_GLOBAL FOOD INSECURITY OUTLOOK_ _21_ the reductions in the predicted prevalence rates are compared. First, to understand the average importance of the different covariates in the model, table 3 summarizes nonlinear and linear variable importance in the final Cubist model.

There is a strong difference between linear (t-statistics of univariate linear regressions) and nonlinear (percentage of times variable is used in Cubist’s base learners) importance. The discrepancy suggests that the model reacts differently to changes in inputs depending on the value ranges and thus by region. Regardless, the high importance of unchanging factors (historical child mortality and country size) and relatively stable variables (the land cover shares), suggest that the Cubist model first partitions based on these variables and then uses relatively simple linear models that use different selections of the remaining variables as local predictors. Counterfactual results are therefore likely to vary substantially across regions.

Table 3—Variable Importance Results.

||Cubist importance|Linear importance|
|---|---|---|
|Historical child mortality (1995-2015 average rate)|78.30|25.00|
|Forest land cover (% of land)|58.45|2.04|
|Agricultural land cover (% of land cover)|54.30|2.35|
|Country size (square kilometer)|49.60|3.65|
|GDP per capita, ppp adjusted|47.60|18.52|
|Agriculture, forestry, and fshing, value added (% of GDP)|44.65|11.05|
|Food imports (% of merchandise imports)|42.10|4.48|
|The 3-year average population growth rate|38.60|16.34|
|Poverty rate at US$1.90|36.65|21.78|
|The 3-year average real GDP growth rate|33.70|1.11|
|2006-’07 to 2008-’12 CPI infation rate change|30.35|6.17|
|Fuel imports (% of merchandise imports)|24.30|0.55|
|The 3-year average CPI infation rate|17.25|1.38|

_Note:_ Linear (t-statistics in single-predictor linear model) and nonlinear (percentage of times variable is used in base learners) variable importance. Rows are ordered by nonlinear importance, as this reflects the role that the variables play in the final model. Both metrics do not truly represent the incremental predictive impact of the variables in a nonlinear context, but they are nonetheless easily interpreted. At each split of the tree, Cubist saves a linear model (after feature selection) that is allowed to have terms for each variable used in the current split or any split above it. Quinlan (1992) discusses a smoothing algorithm where each model prediction is a linear combination of the parent and child model along the tree. As such, the final prediction is a function of all the linear models from the initial node to the terminal node. The first column gives the percentage of times where each variable was used in a condition and/or a linear model. These percentages reflect all the models involved in prediction (as opposed to just the frequency om terminal models). The variable importance used here is thus a linear combination of the usage in the rule conditions and the model. The second column runs a linear regression with the prevalence rates as dependent variable and the row variable as predictor and extracts the linear t-statistic. This shows also that those variables that are linearly important may not necessarily also be key predictors in the nonlinear model vice versa. _Source:_ Results have been estimated by the author for this paper.

The analysis considers five scenarios, each time generated by modifying the 2025 input data and comparing the reduced prevalence rates predicted under