population AgGDP model as measured by the Mean Absolute Deviation (MAD) and Root Mean Square Error (RMSE).<sup>14</sup> While the spatial regression performs the best, global data requirements that allow high enough degrees of freedom is a challenge.

Given these data requirements and challenges, we compare the cross-entropy model to another spatial allocation model based on rural population at the country level. Then we extend a comparison of both models at the global level by mapping the correlation.

One advantage of the cross-entropy is the volume preserving pycnophylactic property, which ensures the sum of the gridded data is the original value and allows the possibility to include all information that is available from mixed levels of data (e.g. You, Wood, et al., 2014). However, this presents a challenge in terms of an assessment of a global model. Previous work on gridded data products includes evaluations of accuracy. Typically, studies evaluate the internal accuracy of the model exploiting multiple geographic levels of data (as mentioned above in Thomas et al., 2019). Similarly, Van Boeckel et al. (2011), who examine duck data in Thailand, conclude that input levels do matter, especially the importance of the presence of administrative level 1 data. Robinson et al. (2014) evaluate the livestock model in Brazil and find a positive association between the model accuracy and the administrative level of the training data used in the model. They also illustrate this inverse relationship of prediction accuracy and level of intensification in the case of chickens in Europe (Robinson et al., 2014). At the local cell level, previous models of land or population have compared results to independent local data (Siebert, D ̈oll, and Hoogeveen, 2002) or identified errors of omission in a gridded population model using the locations from household surveys (e.g. Tiecke et al., 2017).

Since we can not perform an evaluation of prediction accuracy for all countries, we compare the global cross-entropy model with another allocation model, which is similar to the global assessment of maize and rice production in You, Wood, et al. (2014). For the comparison, we construct a proportional allocation model using rural population density following the method in Thomas et al. (2019) for the case of Brazil.<sup>15</sup> Then, we can test the similarity of the two maps. Following Levine et al. (2009), we assume a normal distribution over the 2 million land pixels and perform a pairwise student t test to test the null hypothesis that both maps were identical. This test allows us to examine whether the mean difference in 14Specifically, the MAD and RMSE for each model are respectively: the rural population density model (28,744 and 25,397), Cross-entropy spatial allocation (8,249 and 18,347) and Spatial disaggregation from a regression on agricultural production (7,214 and 16,673).

> 15We use the 2010 Gridded Population of the World version 4 from Center for International Earth Science Information Network - CIESIN - Columbia University (2017) adjusted to the United Nation’s World Population Prospects followed by including the rural area defined by the Global Human Settlement grid for 2015: namely, “Rural cluster”, “Low Density Rural grid cell”, or “Very low density rural grid cell” (Pesaresi and Freire, 2019).

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