Skew-Normal Inflated Models: Mathematical Characterization and Applications to Medical Data with Excess of Zeros and Ones

Author:

Martínez-Flórez Guillermo1ORCID,Tovar-Falón Roger1ORCID,Leiva Víctor2ORCID,Castro Cecilia3ORCID

Affiliation:

1. Department of Mathematics and Statistics, Universidad de Córdoba, Montería 230002, Colombia

2. School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile

3. Centre of Mathematics, Universidade do Minho, 4710-057 Braga, Portugal

Abstract

The modeling of data involving proportions, confined to a unit interval, is crucial in diverse research fields. Such data, expressing part-to-whole relationships, span from the proportion of individuals affected by diseases to the allocation of resources in economic sectors and the survival rates of species in ecology. However, modeling these data and interpreting information obtained from them present challenges, particularly when there is high zero–one inflation at the extremes of the unit interval, which indicates the complete absence or full occurrence of a characteristic or event. This inflation limits traditional statistical models, which often fail to capture the underlying distribution, leading to biased or imprecise statistical inferences. To address these challenges, we propose and derive the skew-normal zero–one inflated (SNZOI) models, a novel class of asymmetric regression models specifically designed to accommodate zero–one inflation presented in the data. By integrating a continuous-discrete mixture distribution with covariates in both continuous and discrete parts, SNZOI models exhibit superior capability compared to traditional models when describing these complex data structures. The applicability and effectiveness of the proposed models are demonstrated through case studies, including the analysis of medical data. Precise modeling of inflated proportion data unveils insights representing advancements in the statistical analysis of such studies. The present investigation highlights the limitations of existing models and shows the potential of SNZOI models to provide more accurate and precise inferences in the presence of zero–one inflation.

Funder

Vice-rectorate for Research of the Universidad de Córdoba, Colombia

Vice-rectorate for Research, Creation, and Innovation (VINCI) of the Pontificia Universidad Católica de Valparaíso (PUCV), Chile

National Agency for Research and Development (ANID) of the Chilean government

Portuguese funds through the CMAT—Research Centre of Mathematics of University of Minho, Portugal

Publisher

MDPI AG

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