Extra‐binomial variation in multilevel logistic models with sparse structures

When discrete response models arc estimated with multilevel, or clustered, data, there is much interest in the distribution of the residuals. With logistic regression it is usually assumed that these residuals are binomially distributed. A common real world situation is where the multilevel data structure is sparse, with relatively few individual cases per cluster. The impact of sparsity on estimates of binomial variation is explored using simulation techniques. This exploration demonstrates that sparsity leads to extra‐binomial variation. The results are discussed in relation to recent data on eyewitness line‐ups, an example with a sparse data structure.