A Latent Gaussian process model for analysing intensive longitudinal data

Chen, Yunxiao; Zhang, Siliang

doi:10.1111/bmsp.12180

Cited by 6 publications

(5 citation statements)

References 29 publications

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“…Finally, the performance of the proposed method under other latent variable models needs to be investigated. For example, the proposed method can also be applied to latent stochastic process models (e.g., Chow et al, 2016 ; Chen & Zhang, 2020 ) that are useful for analyzing intensive longitudinal data. These models bring additional challenges, as stochastic processes need to be sampled in the stochastic step of our algorithm.…”

Section: Discussionmentioning

confidence: 99%

Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework

Zhang

Chen

2022

Psychometrika

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Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of many latent variables, (2) the observed and latent variables being continuous, discrete, or a combination of both, (3) constraints on parameters, and (4) penalties on parameters to impose model parsimony. The estimation often involves maximizing an objective function based on a marginal likelihood/pseudo-likelihood, possibly with constraints and/or penalties on parameters. Solving this optimization problem is highly non-trivial, due to the complexities brought by the features mentioned above. Although several efficient algorithms have been proposed, there lacks a unified computational framework that takes all these features into account. In this paper, we fill the gap. Specifically, we provide a unified formulation for the optimization problem and then propose a quasi-Newton stochastic proximal algorithm. Theoretical properties of the proposed algorithms are established. The computational efficiency and robustness are shown by simulation studies under various settings for latent variable model estimation.

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Section: Discussionmentioning

confidence: 99%

Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework

Zhang

Chen

2022

Psychometrika

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“…GPs have been widely used in many different fields like spatial statistics for interpolation, (Stein, 2012), Machine learning (Rasmussen, 2003), or psychology (Chen & Zhang, 2020). The usage of GPs in multilevel modeling is not new, Diggle (1988) introduced it in a two level-model setting.…”

Section: Homogeneous Consensus Emergence Model (Homcem)mentioning

confidence: 99%

Modelling Consensus Emergence With Nonlinear Dynamics

Baurne¹,

Delmar²,

Wallin³

2022

Preprint

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The study of emergent, bottom-up, processes has long been of interest within organizational and group research. Emergent processes refer to how dynamic interactions among lower-level units (e.g. individuals) over time form a new, shared, construct or phenomena at a higher level (e.g. work group). To properly study emergence of shared constructs one needs models, and data, that both take into account variability across individuals and groups (multilevel), and variability over time (longitudinal). This article makes three contribution to the modelling and theory of of consensus emergence. First, we formulate two separate patterns of consensus emergence; homogeneous and heterogeneous. Homogeneous consensus emergence is characterized by gradual and almost deterministic adjustments of the individual trajectories, whereas heterogeneous consensus emergence show more randomly oscillating trajectories towards consensus. Second, we introduce a model-invariant statistic that measures the strength of the consensus; and allows for comparisons between different models and patterns of consensus emergence. Third, we show how Gaussian Processes can be used to further extend the consensus emergence models, allowing them to capture nonlinear dynamics, on both individual and group level, in emergent processes. Using an established data set, we show that conclusions on the pattern of consensus emergence can change depending on whether the nonlinear group mean change over time is adequately modelled or not. Thus it is crucial to correctly capture the group dynamics to properly understand the consensus emergence.

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“…Given this entirely different focus, their method is very different from GPPM, as introduced in this paper. Chen and Zhang (2019) introduced an alternative model that utilizes GPR for the analysis of (intensive) longitudinal data. Like in the dissertation monograph (Karch, 2016) and the preprint on GPPM (Karch et al, 2017), their method describes the within-person model using GPR.…”

Section: Introductionmentioning

confidence: 99%

“…However, GPPM differs from their approach in terms of recommendations for model specification, implementation, and scope of possible models. Additionally, Chen and Zhang (2019) focus only on explanatory modeling and do not discuss which kind of between-person models can be implemented.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Process Panel Modeling—Machine Learning Inspired Analysis of Longitudinal Panel Data

2020

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In this article, we extend the Bayesian nonparametric regression method Gaussian Process Regression to the analysis of longitudinal panel data. We call this new approach Gaussian Process Panel Modeling (GPPM). GPPM provides great flexibility because of the large number of models it can represent. It allows classical statistical inference as well as machine learning inspired predictive modeling. GPPM offers frequentist and Bayesian inference without the need to resort to Markov chain Monte Carlo-based approximations, which makes the approach exact and fast. GPPMs are defined using the kernel-language, which can express many traditional modeling approaches for longitudinal data, such as linear structural equation models, multilevel models, or state-space models but also various commonly used machine learning approaches. As a result, GPPM is uniquely able to represent hybrid models combining traditional parametric longitudinal models and nonparametric machine learning models. In the present paper, we introduce GPPM and illustrate its utility through theoretical arguments as well as simulated and empirical data.

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A Latent Gaussian process model for analysing intensive longitudinal data

Cited by 6 publications

References 29 publications

Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework

Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework

Modelling Consensus Emergence With Nonlinear Dynamics

Gaussian Process Panel Modeling—Machine Learning Inspired Analysis of Longitudinal Panel Data

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