# A residual for outlier identification in zero adjusted regression models

## TL;DR

This paper introduces a new residual for zero adjusted regression models that improves outlier detection beyond the existing randomized quantile residual, enhancing diagnostic accuracy.

## Contribution

A novel residual specifically designed for outlier detection in zero adjusted regression models, outperforming existing methods in identifying anomalies.

## Key findings

- The new residual effectively detects outliers missed by the randomized quantile residual.
- Simulation studies show the residual has good statistical properties.
- Application results confirm improved outlier identification.

## Abstract

Zero adjusted regression models are used to fit variables that are discrete at zero and continuous at some interval of the positive real numbers. Diagnostic analysis in these models is usually performed using the randomized quantile residual, which is useful for checking the overall adequacy of a zero adjusted regression model. However, it may fail to identify some outliers. In this work, we introduce a residual for outlier identification in zero adjusted regression models. Monte Carlo simulation studies and an application suggest that the residual introduced here has good properties and detects outliers that are not identified by the randomized quantile residual.