Efeito de diferentes estruturas de correlação nos ângulos formados entre componentes principais e interpretáveis em amostras com presença de pontos discrepantes

Abstract

The principal component analysis aims to explain the variance structure of a random vector consisting of p variables, using linear combinations of the original variables. In some situations, the coefficients of the principal components may not be easily interpreted because the number of variables or the presence of outliers. Thus were introduced interpretable components, which are measured by the angle formed between the Principal and Interpretable Component. This paper aims to evaluate the effects of different correlation structures via Monte Carlo simulation and circular statistics on the angles formed between the components in samples with and without contamination. It was found that the structures act differently on the angles, and the CS structure which has the smallest expected angle for the first components in situations of higher correlation coefficient. Still, it was found that the contamination of the sample does not act directly on the magnitude of the expected values of the angles.