Modeling Heterogeneity in Temporal Dynamics: Extending Latent State-Trait Autoregressive and Cross-lagged Panel Models to Mixture Distribution Models

Abstract

Longitudinal models suited for the analysis of panel data, such as cross-lagged panel or autoregressive latent-state trait models, assume population homogeneity with respect to the temporal dynamics of the variables under investigation. This assumption is likely to be too restrictive in a myriad of research areas. We propose an extension of autoregressive and cross-lagged latent state-trait models to mixture distribution models. The models allow researchers to model unobserved person heterogeneity and qualitative differences in longitudinal dynamics based on comparatively few observations per person, while taking into account temporal dependencies between observations as well as measurement error in the variables. The models are extended to include categorical covariates, to investigate the distribution of encountered latent classes across observed groups. The potential of the models is illustrated with an application to self-esteem and affect data in patients with borderline personality disorder, an anxiety disorder, and healthy control participants. Requirements for the models’ applicability are investigated in an extensive simulation study and recommendations for model applications are derived.

KEYWORDS:

• Autoregressive latent state-trait analysis
• (random-intercept) cross-lagged panel model
• mixture structural equation modeling
• person heterogeneity
• ambulatory assessment

Article information

Conflict of interest disclosures: The author(s) declare that there were no conflicts of interest with respect to the authorship or the publication of this article. The authors are unable to share any data publicly as they did not explicitly ask participants to agree to make their anonymized data available online (sharing participants’ data would violate confidentiality).

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: This work was supported by Grant EB 364/6-1 and EI 379/10-1 from the Deutsche Forschungsgemeinschaft (German Research Foundation).

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

Acknowledgments: The authors would like to thank the anonymous reviewers for their valuable feedback and the HPC Service of ZEDAT (https://doi.org/10.17169/refubium-26754), Freie Universität Berlin, for computing time.

Notes

1 Note that there is a large variety of recently introduced modeling strategies for the analysis of intensive longitudinal data (see, e.g., Asparouhov et al., 2018; Beltz et al., 2016; Driver & Voelkle, 2018; Lane et al., 2019; Oravecz et al., 2009; Schuurman & Hamaker, 2019; Song & Zhang, 2014; Voelkle et al., 2014). A detailed description and comparison of these models is beyond the scope of the present article. However, note that in case of multilevel time series models, the required sample sizes do largely depend on the chosen model and its complexity, i.e., the number of parameters that are modeled as random effects and the number of covariates included, the modeling of measurement error, etc (see, e.g., Asparouhov et al., 2018; Schultzberg & Muthén, 2018) and due to the regularizing nature of hierarchical models, the required length of the time series tends to decrease with the number of persons observed on the between-level, and may additionally be reduced by respective prior specifications with bayesian estimation (e.g., Driver & Voelkle, 2018).

2 Subsamples of the current sample were analyzed in Santangelo et al. (2017; 60 BPD and 60 HC participants), Santangelo et al. (2020; 119 BPD participants), and Kockler et al. (2022; all of the AD, 65 of the HC, and 59 of the BPD participants), using different models investigating different research questions.

3 The bootstrap likelihood ratio test (BLRT; McLachlan & Peel, 2000) is not reported due to excessive computation times for drawing only few bootstrap samples.

4 Note that the BLRT was not included in all of the simulation studies.

5 Non-aggregated results per replication as well as results for incorrectly specified numbers of classes are provided by the first author upon request.