Medidas angulares em componentes principais reparametrizados em amostras com valores discrepantes

Abstract

Some types of data, such as angular measurements, require certain restrictions on the use of statistical methods, being treated by circular statistics. Angle measurements are examples of circular data. When considering multivariate statistical techniques, angular measurements are related to the Principal Components and Interpretable Components. Principal Component Analysis is a dimensionality reduction technique which identifies linear combinations that explain most data variations. Interpretable Components use restrictions in order to have a better interpretation of the coefficients of these combinations, restricting the values assumed by the coefficients. Their efficiency compared to the Principal Component is evaluated in relation to the angle formed between the components, which should be minimal. Thus, the objective of this study was to evaluate by computer simulation the effect of outliers in the reparameterization of the principal components by the interpretable components using different mixture probabilities, correlation structures and correlation coefficients, used to generate the samples. We proposed a measure to identify the circular distances between the expected angular values under contamination and without contamination. The results obtained through simulation showed that the angular means of the components differ in regard to the correlation coefficient and the correlation structure used, and that the circular distance measurement proposed identified the effect of outliers through dissimilar points.