Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Computation of multiple correspondence analysis, with code in R

The generalization of simple correspondence analysis, for two categorical variables, to multiple correspondence analysis where they may be three or more variables, is not straighforward, both from a mathematical and computational point of view. In this paper we detail the exact computational steps involved in performing a multiple correspondence analysis, including the special aspects of adjusting the principal inertias to correct the percentages of inertia, supplementary points and subset analysis. Furthermore, we give the algorithm for joint correspondence analysis where the cross-tabulations of all unique pairs of variables are analysed jointly. The code in the R language for every step of the computations is given, as well as the results of each computation.

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.

Perceptual mapping of practical ethics along the value chain: A multiple correspondence analysis with industry and cultural indices as supplementary variables

This paper presents findings from a study investigating a firm s ethical practices along the value chain. In so doing we attempt to better understand potential relationships between a firm s ethical stance with its customers and those of its suppliers within a supply chain and identify particular sectoral and cultural influences that might impinge on this. Drawing upon a database comprising of 667 industrial firms from 27 different countries, we found that ethical practices begin with the firm s relationship with its customers, the characteristics of which then influence the ethical stance with the firm s suppliers within the supply chain. Importantly, market structure along with some key cultural characteristics were also found to exert significant influence on the implementation of ethical policies in these firms.

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.

Canonical correspondence analysis in social science research

The use of simple and multiple correspondence analysis is well-established in socialscience research for understanding relationships between two or more categorical variables.By contrast, canonical correspondence analysis, which is a correspondence analysis with linearrestrictions on the solution, has become one of the most popular multivariate techniques inecological research. Multivariate ecological data typically consist of frequencies of observedspecies across a set of sampling locations, as well as a set of observed environmental variablesat the same locations. In this context the principal dimensions of the biological variables aresought in a space that is constrained to be related to the environmental variables. Thisrestricted form of correspondence analysis has many uses in social science research as well,as is demonstrated in this paper. We first illustrate the result that canonical correspondenceanalysis of an indicator matrix, restricted to be related an external categorical variable, reducesto a simple correspondence analysis of a set of concatenated (or stacked ) tables. Then weshow how canonical correspondence analysis can be used to focus on, or partial out, aparticular set of response categories in sample survey data. For example, the method can beused to partial out the influence of missing responses, which usually dominate the results of amultiple correspondence analysis.

Correspondence analysis and categorical conjoint measurement

We show the equivalence between the use of correspondence analysis (CA)of concadenated tables and the application of a particular version ofconjoint analysis called categorical conjoint measurement (CCM). Theconnection is established using canonical correlation (CC). The second part introduces the interaction e¤ects in all three variants of theanalysis and shows how to pass between the results of each analysis.

[climacteric Syndrome In A Northeastern Brazilian City: A Household Survey].

To assess the prevalence of Climacteric Syndrome (CS) in women from a municipality of Northeastern Brazil which is less developed socioeconomically. A prospective household survey was performed in São Luís, Maranhão, Brazil with 1,210 climacteric women aged 45 to 60 years. Interviews were applied using previously tested standard questionnaires from April to July 2008. The severity of climacteric symptoms was analyzed by circulatory and psychological indexes and the latter were associated with menopausal status. Multiple correspondence analysis was used to assess the relation among climacteric symptoms. Most patients were 55 to 60 years old (35.3%), mulatto (37.9%), with 9-11 years of schooling (39.8%), with a partner (56%), Catholic (73.9%) and belonged to the socioeconomic class C (51.1%). The prevalence of CS was 85.9%, and hot flashes (56.4%) and sweating (50.4%) were the most prevalent symptoms. The most frequent psychological symptoms were nervousness (45%) and emotional liability (44.8%). The severity of vasomotor and psychological symptoms was significantly higher during the peri and postmenopausal period (p<0.05). Vaginal dryness (62.7%) was the most prevalent urogenital complaint. The prevalence of CS was high among women from São Luís, Maranhão, Brazil.

A aprendizagem de conceitos estatísticos numa amostra de alunos do ensino secundário - análise univariada e multivariada

Trabalho de projecto apresentado como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Avaliação da satisfação de alunos em bLearning

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Municipalities of higher vulnerability to Sylvatic Yellow Fever occurrence in the São Paulo State, Brazil

Until 1999 the endemic cases of Sylvatic Yellow Fever were located in the states of northern, midwestern and pre-Amazon regions. Since then, the disease progressively expanded its territory of occurrence, cases being registered beyond the traditional boundaries of endemism. The São Paulo State is considered to be part of this context, since after decades without registration of autochthonous cases of the disease, it reported, in 2000 and 2008-2009, epizootic occurrence in non-human primates and 30 cases in humans. Facts like these, added to the increase in incidences of serious adverse effects resulting from the Yellow Fever vaccination, have highlighted the importance of defining priority municipalities for vaccination against the disease in the state. Two groups of municipalities, some affected and some non-affected by YF, were compared for environmental variables related to the eco-epidemiology of the disease according to literature. The Multiple Correspondence Analysis (MCA) was used to pinpoint the factor able to differentiate the two groups of municipalities and define the levels of risk. The southeast region of the São Paulo State was considered to be the area with a higher number of municipalities classified as high risk and should be considered a priority for the application of prevention measures against Yellow Fever.

Physiotherapy practice in the private sector: organizational characteristics and models.

