From correspondence analysis to multiple and joint correspondence analysis

The generalization of simple (two-variable) correspondence analysis to more than two categorical variables, commonly referred to as multiple correspondence analysis, is neither obvious nor well-defined. We present two alternative ways of generalizing correspondence analysis, one based on the quantification of the variables and intercorrelation relationships, and the other based on the geometric ideas of simple correspondence analysis. We propose a version of multiple correspondence analysis, with adjusted principal inertias, as the method of choice for the geometric definition, since it contains simple correspondence analysis as an exact special case, which is not the situation of the standard generalizations. We also clarify the issue of supplementary point representation and the properties of joint correspondence analysis, a method that visualizes all two-way relationships between the variables. The methodology is illustrated using data on attitudes to science from the International Social Survey Program on Environment in 1993.

The causal factors of international inequality in CO2 emissions per capita: a regression-based inequality decomposition analysis

This paper uses the possibilities provided by the regression-based inequality decomposition (Fields, 2003) to explore the contribution of different explanatory factors to international inequality in CO2 emissions per capita. In contrast to previous emissions inequality decompositions, which were based on identity relationships (Duro and Padilla, 2006), this methodology does not impose any a priori specific relationship. Thus, it allows an assessment of the contribution to inequality of different relevant variables. In short, the paper appraises the relative contributions of affluence, sectoral composition, demographic factors and climate. The analysis is applied to selected years of the period 1993���2007. The results show the important (though decreasing) share of the contribution of demographic factors, as well as a significant contribution of affluence and sectoral composition.

An��lisi factorial confirmat��ria per a variables categ��riques: Aplicaci�� al q��estionari de discapacitat WHODAS-II

Objective: To describe the methodology of Confirmatory Factor Analyis for categorical items and to apply this methodology to evaluate the factor structure and invariance of the WHO-Disability Assessment Schedule (WHODAS-II) questionnaire, developed by the World HealthOrganization.Methods: Data used for the analysis come from the European Study of Mental Disorders(ESEMeD), a cross-sectional interview to a representative sample of the general population of 6 european countries (n=8796). Respondents were administered a modified version of theWHODAS-II, that measures functional disability in the previous 30 days in 6 differentdimensions: Understanding and Communicating; Self-Care, Getting Around, Getting Along withOthers, Life Activities and Participation. The questionnaire includes two types of items: 22severity items (5 points likert) and 8 frequency items (continuous). An Exploratory factoranalysis (EFA) with promax rotation was conducted on a random 50% of the sample. Theremaining half of the sample was used to perform a Confirmatory Factor Analysis (CFA) inorder to compare three different models: (a) the model suggested by the results obtained in theEFA; (b) the theoretical model suggested by the WHO with 6 dimensions; (c) a reduced modelequivalent to model b where 4 of the frequency items are excluded. Moreover, a second orderfactor was also evaluated. Finally, a CFA with covariates was estimated in order to evaluatemeasurement invariance of the items between Mediterranean and non-mediterranean countries.Results: The solution that provided better results in the EFA was that containing 7 factors. Twoof the frequency items presented high factor loadings in the same factor, and one of thempresented factor loadings smaller than 0.3 with all the factors. With regard to the CFA, thereduced model (model c) presented the best goodness of fit results (CFI=0.992,TLI=0.996,RMSEA=0.024). The second order factor structure presented adequate goodness of fit (CFI=0.987,TLI=0.991, RMSEA=0.036). Measurement non-invariance was detected for one of the items of thequestionnaire (FD20 �� Embarrassment due to health problems).Conclusions: AFC confirmed the initial hypothesis about the factorial structure of the WHODAS-II in 6factors. The second order factor supports the existence of a global dimension of disability. The use of 4of the frequency items is not recommended in the scoring of the corresponding dimensions.

Coneixement i gesti�� del dol patol��gic per part dels infermers/es a l'atenci�� prim��ria de Girona

