Individual Pooling for Group-Based Modeling Under the Assumption of Ergodicity

Abstract

Psychology principally utilizes nomothetic, interindividual approaches to model phenomena of interest. However, it is the case that these approaches do not always capture the processes for each individual in the sample. If the research is focused on individual processes, confining analysis to the idiographic level may be more appropriate. One way to overcome the nomothetic inability to capture idiographic processes is to identify those participants who meet the criteria of ergodicity and restrict analysis to the resulting sample. Under these conditions it is quantitatively justifiable to create a group model without concern that it may fail to represent each member's idiographic process. In this study we explore the utility of such a method by (a) applying an ergodic pooling test to a sample of dyads (N = 128) who provided daily (T = 50) self-reports of affect, (b) applying an ergodic pooling test to samples (N = 4) of simulated ergodic time series data (T = 50, 250, and 1,000), (c) modeling dyads and simulated subgroups identified as ergodic, and (d) comparing the results from a model specified at the group level with those from models specified at the individual level.

Notes

We evaluated simulated data with observation sizes of 50, 100, 250, 500, and 1,000 but only report for observation sizes of 50, 250, and 1,000 in this article. The additional analyses at 100 and 500 observations are available upon request.

There was one clear exception, Case 8, to this for the Group 4 simulation at 50 observations.

One possible way to evaluate these results may be the white noise tests of the residuals. We thank one of our reviewers for this suggestion.

It is possible that heterogeneity tests in our examples were significant because the heterogeneity in the concurrent item relations was greater than in the lagged item relations. We evaluated this by testing for differences between the concurrent and lagged portions of block-Toeplitz matrices with averaged matrices. Our results indicate that there were no significant differences in degree of heterogeneity, but this deserves to be explored in more detail in future work.