The Robustness of Statistical Inferences With Latent Levels of Clusters

• In Event: Sharp Statistics in Educational Research

Abstract

This paper quantifies the bias of standard error estimates due to a latent cluster at either the lowest, middle, or highest level within an observed two-level cluster data structure. First, I extend the Moulton’s Variance Inflation formula to capture the standard errors bias with latent clusters at the lowest or highest level in the ordinal least square regressions. For the case of a latent middle-level cluster, the standard error bias is quantified by the standard error differences between a (false) two-level HLM model and a (correct) three-level one. At last, this paper provides a sensitivity analysis tool to verify the statistical inferences with setting the intraclass correlations and average group sizes of the possible latent levels of clusters.

Author

• Zixi Chen, Michigan State University