Inference and local influence diagnostics for unit-Lindley additive partially linear models

2026-06-22

AI Summary

This study addresses the lack of regression methods for unit-interval response variables that simultaneously offer interpretability and flexibility. To this end, we propose a novel model that integrates the unit Lindley distribution within an additive partial linear framework. Nonlinear covariate effects are captured using B-spline basis functions, and model parameters are estimated via penalized log-likelihood, marking the first incorporation of the unit Lindley distribution into such a setting. We explicitly derive the sensitivity measures and the penalized observed information matrix, and develop local influence diagnostics based on case weights and response perturbations. Simulation studies demonstrate accurate parameter estimation, while an application to real psychological assessment data confirms the model’s practical utility and diagnostic effectiveness.

Abstract

This paper introduces a novel regression framework for modeling response variables restricted to the unit interval by proposing unit-Lindley additive partially linear models (UL-APLMs). This model class combines parsimony and interpretability of one-parameter unit-Lindley distribution with the flexibility of additive partial linear structures, enabling the coexistence of linear and smooth covariate effects. Additive terms are modeled using B-spline basis under a penalized likelihood framework to ensure smoothness. Estimation is carried out by maximizing the penalized log-likelihood function. The goodness-of-fit of the models is assessed through residual analysis, whereas the robustness of the parameter estimates and the detection of influential data points are evaluated using the local influence approach, which incorporates curvature diagnostics under case-weight and response perturbation schemes. The sensitivity and penalized observed information matrices are derived explicitly for the proposed model. Simulation studies demonstrate the accuracy of the estimation procedure under various scenarios. Real data on the assessment of the psychological profile of patients with hypopituitarism illustrate the applicability of the model, highlighting the diagnostic importance.

Problem

• unit interval
• regression modeling
• additive partially linear models
• influence diagnostics
• goodness-of-fit

Innovation

• unit-Lindley distribution
• additive partially linear model
• penalized likelihood
• local influence diagnostics
• B-spline smoothing