Utilização de modelos de regressão para dados circulares com ou sem a presença de censura

Abstract

Circular data are present in several phenomena, in the orientation of birds’ flight, wind direction, in addition some measures can be transformed into angular ones, such as times, months and days of the week. Through circular statistics it is possible to provide more adequate results for such situations. Regression models adapted for circular statistics can be classified as linear-circular, circular-linear and circular-circular, according to whether the explanatory or response variables are located on the real line or on a circumference of a unit circle. In this research, initially, a review of the main aspects of circular statistics and their regression models was carried out, using spreadsheets from geographic and meteorological coordinate data. Finally, a proposal was made for the use of a regression model whose response is a measure located on the real line (linear) and the explanatory variable is an angular measure (circular) in the context of survival analysis, with the aim of to study the time for the beginning of assistance to victims of accidents on highways in the state of Minas Gerais. The log-normal model was used to model the response variable, with the circular covariate being censored. The fit was satisfactory, showing that statistics for circular data associated with survival analysis is an excellent tool for this type of study.