Homogeneity Assumptions in the Analysis of Dynamic Processes

Abstract

With the increased use of time series data in human research, ranging from ecological momentary assessments to data passively obtained, researchers can explore dynamic processes more than ever before. An important question researchers must ask themselves is, do I think all individuals have similar processes? If not, how different, and in what ways? Dr. Peter Molenaar’s work set the foundation to answer these questions by providing insight into individual-level analysis for processes that are assumed to differ across individuals in at least some aspects. Currently, such assumptions do not have a clear taxonomy regarding the degree of homogeneity in the patterns of relations among variables and the corresponding parameter values. This paper provides the language with which researchers can discuss assumptions inherent in their analyses. We define strict homogeneity as the assumption that all individuals have an identical pattern of relations as well as parameter values; pattern homogeneity assumes the same pattern of relations but parameter values can differ; weak homogeneity assumes there are some (but not all) generalizable aspects of the process; and no homogeneity explicitly assumes no population-level similarities in dynamic processes across individuals. We demonstrate these assumptions with an empirical data set of daily emotions in couples.

Keywords:

• individual-level analyses
• ergodicity
• person-specific
• idiographic

Article information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: No funding provided.

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design.

Acknowledgments: The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions or the National Institute of Mental Health is not intended and should not be inferred.

Notes

1 Please note that the homogeneity referred to in this paper denotes homogeneity across people rather than across time.

2 When the A matrix is constrained to zero and the off-diagonal elements in Ψ are allowed to be estimated, the model is a vector autoregressive (VAR) model.

3 When conducting time series analysis in SEM, a researcher typically construct an augmented data matrix for each individual with the lagged and non-lagged values of the variables in the same rows. For instance, the augmented data matrix for estimating a first-order VAR model with p variables and T_i time points would be a T_i x 2p matrix, with p columns containing the non-lagged values and p columns containing the lagged values. If a researcher is instead concatenating the original time series data, missing values need to be added to the pooled data matrix to avoid regressing the first response of one individual on the last response of another individual. Failing to do so could introduce bias to the parameter estimates. For a comparison between different methods for aggregating time series data, see Lu and Zhang (2015).

4 Note that while these packages enable researchers to conduct analysis in accordance with the strict homogeneity assumption, it does not mean the creators endorse the use of such methods.

5 GIMME uses the Bonferroni correction to counteract the multiple testing problem. The alpha level is set to .05/N, where N is the number of units of analysis (in this case, N = 64).

6 GIMME has been recently extended to allow for the identification of latent subgroups of individuals based on the pattern and parameter values of associations among variables. This approach, called Subgrouping GIMME (S-GIMME; Gates et al., 2017; Lane et al., 2019) also assumes weak homogeneity.