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Nonlinear Regime-Switching State-Space (RSSS) Models

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  • Sy-Miin Chow
  • Guangjian Zhang

Abstract

Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases—namely, latent “regimes” or classes—during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly. Copyright The Psychometric Society 2013

Suggested Citation

  • Sy-Miin Chow & Guangjian Zhang, 2013. "Nonlinear Regime-Switching State-Space (RSSS) Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 740-768, October.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:4:p:740-768
    DOI: 10.1007/s11336-013-9330-8
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    1. Augustin Kelava & Pascal Kilian & Judith Glaesser & Samuel Merk & Holger Brandt, 2022. "Forecasting Intra-individual Changes of Affective States Taking into Account Inter-individual Differences Using Intensive Longitudinal Data from a University Student Dropout Study in Math," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 533-558, June.
    2. Rosen, Karol & Angeles-Camacho, César & Elvira, Víctor & Guillén-Burguete, Servio Tulio, 2023. "Intra-hour photovoltaic forecasting through a time-varying Markov switching model," Energy, Elsevier, vol. 278(PB).
    3. Yanling Li & Zita Oravecz & Shuai Zhou & Yosef Bodovski & Ian J. Barnett & Guangqing Chi & Yuan Zhou & Naomi P. Friedman & Scott I. Vrieze & Sy-Miin Chow, 2022. "Bayesian Forecasting with a Regime-Switching Zero-Inflated Multilevel Poisson Regression Model: An Application to Adolescent Alcohol Use with Spatial Covariates," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 376-402, June.
    4. Sy-Miin Chow & Zhaohua Lu & Andrew Sherwood & Hongtu Zhu, 2016. "Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation–Maximization (SAEM) Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 102-134, March.
    5. Sy-Miin Chow & Lu Ou & Arridhana Ciptadi & Emily B. Prince & Dongjun You & Michael D. Hunter & James M. Rehg & Agata Rozga & Daniel S. Messinger, 2018. "Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime Switching," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 476-510, June.
    6. Zhao-Hua Lu & Sy-Miin Chow & Nilam Ram & Pamela M. Cole, 2019. "Zero-Inflated Regime-Switching Stochastic Differential Equation Models for Highly Unbalanced Multivariate, Multi-Subject Time-Series Data," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 611-645, June.
    7. Sy-Miin Chow & Jungmin Lee & Abe D. Hofman & Han L. J. Maas & Dennis K. Pearl & Peter C. M. Molenaar, 2022. "Control Theory Forecasts of Optimal Training Dosage to Facilitate Children’s Arithmetic Learning in a Digital Educational Application," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 559-592, June.

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