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

• Main Author: Reinhard Schunck
• Format: Article
• Language: English
• Published: GESIS - Leibniz-Institute for the Social Sciences, Mannheim 2016-06-01
• Series: Methoden, Daten, Analysen
• Subjects: multilevel modeling; hierarchical linear model; sample size; survey research; cluster sampling
• Online Access: https://mda.gesis.org/index.php/mda/article/view/2016.005/48

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.