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Aggregated Versus Individual Land-Use Models: Modeling Spatial Autocorrelation to Increase Predictive Accuracy

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Abstract

The objective of this paper is to compare the predictive accuracy of individual and aggregated econometric models of land-use choices. We argue that modeling spatial autocorrelation is a comparative advantage of aggregated models due to the smaller number of observation and the linearity of the outcome. The question is whether modeling spatial autocorrelation in aggregated models is able to provide better predictions than individual ones. We consider a complete partition of space with four land-use classes: arable, pasture, forest, and urban. We estimate and compare the predictive accuracies of individual models at the plot level (514,074 observations) and of aggregated models at a regular 12 × 12 km grid level (3,767 observations). Our results show that modeling spatial autocorrelation allows to obtain more accurate predictions at the aggregated level when the appropriate predictors are used.

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Notes

  1. 1 In the literature, “individual data” corresponds both to “sample plot” and “parcel level” data (see for example [54]). Our “individual” data are “sample plot” data, also called “micro level data” by [66] or “disaggregate data” by [13]. For more reviews of land-use modeling, see [29, 30].

  2. 2 In the following of this paper, we call spatial models those that model spatial autocorrelation explicitly. Conversely, we call aspatial models those that can include spatial effects without explicitly estimating spatial autocorrelation.

  3. 3 Other estimation procedures have also been proposed in the literature: EM method [47], the generalized method of moments [53], the method of maximum pseudo-likelihood [62], and the method composite maximum likelihood [22, 61]. For a detailed review of the inclusion of spatial autocorrelation in discrete choice models, see [23] and [62].

  4. 4 These assumptions can be relaxed in the empirical part by including interactions between explanatory variables or by specifying random coefficients.

  5. 5 For the USA, [45] makes an important data gathering effort to construct county-level returns for crops, pastures, forests and urban. The other studies use more partial information about returns, in very heterogeneous ways depending on the research questions.

  6. 6 We argue that data about land price are in general available at fine spatial scales, and it is at least true for our case study of France.

  7. 7 We have also considered two other specifications that have been proposed in the literature to deal with this problem: the fractional logit model proposed by [52] and the fractional Dirichelet model proposed by [49]. As they do not perform better that the specifications included in the paper, we do not report the results but they are available from the authors upon request.

  8. 8 We choose the reference modality as the land use with the less number of shares equal to zero. Because it is still possible to have some zeros at the denominator, we add 𝜖=.0001 at the numerator and the denominator of Eq. 7. This is a minor drawback that can be visually evaluated from Figs. 4 and 5 from Supporting Information (SI). More rigorously, it will be also evaluated by comparing the predictions with those from other models, as we consider this as a necessity for estimating linearized logistic models, always used in the literature.

  9. 9 The case figure considered by [31] (“leave-one-out” predictors) and also by [51] (“ex-sample predictors”) is different from ours as they are concerned with a particular case of prediction: the case where for a cross-section of observations, part of the observations on the dependent variable is missing and needs to be predicted.

  10. 10 We dropped from the data observations that concern salt marshes, ponds, lakes, rivers, marshes, wetlands, glaciers, eternal snow, wastelands, and moors, which accounted for about 7 % of observations. Our final sample counts N = 514,074 points.

  11. 11 One can consider that, because of the higher number of observations, the individual models can contain additional terms such as interactions between variables or polynomials. To keep our comparative exercise simple, we choose to not consider this possibility of more complex regression functions as a comparative advantage of individual models.

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Acknowledgments

The research leading to these results has received funding from the European Union by the European Commission within the Seventh Framework Programme in the frame of RURAGRI ERA-NET under Grant Agreement 235175 TRUSTEE (ANR–13–RURA–0001–01) and the French Agence Nationale de la Recherche through the ModULand project (ANR–11–BSH1–005). The authors only are responsible for any omissions or deficiencies. Neither the TRUSTEE project and any of its partner organizations, nor any organization of the European Union or European Commission are accountable for the content of this research.

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Authors and Affiliations

  1. UMR CESAER, INRA, AgroSup Dijon, Université Bourgogne Franche Comté, 21000, Dijon, France

    Jean-Sauveur Ay & Julie Le Gallo

  2. Economie Publique, INRA, AgroParisTech, Université Paris-Saclay, 78850, Thiverval-Grignon, France

    Raja Chakir

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  1. Jean-Sauveur Ay
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Correspondence to Jean-Sauveur Ay.

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Appendix

Appendix

1.1 A.1 Spatial Coefficient from Aggregated Models

Table 6 Spatial coefficients for long run models
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Table 7 Spatial coefficients for short run models
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Fig. 1
figure 1

Observed 2003 land use shares (first row) and long run predictions from different land-use models

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Fig. 2
figure 2

Observed 2003 land use shares (first row) and short run predictions from different land-use models

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Ay, JS., Chakir, R. & Gallo, J.L. Aggregated Versus Individual Land-Use Models: Modeling Spatial Autocorrelation to Increase Predictive Accuracy. Environ Model Assess 22, 129–145 (2017). https://doi.org/10.1007/s10666-016-9523-5

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