# **4.2 Accuracy of population density predictions based on census population counts**

Poisson regression results using the census data for all villages, based on the variables selected from LASSO regularization indicate that satellite indicators have exceptionally strong predictive power in predicting village level population density (Table 5). At the national level, publicly available indicators explain a large amount of variation in village population density. In this case, the value added in using high-resolution indicators (out-of-sample _R_<sup>2</sup> is 0.75) as opposed to low resolution indicators (out-of-sample _R_<sup>2</sup> is 0.702) is minimal. In the 55 sub-districts, adding proprietary contextual features to public imagery-based models does not improve the prediction accuracy (out-of-sample _R_<sup>2</sup> remains at around 0.7). However, adding object classifiers to the model improves the out-of-sample _R_<sup>2</sup> by 10 points (0.83).<sup>20</sup> The results differ across sectors. Using the full national sample, the publicly available satellite indicators explain more variation in population density in the rural and estate sectors (0.808) than the urban sector (0.569) (panel A in Table 6). In the sample with 55 sub-districts, the predictive power of urban population density increases tremendously when adding the proprietary contextual and object features, relative to only including publicly available indicators (0.804 compared to 0.525). Adding proprietary indicators leads only to a limited improvement in rural areas (0.869 compared to 0.838) (panel B in Table 6). This result is consistent with greater uniformity in the relationship between built-up area and population density in rural areas, where simple measures of built-up area are sufficient to predict population density. In urban areas, due to the complex nature of the relationship between population density and buildings where the latter can be both commercial and residential, advanced measures such as object classifiers and contextual measures are required for better prediction.

Random forest (RF) models provide similar results overall and across sector-types (Table 7). The out-of-bag _R_<sup>2</sup> , RMSE, and MAE obtained from the RF models are comparable to the corresponding statistics obtained from the post-LASSO Poisson models. The accuracy pattern across resolution types seen in the LASSO results is also maintained in the RF results. Strikingly, the tremendous improvement in predictive accuracy from using very high resolution indicators in urban areas is corroborated by the RF results. These results collectively indicate that LASSO selection performs as well as random forest models in this setting.<sup>21</sup>

> 20 The out-of-sample _R_ 2 obtained in Table 5 are similar to those obtained in models that do not include log village area (supplementary Table S8), especially in models using higher-resolution indicators. The marginal effects of LASSO-selected variables from the model originally using all public and proprietary indicators are provided in supplementary Table S9. This refers to the model which uses the 55-sub-district sample and _all_ imagery in Table 5.

> 21 While random forest models are known to outperform LASSO models in some contexts (Mullainathan and Spiess, 2017), these results are based on linear LASSO models. The use of Poisson regression in our context may negate the predictive advantage of random forest models, which are traditionally better able to account

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