J. C. G. D. Costa

Multiple correspondence analysis in predictive logistic modelling: Application to a living-donor kidney transplantation data

This work deals with the use of multiple correspondence analysis (MCA) and a weighted Euclidean distance (the tolerance distance) as an exploratory tool in developing predictive logistic models. The method was applied to a living-donor kidney transplant data set with 109 cases and 13 predictors. This approach, followed by backward and forward selection procedures, yielded two models, one with four and another with two predictors. These models were compared to two other models, ordinarily built by backward and forward stepwise selection, which yielded, respectively, five and two predictors. After internal validation, the models performance statistics showed similar results. Likelihood ratio tests suggested that backward approach achieved a better fit than the forward modelling in both methods and the Vuongs non-nested test between backward-built models suggested that these were undistinguishable. We conclude that the tolerance distance, in combination with MCA, could be a feasible method for variable selection in logistic modelling, when there are several categorical predictors.

Validation in Principal Components Analysis Applied to EEG Data

The well-known multivariate technique Principal Components Analysis (PCA) is usually applied to a sample, and so component scores are subjected to sampling variability. However, few studies address their stability, an important topic when the sample size is small. This work presents three validation procedures applied to PCA, based on confidence regions generated by a variant of a nonparametric bootstrap called the partial bootstrap: (i) the assessment of PC scores variability by the spread and overlapping of “confidence regions” plotted around these scores; (ii) the use of the confidence regions centroids as a validation set; and (iii) the definition of the number of nontrivial axes to be retained for analysis. The methods were applied to EEG data collected during a postural control protocol with twenty-four volunteers. Two axes were retained for analysis, with 91.6% of explained variance. Results showed that the area of the confidence regions provided useful insights on the variability of scores and suggested that some subjects were not distinguishable from others, which was not evident from the principal planes. In addition, potential outliers, initially suggested by an analysis of the first principal plane, could not be confirmed by the confidence regions.

Análise de Correspondência: bases teóricas na interpretação de dados categóricos em Ciências da Saúde

Categorical variables are common in the biomedical field, and many descriptive methods have been proposed for revealing intrinsic patterns in data. Correspondence Analysis is an especially useful method for categorical data analysis of large contingency tables. Although numerous studies have been published on this method, most Portuguese-language articles have failed to explore its full potential, focusing only on graphical interpretation. The current paper reviews the method, showing that graphical analysis can be enriched by the right statistics. The article presents the mathematical basis for correspondence analysis and its most frequently used statistics. The procedure has shown that such statistics enrich symmetric map evaluation, that a low relative frequency category can be represented by supplementary category points, and that inertia contributions are highly related to residual analysis of contingency tables, not easily visualized by symmetric maps. Correspondence Analysis has proven advantageous when compared to principal components analysis.Na area biomedica, a ocorrencia de dados categoricos e comum, e metodos de analise especificos para este tipo de dado sao usados para revelar padroes existentes. A Analise de Correspondencia e uma dessas tecnicas, utilizada na analise de tabelas de contingencia de grande porte. A maioria dos trabalhos publicados em periodicos brasileiros foca apenas na sua interpretacao grafica, nao abordando outras potencialidades da tecnica. O objetivo do trabalho e mostrar a tecnica nao limitada a analise grafica, mas tambem utilizar estatisticas que permitem sua analise quantitativa. Exemplo mostra que a analise grafica e enriquecida com a utilizacao dessas estatisticas, e que a inclusao de uma categoria com baixa ocorrencia pode ser considerada como categoria suplementar devido a sua baixa contribuicao a inercia. Assim, diminui-se a subjetividade na analise, sendo possivel revelar a relacao entre as categorias com a analise de residuos, aspecto este nao facilmente observado graficamente. Comparacao com a Analise de Componentes Principais mostrou a vantagem da tecnica.

Correspondence Analysis: a theoretical basis for categorical data interpretation in Health Sciences

Categorical variables are common in the biomedical field, and many descriptive methods have been proposed for revealing intrinsic patterns in data. Correspondence Analysis is an especially useful method for categorical data analysis of large contingency tables. Although numerous studies have been published on this method, most Portuguese-language articles have failed to explore its full potential, focusing only on graphical interpretation. The current paper reviews the method, showing that graphical analysis can be enriched by the right statistics. The article presents the mathematical basis for correspondence analysis and its most frequently used statistics. The procedure has shown that such statistics enrich symmetric map evaluation, that a low relative frequency category can be represented by supplementary category points, and that inertia contributions are highly related to residual analysis of contingency tables, not easily visualized by symmetric maps. Correspondence Analysis has proven advantageous when compared to principal components analysis.Na area biomedica, a ocorrencia de dados categoricos e comum, e metodos de analise especificos para este tipo de dado sao usados para revelar padroes existentes. A Analise de Correspondencia e uma dessas tecnicas, utilizada na analise de tabelas de contingencia de grande porte. A maioria dos trabalhos publicados em periodicos brasileiros foca apenas na sua interpretacao grafica, nao abordando outras potencialidades da tecnica. O objetivo do trabalho e mostrar a tecnica nao limitada a analise grafica, mas tambem utilizar estatisticas que permitem sua analise quantitativa. Exemplo mostra que a analise grafica e enriquecida com a utilizacao dessas estatisticas, e que a inclusao de uma categoria com baixa ocorrencia pode ser considerada como categoria suplementar devido a sua baixa contribuicao a inercia. Assim, diminui-se a subjetividade na analise, sendo possivel revelar a relacao entre as categorias com a analise de residuos, aspecto este nao facilmente observado graficamente. Comparacao com a Analise de Componentes Principais mostrou a vantagem da tecnica.

