Comparação de métodos para definição do número ótimo de grupos em análise de agrupamento

• Autor(a) principal: Alves, Suelem Cristina
• Data de Publicação: 2012
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: http://locus.ufv.br/handle/123456789/4051
• topic: Simulação; Curvas de crescimento; Modelo de von Bertalanffy; Método de Mojena; Simulation; Growth curves; Von Bertalanffy model; Mojena method; CNPQ::CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA

Studies that use hierarchical cluster analysis have a problem in determining the optimal number of groups due to lack of objective criteria. Researches involving the adjustment of nonlinear models to data on growth or survival, in which the main interest is to determine how many curves are needed to describe the behavior of the individuals analyzed, use this technique. Some researchers use indices BSS (Between-group Sum of Squares), SPRSQ (Semi-partial R-Squared), RMSSTD (Root Mean Square Standard Deviation), RS (R-Squared) and Mojena method, as a means of assistance in this decision. However, it is not known which one is the best choice to determine that value. The comparison of these statistics was the aim of this study. The entire methodology used the Ward s method to cluster the observations, the von Bertalanffy model to fit the curves, and a specific function, based on the law of cosines and the idea of the Modified Maximum Curvature Method, to calculate the number of groups indicated by the indices. In chapter 1, a real case study was developed. The data set had seven animal growth curves, forming three groups. After grouping the parameter estimates and the calculation of statistics, it was found that only the index SPRSQ pointed to the correct number of groups. Using a function to re-scale the axis of the indices according to the axis of the number of groups, to improve the results obtained, only RMSSTD did not indicate the expected value. Chapter 2 describes the use of simulation to find out which of the statistics mentioned had the highest percentage of accuracy in determining the optimal number of groups in two cases. In the first one, the observations came from a single generator curve and, in the other, the individuals belonged to three different populations. In the case of a single curve, the RS index pointed to the optimal number of groups in most cases. For the case in which there were three different populations, the Mojena method was the one that indicated the right number of groups more often. In these cases, the use of the function that re-scales the axes did not show efficiency to improve the percentage of correct indices. In general, the indices RS and SPRSQ were the most appropriate to assist in determining the optimal number of groups.