Integrated nested Laplace approximation for the analysis of count data via the combined model: A simulation study

ABSTRACT

The combined model accounts for different forms of extra-variability and has traditionally been applied in the likelihood framework, or in the Bayesian setting via Markov chain Monte Carlo. In this article, integrated nested Laplace approximation is investigated as an alternative estimation method for the combined model for count data, and compared with the former estimation techniques. Longitudinal, spatial, and multi-hierarchical data scenarios are investigated in three case studies as well as a simulation study. As a conclusion, integrated nested Laplace approximation provides fast and precise estimation, while avoiding convergence problems often seen when using Markov chain Monte Carlo.

KEYWORDS:

• Bayesian inference
• Combined model
• Count data
• Integrated nested Laplace approximation
• Spatial data analysis

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F15
• Secondary 62-07

Acknowledgment

The authors would also like to thank Kim Van Kerckhove, who maintains and provided them the Flemish Contact dataset.

Additional information

Funding

Financial support from the IAP research network #P7/06 of the Belgian Government (Belgian Science Policy) and the Research Foundation Flanders (12S7217N) is gratefully acknowledged.