Fast two-stage estimator for clustered count data with overdispersion

ABSTRACT

Clustered count data are commonly analysed by the generalized linear mixed model (GLMM). Here, the correlation due to clustering and some overdispersion is captured by the inclusion of cluster-specific normally distributed random effects. Often, the model does not capture the variability completely. Therefore, the GLMM can be extended by including a set of gamma random effects. Routinely, the GLMM is fitted by maximizing the marginal likelihood. However, this process is computationally intensive. Although feasible with medium to large data, it can be too time-consuming or computationally intractable with very large data. Therefore, a fast two-stage estimator for correlated, overdispersed count data is proposed. It is rooted in the split-sample methodology. Based on a simulation study, it shows good statistical properties. Furthermore, it is computationally much faster than the full maximum likelihood estimator. The approach is illustrated using a large dataset belonging to a network of Belgian general practices.

KEYWORDS:

• Generalized linear mixed model
• hierarchical data
• negative binomial model
• poisson model
• random effects

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Alvaro J. Flóreza  http://orcid.org/0000-0001-6127-8733

Geert Molenberghsa  http://orcid.org/0000-0002-6453-5448

Additional information

Funding

Financial support from the IAP research network P7 = 06 of the Belgian Government (Belgian Science Policy) is gratefully acknowledged. Alvaro J. Flórez acknowledges funding from the European Seventh Framework programme FP7 2007-2013 under grant agreement Nr. 602552.