The size of the training data does not significantly affect the accuracy of the predictions (Table 8). Using a sample of 1,178 villages in the 55 sub-districts, the out-of-sample _R_<sup>2</sup> using all the available satellite data is 0.842, as seen earlier in Table 5. The accuracy increases marginally to 0.843 if we reduce the training sample by half, with a mild reduction to 0.832 if we further reduce the sample size by another one-half. There is only a small increase in the MAE and RMSE with the reduced sample sizes. Overall, these results indicate that changing the training sample size does not significantly change the prediction accuracy.

# **4.3 Survey-Based Predictions and Validation with the Census**

While it is encouraging that satellite data accurately predict census population density, they do not conclusively show that survey data can be used to accurately approximate population density. We now turn to examining this by testing the accuracy of a survey-based model in the 55 sub-districts sample where we estimate a Poisson model of HIES population density in HIES-villages, and obtain out-of-sample density predictions in the non-HIES villages.

The results from a model using both public and proprietary satellite imagery-based indicators are provided in panel A, columns (1)-(3), in Table 9. The _R_<sup>2</sup> , Spearman Rank Correlation (SRC), and Mean Absolute Error (MAE) between the density predictions and the census density are 0.79, 0.91, and 664, respectively. This model uses the inverse of village population as weights. If the weights are corrected based on probability of the village being selected into the HIES, we obtain similar results: 0.78, 0.92, and 665 for the same measures. Considering the _R_<sup>2</sup> and SRC, our model performs equally well compared to the census based model, and better than all “top-down” estimates except Facebook and Worldpop 2015 (panel C).<sup>22</sup> In panel B, we present the same results based on a model using only publicly available satellite imagery. Interestingly, similar out-of-sample prediction accuracies are obtained using only public imagery (0.75, 0.92, and 663, and 0.77, 0.92, and 657 for the three measures using the two types of weights).

We multiplied these density predictions with village-level area to obtain population count predictions, which are reported in columns (4)-(6). The relative performance of the population count predictions, in comparison to the top-down estimates, is similar to those of the population density predictions. The _R_<sup>2</sup> and SRC are generally lower for population counts compared to density predictions, but the MAEs are also lower.

> for non-linear relationships. Further, studies predicting population counts and density have specifically shown mixed results on comparative performances between random forest and LASSO-based predictions (Anderson et al., 2014).

> 22 The out-of-sample _R_ 2, SRC, MAE, in that order, for the “top-down” measures are the following : WorldPop 2015 (0.99, 1.00, and 312) and Facebook’s HRSL (0.91, 0.97, and 417), GHSL (0.84, 0.88, and 639), GPW 2015 (0.68, 0.90, and 1029), GPW 2010 (0.29, 0.28, and 1550), WorldPop 2010 (0.31, 0.81, and 1206), and LandScan (0.04, 0.10, and 2562).

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