🤖 AI Summary
This study addresses the limitations of existing circular logistic regression methods, which are confined to symmetric link functions and struggle to effectively model the relationship between circular predictors and binary or binomial responses. The authors propose a generalized linear framework that incorporates circular covariates into the linear predictor via sine and cosine transformations and, for the first time, systematically evaluates the performance of both symmetric and asymmetric link functions. Through Monte Carlo simulations based on the von Mises distribution—assessed using AIC, deviance, and empirical analyses of meteorological and seismic data—the study reveals that link function choice significantly impacts model performance when circular data are dispersed and responses are imbalanced. Under high concentration, symmetric links demonstrate greater robustness, whereas asymmetric links tend to be unstable. This work extends the theoretical boundaries of circular–binary response modeling and offers practical guidance for applied researchers.
📝 Abstract
Circular (directional) data arise whenever observations are measured as angles on the unit circle, such as wind direction, time of day, or calendar phase, and require statistical methods that respect the periodicity of the domain $[0; 2π)$. While circular-linear and linear-circular regression models are well established, regression models for a binary or binomial response observed jointly with a circular predictor remain largely undeveloped, with the sole closely related study restricted to the symmetric logit link. This paper develops and evaluates a circular logistic regression framework in which the linear predictor is expressed through the cosine and sine of the circular covariate, and compares the performance of symmetric link functions (logit, probit) against asymmetric alternatives (complementary log-log, Cauchit, and a skew-logit power link) under a generalized linear model formulation. A Monte Carlo simulation generates circular predictors from the von Mises distribution under two concentration regimes and evaluates model fit using the Akaike Information Criterion (AIC) and deviance. The methodology is illustrated with two real data sets: daily rainfall occurrence and wind direction recorded in Macomb, Illinois, and monthly earthquake counts in Western Anatolia, Turkiye, the latter used to connect the binary circular model to the related circular Poisson regression framework for count outcomes. Results indicate that the choice of link function matters most when the circular predictor is broadly dispersed and the response is markedly unbalanced; under high concentration of the predictor, symmetric links are preferred and asymmetric links are prone to instability. Practical guidelines and directions for future software development are discussed.