# Comparison of WAIC and posterior predictive approaches for N-mixture models

## TL;DR

This paper compares different model selection methods for N-mixture models in ecology and finds that WAICj is more accurate than other approaches.

## Contribution

The study introduces WAICj as a more accurate model selection method for N-mixture models, even with temporal correlation.

## Key findings

- WAICj outperformed conditional WAIC and posterior-predictive loss in simulated and real-world N-mixture models.
- The results show WAICj is robust for model selection in both single-season and multi-season ecological data.
- Case studies using eBird data confirmed the effectiveness of WAICj in practical ecological modeling.

## Abstract

Hierarchical models are common for ecological analysis, but determining appropriate model selection methods remains an ongoing challenge. To confront this challenge, a suitable method is needed to evaluate and compare available candidate models. We compared performance of conditional WAIC, a joint-likelihood approach to WAIC (WAICj), and posterior-predictive loss for selecting between candidate N-mixture models. We tested these model selection criteria on simulated single-season N-mixture models, simulated multi-season N-mixture models with temporal auto-correlation, and three case studies of single-season N-mixture models based on eBird data. WAICj proved more accurate than the standard conditional formulation or posterior-predictive loss, even when models were temporally correlated, suggesting WAICj is a robust alternative to model selection for N-mixture models.