When can group level clustering be ignored? Multilevel models versus single-level models with sparse data

摘要

Objective: The use of multilevel modelling with data from population-based surveys is often limited by the small number of cases per level-2 unit, prompting many researchers to use single-level techniques such as ordinary least squares regression. Design: Monte Carlo simulations are used to investigate the effects of data sparseness on the validity of parameter estimates in two-level versus single-level models. Setting: Both linear and non-linear hierarchical models are simulated in order to examine potential differences in the effects of small group size across continuous and discrete outcomes. Results are then compared with those obtained using disaggregated techniques (ordinary least squares and logistic regression). Main results: At the extremes of data sparseness (two observations per group), the group level variance components are overestimated in the two-level models. But with an average of only five observations per group, valid and reliable estimates of all parameters can be obtained when using a two-level model with either a continuous or a discrete outcome. In contrast, researchers run the risk of Type I error (standard errors biased downwards) when using single-level models even when there are as few as two observations per group on average. Bias is magnified when modelling discrete outcomes. Conclusions: Multilevel models can be reliably estimated with an average of only five observations per group. Disaggregated techniques carry an increased risk of Type I error, even in situations where there is only limited clustering in the data.