Multiple Correspondence Analysis Applied to EEG Attributes

A multivariate technique called Multiple Correspondence Analysis (MCA) was applied to EEG data obtained from 24 subjects submitted to a stabilometric protocol. The approach was able to combine three continuous variables extracted from the periodogram, such as the alpha band power, and the categorical variables Gender included as a dichotomous variable coded ”M” (male) and ”F” (female) and the protocol conditions of eyes closed and eyes open. The solution is based on an analysis of the proximities between categories in MCA orthogonal axes called “symmetric maps”. Results suggested associations between females and eyes closed and higher levels of the alpha, beta and theta bands. On the other hand, eyes open was related to lower levels of the beta band and, in a lesser degree, to males.

Análisis de Correspondencia: bases teóricas para la interpretación de datos categóricos en Ciencias de Salud

Categorical variables are common in the biomedical field, and many descriptive methods have been proposed for revealing intrinsic patterns in data. Correspondence Analysis is an especially useful method for categorical data analysis of large contingency tables. Although numerous studies have been published on this method, most Portuguese-language articles have failed to explore its full potential, focusing only on graphical interpretation. The current paper reviews the method, showing that graphical analysis can be enriched by the right statistics. The article presents the mathematical basis for correspondence analysis and its most frequently used statistics. The procedure has shown that such statistics enrich symmetric map evaluation, that a low relative frequency category can be represented by supplementary category points, and that inertia contributions are highly related to residual analysis of contingency tables, not easily visualized by symmetric maps. Correspondence Analysis has proven advantageous when compared to principal components analysis.Na area biomedica, a ocorrencia de dados categoricos e comum, e metodos de analise especificos para este tipo de dado sao usados para revelar padroes existentes. A Analise de Correspondencia e uma dessas tecnicas, utilizada na analise de tabelas de contingencia de grande porte. A maioria dos trabalhos publicados em periodicos brasileiros foca apenas na sua interpretacao grafica, nao abordando outras potencialidades da tecnica. O objetivo do trabalho e mostrar a tecnica nao limitada a analise grafica, mas tambem utilizar estatisticas que permitem sua analise quantitativa. Exemplo mostra que a analise grafica e enriquecida com a utilizacao dessas estatisticas, e que a inclusao de uma categoria com baixa ocorrencia pode ser considerada como categoria suplementar devido a sua baixa contribuicao a inercia. Assim, diminui-se a subjetividade na analise, sendo possivel revelar a relacao entre as categorias com a analise de residuos, aspecto este nao facilmente observado graficamente. Comparacao com a Analise de Componentes Principais mostrou a vantagem da tecnica.

Principal Components Clustering through a Variance-Defined Metric

This work aims at proposing a clustering procedure through a new metric, a weighted Euclidean distance, in which the weights are the ratio of corresponding eigenvalues and the largest eigenvalue found after a Principal Components Analysis. In order to illustrate the method, the procedure was carried out on twenty-one newborn EEG segments, classified as TA (Trace Alternant) or HVS (High Voltage Slow) patterns. The observed clustering structure was assessed by the cophenetic and agglomerative coefficients. Results showed that, despite its unlikely existence, a clustering structure was suggested by the traditional approach. This structure, however, was not confirmed by the proposed method.

Self-Organizing Maps for Categorical Data: Application to an ISO 9000 Accreditation Assessment

Self-Organizing Maps (SOM) usually deal with quantitative inputs, but an algorithm for handling qualitative variables as inputs, using a Multiple Correspondence Analysis (MCA) framework, has already been proposed (the KMCA). This work suggests an alternative approach, also using the MCA framework, but calculating the category profiles of a complete disjunctive table (in MCA nomenclature, the Indicator Matrix). An illustrative example of the method is shown, concerning the assessment of an ISO 9000 standard adoption in a general hospital in Rio de Janeiro, Brazil. Questionnaires of 369 respondents pertaining to this implementation were analyzed. From a 9x9 hexagonal SOM’s grid, the main results suggested an indifferent and slightly positive perception of quality improvement between employees. Further studies repeating the strategy in the same institution should be carried out to evaluate the present state of the standard implantation.

Employees’ Commitment for ISO 9000 Implantation in a Philanthropic General Hospital: A Case Study by Multiple Correspondence Analysis

ISO 9000 accreditation is becoming an important part of healthcare institutions, allowing for the development of a trustful relationship among institutions, patients, employees and government agencies. However, usually it has been difficult to assess ISO 9000 adoption processes, mainly because of the subjectivity and qualitative nature of the indexes used in it. This difficult may generate doubts among employees and clinical staff about the effectiveness of the process. Multiple Correspondence Analysis (MCA) is a multivariate method with a potential for use in ISO accreditation assessment, since it is able to handle qualitative data. Its basic idea is that the association between categories of variables is graphically suggested by means of their closeness, but clear interpretations are still not straightforward, since more than one graph (besides other statistics), would have to be analyzed by the user. This work shows an example of an assessment of employees’ perception after four years of ISO 9000 certification through a questionnaire using MCA and a tolerance region (the associative ellipsoid), which may be thought of as a limit indicating the existence of association between variables, within a reference and constant distance. A leave-one-out validation procedure was also carried out for result assessment. The estimated reference distance was 0.154 indicating stable associations between indifferent and slightly positive categories. No association between professional classes and specific questions could be detected.