Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022 Dec 5;50(14):2914-2933.
doi: 10.1080/02664763.2022.2147150. eCollection 2023.

Interpretable, predictive spatio-temporal models via enhanced pairwise directions estimation

Heng-Hui Lue  1 , ShengLi Tzeng  2
Affiliations

Interpretable, predictive spatio-temporal models via enhanced pairwise directions estimation

Heng-Hui Lue et al. J Appl Stat. .

Abstract

This article concerns predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to capture nonlinear mean structures without requiring a prespecified parametric model. In addition to prediction as a common interest, this approach emphasizes the exploration of geometric information from the data. The method of Pairwise Directions Estimation (PDE) is implemented in our approach as a data-driven function searching for spatial patterns and temporal trends. The benefit of using geometric information from the method of PDE is highlighted, which aids effectively in exploring data structures. We further enhance PDE, referring to it as PDE+, by incorporating kriging to estimate the random effects not explained in the mean functions. Our proposal can not only increase prediction accuracy but also improve the interpretation for modeling. Two simulation examples are conducted and comparisons are made with several existing methods. The results demonstrate that the proposed PDE+ method is very useful for exploring and interpreting the patterns and trends for spatio-temporal data. Illustrative applications to two real datasets are also presented.

Keywords: Covariates; dimension reduction; kriging; semi-parametric models; spatio-temporal data; visualization.

PubMed Disclaimer

Conflict of interest statement

No potential conflict of interest was reported by the author(s).

Figures

Figure 1.
Figure 1.
Plots of (A) the first and (B) the second basis functions with (C) the first and (D) the second scaled coefficient functions for a randomly selected simulation from model in (16) and (17).
Figure 2.
Figure 2.
Plots of (A) the first and (B) the second basis functions with (C) the first and (D) the second scaled coefficient functions for a randomly selected simulation from model in (18) and (19).
Figure 3.
Figure 3.
Plots of (A) the average daily temperatures over individual locations, (B) the spatial distribution of locations, (C) the first and (D) the second basis functions, and (E) the first and (F) the second scaled coefficient functions for Canadian Weather data.
Figure 4.
Figure 4.
Plots of (A) the monthly averages of PM 10 concentrations over individual locations, (B) the spatial distribution of locations, (C) the first and (D) the second basis functions, and (E) the first and (F) the second scaled coefficient functions for German PM 10 data.
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

References

    1. Bakar K.S. and Sahu S.K., sptimer: spatio-temporal bayesian modelling using R, J. Stat. Softw. 63 (2015), pp. 1–32.
    1. Banerjee S., Gelfand A.E., Finley A.O., and Sang H., Gaussian predictive process models for large spatial data sets, J. R. Stat. Soc. Series B. Stat. Methodol. 70 (2008), pp. 825–848. - PMC - PubMed
    1. Braud I. and Obled C., On the use of empirical orthogonal function (EOF) analysis in the simulation of random fields, Stoch. Hydrol. Hydraul. 5 (1991), pp. 125–134.
    1. Coudret R., Girard S., and Saracco J., A new sliced inverse regression method for multivariate response, Comput. Stat. Data. Anal. 77 (2014), pp. 285–299.
    1. Cressie N., Statistics for Spatial Data, John Wiley & Sons, Hoboken, 2015.

LinkOut - more resources