Análise de componentes principais aplicada à estimação de parâmetros no modelo de regressão logística quadrático
DOI:
https://doi.org/10.5540/tema.2013.014.01.0057Abstract
A literatura disponível mostra que a quase totalidade dos trabalhos sobre o modelo de regressão logística considera apenas o modelo com funções discriminantes lineares. Entretanto, há situações nas quais funções discriminantes quadráticas são de grande utilidade e podem apresentar melhores resultados. Porém, o modelo de regressão logística quadrático envolve a estimação de um grande número de parâmetros desconhecidos, o que pode levar a algumas dificuldades, do ponto de vista computacional, especialmente quando há um grande número de variáveis independentes no conjunto de dados. Neste trabalho utiliza-se um conjunto de componentes principais das variáveis independentes a fim de reduzir as dimensões do modelo a ser estimado, com variáveis independentes contínuas, bem como os custos computacionais para a estimação de parâmetros na regressão logística quadrática politômica, sem perda de eficiência. Simulações com conjuntos de dados extraídos da literatura disponível mostram que o modelo de regressão logística quadrático, com componentes principais, é computacionalmente viável e, geralmente, produz resultados melhores que aqueles obtidos pelo modelo de regressão logística clássico, em termos de taxas de classificações corretamente efetuadas.References
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