Aggregating and Testing Intra-Individual Correlations: Methods and Comparisons

From a longitudinal study, we have repeatedly measured data from multiple individuals at multiple occasions. For each individual, the relation between 2 variables can be measured by the Pearson's correlation. The question is how to aggregate the multiple correlations and conduct statistical inference on the aggregated intra-individual correlation. Several methods are proposed to aggregate and test intra-individual correlations: (a) a meta-analysis method based on Fisher's Z transformed correlations, (b) a meta-analysis method based on the Pearson's correlations, and (c) a multilevel modeling method using data standardized within each individual. The performance of the methods after bias corrections was compared using simulations with considering factors including numbers of individuals, numbers of time points, population effect sizes, and their distribution forms (homogeneous vs heterogeneous). The results from the simulation studies show that estimation biases were found using the meta-analytic methods and suggestions on when and how to correct biases were provided based on the simulation results. Furthermore, the performance of the 3 methods after necessary bias corrections was found to be comparable and reasonably good, indicating that all 3 methods worked for aggregating and testing intra-individual correlations. An empirical daily diary data set was then used to illustrate the applications of the 3 methods. The assumptions, advantages and disadvantages, and possible extensions of the 3 methods were discussed.