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Redundant Overdispersion Parameters in Multilevel Models for Categorical Responses

London School of Economics
Norwegian Institute of Public Health

Sophia Rabe-Hesketh

University of California, Berkeley
University of London

In some distributions, such as the binomial distribution, the variance is determined by the mean. However, in practice, overdispersion is often observed where the variance is larger than that predicated by the mean, and underdispersion is sometimes observed where the variance is smaller. It is well known that overdispersion or underdispersion cannot be modeled for dichotomous responses having a Bernoulli distribution. Redundant overdispersion parameters are nevertheless often included when multilevel or hierarchical models for categorical responses are estimated using quasi-likelihood methods and in generalized estimating equations. This may be due to the popularity of an algorithmic model formulation.

Key Words: overdispersion • underdispersion • extrabinomial variation • quasi-likelihood • scale parameter • multilevel model • hierarchical model • generalized linear mixed model • generalized estimating equations

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