We also verified the impact of the inclusion of weights in the covariates by testing it on predictions of millet yields in the 2017 data set. We find that in average, the standard errors of the imputed mean from a model with survey weights was only 0.38% larger than in the case of a model without weights. The bias is also slightly larger as we find than in average, the root mean square error is 0.5% when including weights. As these results seem to be of little practical concern, we believe it will not affect the lessons gleaned from the imputation exercises conducted in this work and we leave changes to the covariates sets that could allow for the inclusion of survey weights<sup>18</sup> for future work.

# **5.1.3 Prediction accuracy by crops**

Figure 5 provides a graphical representation of the distribution of the _R_<sup>2</sup> of the regression of the CC yields on the ML prediction for yields levels predictions,<sup>19</sup> by crop. There appears to be significant heterogeneity in the performance of the ML algorithms across crops: the _R_<sup>2</sup> for cowpea ranges between 0.1 and 0.42 while that of rice ranges between 0.41 and 0.7. The comparison of these crops is a good case and point for what is the most likely candidate explanation for the disparity in ML prediction performance across crops: the rate of intercropping, which refers to the practice of growing multiple crops in the same field simultaneously. In fact plots with cowpea are the highest intercropping rate (0.26) while rice is not on intercropped plots. Moreover the median performance of the ML algorithm is in general increasing with the rate of intercropping if we focus on sorghum, maize and groundnut. The predictions for millet have a higher performance than those of sorghum or maize even though it has a higher intercropping rate, but we can attribute that to the fact that the number of plots of millet is significantly more important. Another factor that likely explains the heterogeneity in ML predictive performance across crops is the degree of commercialization. Rice and groundnut are also cash crops, hence farmers of these crops use units that have more standardized weights. This also explains why SR yields appears at a higher predictive rank for rice and groundnut than millet or maize for example (see Table 5).

# **5.1.4 Training set size**

This section assesses the minimum share of plot observations that can be sub-sampled for crop-cutting measurements while still obtaining a reliable predicted measure of CC yields. The predictive accuracy, measured in terms of _R_<sup>2</sup> (coefficient of determination), of the ML prediction is evaluated for different sizes of the training dataset. The training dataset sizes considered are 10, 25, 33, 50, 67, and 75 percent of the CC measures. This evaluation is performed for each crop individually and for the entire set of crops across 50 different simulations.

The results, depicted in Figure 6, show that the _R_<sup>2</sup> of CC yields on the ML prediction increases as the percentage of the training dataset size grows. However, the marginal gain in accuracy diminishes as the training dataset size increases, particularly for logs imputation.

> 18One way to correct these issues as noted by Quartagno et al. (2019) is to include in the model (i) the weights, (ii) all the domain indicators (i.e., all relevant covariates of the weighted regression), and (iii) their interactions for valid MI inference in general.

> 19See Figure B.1 for results with the log yield predictions.

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