Per entendre l���experi��ncia d���una p��rdua i dur a terme una intervenci�� amb una valoraci�� hol��stica del pacient amb dol, ��s ��til con��ixer que aquesta p��rdua ��s present a la vida humana i que tota persona ��s susceptible a viure-la. Cada pas que fem en el nostre cam�� perdem coses, des de persones a un objecte significatiu, fins a les coses m��s ef��meres com ��s la joventut, els somnis o les idees que ens permeten l���enfrontament a les dures ���realitats de la vida���L���objectiu d���aquest estudi ��s valorar el coneixement del concepte de dol, dol patol��gic i d��na a con��ixer quin ��s el proc��s de dol a partir de la teoria de les etapes d��� Elisabet K��bler-Ross, Parkes i Worden com els pares de les tasques d���aquest proc��s. Per altra banda pret��n, donar a con��ixer la detecci�� d���un dol per aix�� evitar la cronificaci�� d���aquest i que el pacient pugui dur a terme un bonacompanyament del dolLa metodologia es realitzar�� a partir d���un estudi d���an��lisis qualitatiu i quantitatiu, descriptiu i bivariant en els professionals d���infermeria de les ��rees b��siques de salut de la ciutat de Girona: Girona 1(CAP Santa Clara), Girona 2 (CAP Can Gibert del Pla), Girona 3 (CAP de Montilivi) i Girona 4(CAP Taial��)Per l���an��lisi estad��stica descriptiva i bivariant s���utilitzar�� el programa SPSS v20 per l���an��lisi quantitativa i el programa N-Vivo 10 per l���an��lisi qualitativa. I per l���obtenci�� dels resultats es realitzar�� una an��lisis descriptiva bivariant. Els resultats obtinguts en aquest estudi ens ajudaran a detectar necessitats relacionades amb la formaci�� i l���aprenentatge dels professionals de l���atenci�� prim��ria i la manca de recursos en relaci�� al dol

Limitations and biases of conventional analysis of climate change. Towards an analysis coherent with sustainable development

This paper shows the numerous problems of conventional economic analysis in the evaluation of climate change mitigation policies. The article points out the many limitations, omissions, and the arbitrariness that have characterized most evaluation models applied up until now. These shortcomings, in an almost overwhelming way, have biased the result towards the recommendation of a lower aggressiveness of emission mitigation policies. Consequently, this paper questions whether these results provide an appropriate answer to the problem. Finally, various points that an analysis coherent with sustainable development should take into account are presented.

Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuouslycored boreholes, 100 to 220m deep were drilled in the northern part of the PoPlain by Regione Lombardia in the last five years. Quantitative provenanceanalysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carriedout by using multivariate statistical analysis (principal component analysis, PCA,and similarity analysis) on an integrated data set, including high-resolution bulkpetrography and heavy-mineral analyses on Pleistocene sands and of 250 majorand minor modern rivers draining the southern flank of the Alps from West toEast (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations,metamorphic and quartzofeldspathic detritus from the Western and Central Alpswas carried from the axial belt to the Po basin longitudinally parallel to theSouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenariorapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset ofthe first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA andsimilarity analysis from core samples show that the longitudinal trunk river at thistime was shifted southward by the rapid southward and westward progradation oftransverse alluvial river systems fed from the Central and Southern Alps.Sediments were transported southward by braided river systems as well as glacialsediments transported by Alpine valley glaciers invaded the alluvial plain.Kew words: Detrital modes; Modern sands; Provenance; Principal ComponentsAnalysis; Similarity, Canberra Distance; palaeodrainage

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed atdifferent points in time. Inherently, then, a compositional time series is a multivariatetime series with important constraints on the variables observed at any instance in time.Although this type of data frequently occurs in situations of real practical interest, atrawl through the statistical literature reveals that research in the field is very much in itsinfancy and that many theoretical and empirical issues still remain to be addressed. Anyappropriate statistical methodology for the analysis of compositional time series musttake into account the constraints which are not allowed for by the usual statisticaltechniques available for analysing multivariate time series. One general approach toanalyzing compositional time series consists in the application of an initial transform tobreak the positive and unit sum constraints, followed by the analysis of the transformedtime series using multivariate ARIMA models. In this paper we discuss the use of theadditive log-ratio, centred log-ratio and isometric log-ratio transforms. We also presentresults from an empirical study designed to explore how the selection of the initialtransform affects subsequent multivariate ARIMA modelling as well as the quality ofthe forecasts

Asymptotic robustness in multi-sample analysis of multivariate linear relations

Standard methods for the analysis of linear latent variable models oftenrely on the assumption that the vector of observed variables is normallydistributed. This normality assumption (NA) plays a crucial role inassessingoptimality of estimates, in computing standard errors, and in designinganasymptotic chi-square goodness-of-fit test. The asymptotic validity of NAinferences when the data deviates from normality has been calledasymptoticrobustness. In the present paper we extend previous work on asymptoticrobustnessto a general context of multi-sample analysis of linear latent variablemodels,with a latent component of the model allowed to be fixed across(hypothetical)sample replications, and with the asymptotic covariance matrix of thesamplemoments not necessarily finite. We will show that, under certainconditions,the matrix $\Gamma$ of asymptotic variances of the analyzed samplemomentscan be substituted by a matrix $\Omega$ that is a function only of thecross-product moments of the observed variables. The main advantage of thisis thatinferences based on $\Omega$ are readily available in standard softwareforcovariance structure analysis, and do not require to compute samplefourth-order moments. An illustration with simulated data in the context ofregressionwith errors in variables will be presented.

Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.

Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing oneor more parameters in their definition. Methods that can be linked in this way arecorrespondence analysis, unweighted or weighted logratio analysis (the latter alsoknown as "spectral mapping"), nonsymmetric correspondence analysis, principalcomponent analysis (with and without logarithmic transformation of the data) andmultidimensional scaling. In this presentation I will show how several of thesemethods, which are frequently used in compositional data analysis, may be linkedthrough parametrizations such as power transformations, linear transformations andconvex linear combinations. Since the methods of interest here all lead to visual mapsof data, a "movie" can be made where where the linking parameter is allowed to vary insmall steps: the results are recalculated "frame by frame" and one can see the smoothchange from one method to another. Several of these "movies" will be shown, giving adeeper insight into the similarities and differences between these methods.

Analysis of matched matrices

We consider the joint visualization of two matrices which have common rowsand columns, for example multivariate data observed at two time pointsor split accord-ing to a dichotomous variable. Methods of interest includeprincipal components analysis for interval-scaled data, or correspondenceanalysis for frequency data or ratio-scaled variables on commensuratescales. A simple result in matrix algebra shows that by setting up thematrices in a particular block format, matrix sum and difference componentscan be visualized. The case when we have more than two matrices is alsodiscussed and the methodology is applied to data from the InternationalSocial Survey Program.

Use of NIR spectroscopy and multivariate process spectra calibration methodology for pharmaceutical solid samples analysis

Accomplish high quality of final products in pharmaceutical industry is a challenge that requires the control and supervision of all the manufacturing steps. This request created the necessity of developing fast and accurate analytical methods. Near infrared spectroscopy together with chemometrics, fulfill this growing demand. The high speed providing relevant information and the versatility of its application to different types of samples lead these combined techniques as one of the most appropriated. This study is focused on the development of a calibration model able to determine amounts of API from industrial granulates using NIR, chemometrics and process spectra methodology.

EEG signal analysis via a cleaning procedure based on multivariate empirical mode decomposition

Artifacts are present in most of the electroencephalography (EEG) recordings, making it difficult to interpret or analyze the data. In this paper a cleaning procedure based on a multivariate extension of empirical mode decomposition is used to improve the quality of the data. This is achieved by applying the cleaning method to raw EEG data. Then, a synchrony measure is applied on the raw and the clean data in order to compare the improvement of the classification rate. Two classifiers are used, linear discriminant analysis and neural networks. For both cases, the classification rate is improved about 20%.

Cooking and Active Leisure TAS Program, Spain: A Program Impact Pathways (PIP) analysis

Background. The ���Cooking and Active Leisure��� Tu y Al��cia por la Salud (CAL-TAS) Program is a schoolbased pilot that addresses healthy lifestyle needs of Spanish secondary school students with initiatives that research has proven to improve dietary and physical activity behaviors. Objective. The objectives were to perform a Program Impact Pathways (PIP) analysis to describe key activities and processes of the CAL-TAS Program, identify Critical Quality Control Points (CCPs), and identify a suite of common indicators of healthy lifestyles to be applied across participant schools. Methods. The CAL-TAS Program designers and implementation team developed this PIP analysis through an iterative process and presented the results for feedback at the seven-country Healthy Lifestyles Program Evaluation Workshop held in Granada, Spain, 13���14 September 2013, under the auspices of the Mondel��z International Foundation. Results. The team identified three PIP CCPs: teachers��� motivation and training, changes in students��� knowledge of healthy lifestyles, and changes in students��� healthy lifestyle behavior. The selected indicators of the program���s impact on healthy lifestyles are adequacy of food intake, level of knowledge of healthy lifestyles gained, and adequacy of physical activity level according to World Health Organization recommendations. A clear definition of impact indicators, as well as collection of accurate data on healthy lifestyle behaviors and knowledge, is essential to understanding the effectiveness of this program before it can be scaled up. Conclusions. CAL-TAS is an effective secondary school-based program encouraging healthy lifestyles. The PIP analysis was instrumental in identifying CCPs to sustain and improve the quality of the program. The team hopes to sustain and improve the program through these program evaluation recommendations.