència i la intensitat de l'ús d'Internet, i les relacions observades es mantenen quan es controlen per variables sociodemogràfiques. A partir d'aquest estudi es pot afirmar que Internet és una plataforma important per a la construcció d'autonomia en la societat xarxa. En general, la societat catalana sembla que canviï de manera similar a altres societats en transició, amb l'èmfasi afegit del paper del territori i la família a l'hora d'enfortir les relacions socials, amb la contribució positiva d'Internet a un dens patró d'interacció social.

La societat xarxa a Catalunya. Informe de recerca I

Aquest estudi analitza les pràctiques diàries, els valors socials i les actituds de la població catalana en el procés de transició cap a la societat xarxa. Analitza el comportament de les persones a Internet i fora d'Internet, investigant el paper específic dels usos d'Internet a l'hora d'influenciar pràctiques i actituds. Es basa en les respostes a una enquesta de 3.005 individus, una mostra representativa de la població catalana el 2002. L'enquesta es va fer entre el febrer i el maig del 2002, i es basava en entrevistes cara a cara a partir d'un qüestionari de 179 preguntes. Es van utilitzar fonts secundàries per a situar els resultats catalans, particularment sobre els usos d'Internet, en el context global. L'anàlisi es va completar el 2007 incorporant-hi noves dades secundàries. L'estudi va cobrir pràctiques socials de treball, comunicació, sociabilitat, usos d'espai i temps, usos d'Internet, identitat cultural, pràctica política, associacionisme i formació de projectes d'autonomia. Es van construir diversos models estadístics per a proporcionar una anàlisi causal de cada una d'aquestes àrees d'estudi. El descobriment més significatiu fa referència a la relació entre els usos d'Internet i la construcció d'autonomia per part d'actors socials. Fent servir anàlisis factorial, l'estudi va definir cinc índexs d'autonomia que eren estadísticament independents: autonomia personal, autonomia professional, autonomia comunicativa, autonomia corporal i autonomia sociopolítica. Cada un d'aquests índexs d'autonomia independents estan fortament associats amb la freqüència i la intensitat de l'ús d'Internet, i les relacions observades es mantenen quan es controlen per variables sociodemogràfiques. A partir d'aquest estudi es pot afirmar que Internet és una plataforma important per a la construcció d'autonomia en la societat xarxa. En general, la societat catalana sembla que canviï de manera similar a altres societats en transició, amb l'èmfasi afegit del paper del territori i la família a l'hora d'enfortir les relacions socials, amb la contribució positiva d'Internet a un dens patró d'interacció social.