BACKGROUND: Even if a large proportion of physiotherapists work in the private sector worldwide, very little is known of the organizations within which they practice. Such knowledge is important to help understand contexts of practice and how they influence the quality of services and patient outcomes. The purpose of this study was to: 1) describe characteristics of organizations where physiotherapists practice in the private sector, and 2) explore the existence of a taxonomy of organizational models. METHODS: This was a cross-sectional quantitative survey of 236 randomly-selected physiotherapists. Participants completed a purpose-designed questionnaire online or by telephone, covering organizational vision, resources, structures and practices. Organizational characteristics were analyzed descriptively, while organizational models were identified by multiple correspondence analyses. RESULTS: Most organizations were for-profit (93.2%), located in urban areas (91.5%), and within buildings containing multiple businesses/organizations (76.7%). The majority included multiple providers (89.8%) from diverse professions, mainly physiotherapy assistants (68.7%), massage therapists (67.3%) and osteopaths (50.2%). Four organizational models were identified: 1) solo practice, 2) middle-scale multiprovider, 3) large-scale multiprovider and 4) mixed. CONCLUSIONS: The results of this study provide a detailed description of the organizations where physiotherapists practice, and highlight the importance of human resources in differentiating organizational models. Further research examining the influences of these organizational characteristics and models on outcomes such as physiotherapists' professional practices and patient outcomes are needed.

Preferential binding of the methyl-CpG binding domain protein 2 at methylated transcriptional start site regions.

Methyl-CpG Binding Domain (MBD) proteins are thought to be key molecules in the interpretation of DNA methylation signals leading to gene silencing through recruitment of chromatin remodeling complexes. In cancer, the MBD-family member, MBD2, may be primarily involved in the repression of genes exhibiting methylated CpG at their 5' end. Here we ask whether MBD2 randomly associates methylated sequences, producing chance effects on transcription, or exhibits a more specific recognition of some methylated regions. Using chromatin and DNA immunoprecipitation, we analyzed MBD2 and RNA polymerase II deposition and DNA methylation in HeLa cells on arrays representing 25,500 promoter regions. This first whole-genome mapping revealed the preferential localization of MBD2 near transcription start sites (TSSs), within the region analyzed, 7.5 kb upstream through 2.45 kb downstream of 5' transcription start sites. Probe by probe analysis correlated MBD2 deposition and DNA methylation. Motif analysis did not reveal specific sequence motifs; however, CCG and CGC sequences seem to be overrepresented. Nonrandom association (multiple correspondence analysis, p < 0.0001) between silent genes, DNA methylation and MBD2 binding was observed. The association between MBD2 binding and transcriptional repression weakened as the distance between binding site and TSS increased, suggesting that MBD2 represses transcriptional initiation. This hypothesis may represent a functional explanation for the preferential binding of MBD2 at methyl-CpG in TSS regions.

Preliminary results of random amplification of polymorphic DNA among Triatominae of the phyllosoma complex (Hemiptera, Reduviidae)

In Mexico, Triatoma longipennis (Usinger), Triatoma picturata (Usinger), and Triatoma pallidipennis (Stal), primary Chagas disease vector species of the phyllosoma complex, were analyzed by randomly amplified polymorphic DNA (RAPD). Sixteen decametric primers resolved individual profiles not identical, but partially discriminative between species. Analysis based on pairwise presence/absence comparisons between the three species was performed using three primers and two outgroup species Triatoma infestans (Klug) and Triatoma barberi (Usinger). Fifty-three bands in total were scored, although only two bands were constant among the three phyllosoma complex species. Two other bands were constant only for T. longipennis and T. picturata together, and not present in T. pallidipennis. Neighbor Joining tree and the multiple correspondence analysis discriminated T. pallidipennis clearly from the other two species, although there was overlap between T. longipennis and T. picturata. The results indicate a close relationship between the studied species and support the hypothesis of their recent evolution. The suitability of RAPD to discern populations within the species is discussed.

Social meets molecular: Combining phylogenetic and latent class analyses to understand HIV-1 transmission in Switzerland.

Switzerland has a complex human immunodeficiency virus (HIV) epidemic involving several populations. We examined transmission of HIV type 1 (HIV-1) in a national cohort study. Latent class analysis was used to identify socioeconomic and behavioral groups among 6,027 patients enrolled in the Swiss HIV Cohort Study between 2000 and 2011. Phylogenetic analysis of sequence data, available for 4,013 patients, was used to identify transmission clusters. Concordance between sociobehavioral groups and transmission clusters was assessed in correlation and multiple correspondence analyses. A total of 2,696 patients were infected with subtype B, 203 with subtype C, 196 with subtype A, and 733 with recombinant subtypes (mainly CRF02_AG and CRF01_AE). Latent class analysis identified 8 patient groups. Most transmission clusters of subtype B were shared between groups of gay men (groups 1-3) or between the heterosexual groups "heterosexual people of lower socioeconomic position" (group 4) and "injection drug users" (group 8). Clusters linking homosexual and heterosexual groups were associated with "older heterosexual and gay people on welfare" (group 5). "Migrant women in heterosexual partnerships" (group 6) and "heterosexual migrants on welfare" (group 7) shared non-B clusters with groups 4 and 5. Combining approaches from social and molecular epidemiology can provide insights into HIV-1 transmission and inform the design of prevention strategies.