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Uncertainty in grid data: a theory and comprehensive robustness test

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Abstract

This methodological note makes two novel contributions to spatial political and conflict research using grid data. First, it develops a methodological theory of how uncertainty specific to grid data affects inference. Second, it introduces a comprehensive robustness test on sensitivity to this uncertainty, implemented in R. The uncertainty stems from (1) establishing the correct size of grid cells, (2) deciding the correct locations where the dividing lines of grid data are drawn, and (3) a greater effect of measurement errors due to finer grid cells. The proposed test diversifies grid cell sizes, by aggregating original grid cells into a multiple of these grid cells. The test also varies the locations of the diving lines, by using different starting points of grid cell aggregation (e.g., starting the aggregation from the corner of the entire map or one grid cell of the original size away from the corner). I apply the test to Theisen et al. (Int. Secur. 36(3):79–106, 2011), who utilize the PRIO-GRID data (Tollefsen et al., J. Peace Res. 49(2):363–374, 2012), to substantiate its use.

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Notes

  1. Depending on the setting, after the aggregation a few grid cells might remain unaggregated or partially aggregated because the aggregated size of grid cells might not evenly divide the entire map. This point is discussed further in the next section.

  2. In theory, both “x” and “y” can be observed exactly in the same location, but such a case is not included here for legibility.

  3. Note the difference between the correct (range of) grid cell size, which should be justified theoretically, and the locations where the dividing lines of grid data are drawn, which cannot be justified theoretically.

  4. This requirement is in addition to the general requirement for the identification of the average treatment effect: both areas with “x” and those without “x” are (conditionally) exchangeable as treatment/control groups. See, for example, Hernán and Robins (2020).

  5. For simplicity, I focus on the case of grid cells with “x” (i.e., where the presence of X is observed), but the same logic applies to counterfactual states (i.e., whether the grid cells would correctly capture the causal relationship between X and Y if “x” were observed).

  6. Again, for simplicity, I focus on the case of grid cells with observed “x,” but the same logic applies to how to define grid cells for the correct specification of counterfactual states.

  7. More specifically, the test is applied to Model 2 in Theisen et al. (2011). Their replication dataset can be obtained from the Peace Research Institute Oslo website at https://www.prio.org/publications/5109 (accessed on January 7, 2022).

  8. As explained in Sect. 2, the exceptions are grid cells at the periphery when an aggregated grid cell size cannot divide the entire map evenly, and/or when the starting point of grid cell aggregation is shifted.

  9. The statistical analysis was done on RStudio (RStudio Team 2020) running R version 4.1.2 (R Core Team 2021). The data visualization was done by the ggplot2 package (Wickham 2016).

  10. Different grid cell sizes create different numbers of observations and change the baseline likelihood of the onset of civil armed conflict, although, in all grid cell sizes used here, the onsets of civil armed conflict remain rare events (less than \(0.5\%\) of the observations). Therefore, the comparison of effect sizes across models is more meaningful on the log odds ratio scale, the relative scale of an effect, than on the probability scale, the absolute scale of an effect.

  11. Fuzzy-set qualitative comparative analysis (Ragin 2000) is another promising method. For examples in political and conflict research, see Bretthauer (2015), Haesebrouck (2017). For other examples, see Kusa et al. (2021), Medina-Molina et al. (2022), Romero-Castro et al. (2022). I thank an anonymous reviewer for this point.

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Acknowledgements

I would like to thank seminar participants at Dublin City University, the editors, and the anonymous reviewers, for their helpful comments, and Johan A. Dornschneider-Elkink for encouraging me to independently develop his initial idea on this topic. The accompanying R package,“rbstgrid,” has been co-developed with Johan A. Dornschneider-Elkink at the School of Politics and International Relations, University College Dublin, and is available at https://akisatosuzuki.github.io/programs.html. The views expressed are my own unless otherwise stated, and do not necessarily represent those of the institutes/organizations to which I am/have been related.

Funding

I would like to acknowledge the receipt of funding from the Irish Research Council (the Grant Number: GOIPD/2018/328) for the development of this work.

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  1. School of Politics and International Relations, University College Dublin, Belfield, Dublin 4, Ireland

    Akisato Suzuki

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Suzuki, A. Uncertainty in grid data: a theory and comprehensive robustness test. Qual Quant 57, 4477–4491 (2023). https://doi.org/10.1007/s11135-022-01555-x

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