Mixed models for assessing correlation in the presence of replication

The need to assess correlation in settings where multiple measurements are available on each of the variables of interest often arises in environmental science. However, this topic is not covered in introductory statistics texts. Although several ad hoc approaches can be used, they can easily lead to invalid conclusions and to a difficult choice of an appropriate measure of the correlation. Lam et al. approached this problem by using maximum likelihood estimation in cases where the replicate measurements are linked over time, but the method requires specialized software. We reanalyze the data of Lam et al. using PROC MIXED in SAS and show how to obtain the parameter estimates of interest with just a few lines of code. We then extend Lam et al.'s method to settings where the replicate measurements are not linked. Analysis of the unlinked case is illustrated with data from a study designed to assess correlations between indoor and outdoor measurements of benzene concentration in the air.