A0781
Title: Quantile-based major axes for bivariate allometric analysis
Authors: Luca Bagnato - Catholic University of the Sacred Heart (Italy) [presenting]
Antonio Punzo - University of Catania (Italy)
Cristina Tortora - San Jose State University (United States)
Antonello Maruotti - Libera Università Maria Ss Assunta (Italy)
Abstract: Allometric studies commonly explore the relationship between two log-transformed morphological variables using linear models, with major axis (MA) and common major axis (CMA) methods traditionally defined in terms of the mean structure. A novel extension of these methods is proposed by introducing quantile-based major axes, allowing the investigation of allometric relationships across different parts of the joint distribution. The approach is grounded in the concept of directional quantiles, which define regression lines corresponding to specific quantile levels along given directions. The estimation is formulated within a quasi-maximum likelihood framework based on the asymmetric Laplace distribution, enabling robust and flexible inference. This leads to the definition of both quantile major axes and a quantile-based common major axis (QCMA), which facilitates meaningful group comparisons beyond the mean. Applications to simulated and real morphological data demonstrate that the methodology uncovers heterogeneity and asymmetry in allometric patterns that remain hidden under traditional mean-based analyses. The proposed framework enriches the toolkit for allometric research, especially in the presence of non-normality, outliers, or distributional skewness.
