Spatial dynamic factor analysis

By Hedibert Freitas Lopes, Esther Salazar, Dani Gamerman. 2008

155 citations recorded by the source corpus.

A new class of space-time models derived from standard dynamic factor models is proposed. The temporal dependence is modeled by latent factors while the spatial dependence is modeled by the factor loadings. Factor analytic arguments are used to help identify temporal components that summarize most of the spatial variation of a given region. The temporal evolution of the factors is described in a number of forms to account for different aspects of time variation such as trend and seasonality. The spatial dependence is incorporated into the factor loadings by a combination of deterministic and stochastic elements thus giving them more flexibility and generalizing previous approaches. The new structure implies nonseparable space-time variation to observables, despite its conditionally independent nature, while reducing the overall dimensionality, and hence complexity, of the problem. The number of factors is treated as another unknown parameter and fully Bayesian inference is performed via a reversible jump Markov Chain Monte Carlo algorithm. The new class of models is tested against one synthetic dataset and applied to pollution data obtained from the Clean Air Status and Trends Network (CASTNet). Our factor model exhibited better predictive performance when compared to benchmark models, while capturing important aspects of spatial and temporal behavior of the data.

Subfields: Economics and Econometrics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/b845bc1d41547ae16fca6d5e149a404ea888c275

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Citations in the corpus

Gaussian predictive process models for large spatial data sets (2008, background): “Lastly, we can draw a connection to recent work in spatial dynamic factor analysis (see, for example, Lopes et al. (2006) and references therein), where K is viewed as an n × m matrix of factor loadings.”
Basis-Function Models in Spatial Statistics (2021, methodology): “In the spatiotemporal setting, this type of model has been used for analysing Gaussian data (Lopes et al., 2008) and, using the GLMM framework, non-Gaussian data (Lopes et al.”
Hierarchical statistical modeling of big spatial datasets using the exponential family of distributions (2013, methodology): “When the data are Gaussian, reducedrank-modeling approaches for the hidden Gaussian process Y (·) have been developed to deal with this computational challenge (e.g., Wikle et al., 2001; Cressie and Johannesson, 2006, 2008; Banerjee et al., 2008; Stein, 2008; Lopes et al., 2008).”
Factor stochastic volatility with time varying loadings and Markov switching regimes (2007, background): “Lopes and West (2004) examine the problem of determining the number of factors in a static factor model while 7 showing that the order of the variable is immaterial. The same is not necessarily true when both common and specific factors exhibit temporal dynamics. Vrontros et al. (2003), for instance”
Bayesian Inference for the Spatial Random Effects Model (2011, methodology): “Moreover, Lopes, Salazar, and Gamerman (2008) assume that both S and K are random and hence they are modeled in the parameter model, which raises an issue of “practical” identifiability.”