striking observation from Figure 3 is how much more important SR yields are in comparison to the rest of the covariates when it comes to log predictions. We assess the relative importance of covariates in the accuracy of the prediction in the following subsection.

# **5.1.2 Relative importance of SR yields and GPS extracted variables**

We run the ensemble of methods described in Appendix A for 25 different cross-validation splits to predict CC yields, testing for the inclusion of SR yields and geospatial variables extracted using the EA GPS coordinates<sup>16</sup> among the set of predictors. This approach allows us to evaluate the impact and relevance of these specific variables in the context of our machine learning models and the overall accuracy of the yield predictions.

Table 6<sup>17</sup> shows the impact of including SR yields and/or GPS extracted variables on the quality of the predictions, measured in terms of _R_<sup>2</sup> for the whole set of crops and individually for each crop. The reference model set up does not include SR or geospatial variables in the set of covariates.

First, including SR yield or GPS extracted variables increases unambiguously the accuracy of yield prediction as the difference in _R_<sup>2</sup> is for the most part positive and statistically significant. Second, combining SR and GPS provides on average better accuracy than using one or the other set of covariates. Third, there is some heterogeneity in terms of crops. The SR yield variable is more relevant for sorghum and cowpea imputations, although the overall accuracy of prediction of SR yield without including GPS extracted variables is low. GPS extracted variables, both with and without including SR yields, are particularly important for groundnut, sorghum and millet yield predictions. Finally, cowpea yield prediction benefits particularly from the inclusion of both SR yield and GPS extracted variables. The heterogeneity of the impact of the different combinations of covariates for each crop predictions is difficult to interpret especially since the coefficients are in general not statistically different to each other. As such, the main lesson that we retain here is that combining the subjective measure of yields and the objective covariates is always the most beneficial to improve the accuracy of the predictions. This conclusion is also robust to the use of alternative model performance metrics. This is confirmed in Table B.6 which shows how the inclusion of different covariates impacts the performance as measured by the root mean square of the predictions when we model level yields: we find that for all crops including both SR yields and geospatial variables improve the model performance (reduce the root mean square error) the most. The improvement is marginal although significant when SR is included without geospatial variables, highlighting the fact that geospatial variables are the most potent in improving the predictions. Looking at the base root mean square error across crops, it appears that in average the prediction from cowpea yield in average the best prediction, but that is because the average yield for cowpea is smaller than the other crops and as such small deviations from when squared are amplified.

> 16The GPS extracted variables used the publicly available coordinates which have been scrambled for privacy purposes. As discussed in Michler et al. (2022), the degree to which spatial anonymization introduces mismeasurement is a function of which remote sensing weather product is used in the analysis. Care must be taken in choosing a remote sensing weather product when looking to integrate it with publicly available survey data. As such, the results might vary with other types of weather products.

> 17See Table B.4 for the results for log yields, which do not differ significantly from the levels.

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