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Modeling temporally misaligned data across space: The case of total pollen concentration in Toronto

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  • Sara Zapata‐Marin
  • Alexandra M. Schmidt
  • Scott Weichenthal
  • Eric Lavigne

Abstract

Due to the high costs of monitoring environmental processes, measurements are commonly taken at different temporal scales. When observations are available at different temporal scales across different spatial locations, we name it temporal misalignment. Rather than aggregating the data and modeling it at the coarser scale, we propose a model that accounts simultaneously for the fine and coarser temporal scales. More specifically, we propose a spatiotemporal model that accounts for the temporal misalignment when one of the scales is the sum or average of the other by using the properties of the multivariate normal distribution. Inference is performed under the Bayesian framework, and uncertainty about unknown quantities is naturally accounted for. The proposed model is fitted to data simulated from different spatio‐temporal structures to check if the proposed inference procedure recovers the true values of the parameters used to generate the data. The motivating example consists of measurements of total pollen concentration across Toronto, Canada. The data were recorded daily for some sites and weekly for others. The proposed model estimates the daily measurements at sites where only weekly data was recorded and shows how the temporal aggregation of the measurements affects the associations with different covariates.

Suggested Citation

  • Sara Zapata‐Marin & Alexandra M. Schmidt & Scott Weichenthal & Eric Lavigne, 2023. "Modeling temporally misaligned data across space: The case of total pollen concentration in Toronto," Environmetrics, John Wiley & Sons, Ltd., vol. 34(8), December.
  • Handle: RePEc:wly:envmet:v:34:y:2023:i:8:n:e2820
    DOI: 10.1002/env.2820
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    References listed on IDEAS

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    1. Holan, Scott H. & Toth, Daniell & Ferreira, Marco A. R. & Karr, Alan F., 2010. "Bayesian Multiscale Multiple Imputation With Implications for Data Confidentiality," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 564-577.
    2. E. Marian Scott, 2023. "Framing data science, analytics and statistics around the digital earth concept," Environmetrics, John Wiley & Sons, Ltd., vol. 34(2), March.
    3. Phuong T. Vu & Adam A. Szpiro & Noah Simon, 2022. "Spatial matrix completion for spatially misaligned and high‐dimensional air pollution data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.
    4. C. Forlani & S. Bhatt & M. Cameletti & E. Krainski & M. Blangiardo, 2020. "A joint Bayesian space–time model to integrate spatially misaligned air pollution data in R‐INLA," Environmetrics, John Wiley & Sons, Ltd., vol. 31(8), December.
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    Cited by:

    1. Eric Yanchenko & Howard D. Bondell & Brian J. Reich, 2024. "Spatial regression modeling via the R2D2 framework," Environmetrics, John Wiley & Sons, Ltd., vol. 35(2), March.

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