Cluster Size and Aggregated Level 2 Variables in Multilevel Models. A Cautionary Note

2016/05/18 by Schunck, Reinhard
#cluster sampling #hierarchical linear model #multilevel modeling #sample size #survey research

paper · doi:10.12758/mda.2016.005

Abstract

This paper explores the consequences of small cluster size for parameter estimation in multilevel models. In particular, the interest lies in parameter estimates (regression weights) in linear multilevel models of level 2 variables that are functions of level 1 variables, as for instance the cluster-mean of a certain property, e.g. the average income or the proportion of certain people in a neighborhood. To this end, a simulation study is used to determine the effect of varying cluster sizes and number of clusters. The results show that small cluster sizes can cause severe downward bias in estimated regression weights of aggregated level 2 variables. Bias does not decrease if the number of clusters (i.e. the level 2 units) increases.

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