When Does Combining Software-Effort Estimates Help? Evidence from Four Public Project Datasets

Azzeddine Ihsine, Sara Ihsine

Combining estimates can reduce individual prediction errors, but an ensemble may also dilute an unusually accurate estimator or repeat errors shared by its members. We study these competing effects on four archival software-effort datasets (Kitchenham: 145 projects, Desharnais: 77, China: 499, Maxwell: 63) with 100 repeated 70/30 training and test partitions per dataset. Three conventional models (parametric regression, analogy, and random forest) are combined with each other and, in Kitchenham, with a recorded human estimate. Out-of-fold calibration errors drive five combination rules: equal weighting, inverse-MSE weighting, a nonnegative simplex combination, signed Bates-Granger weighting, and Bates-Granger with covariance shrinkage. All preprocessing is learned within training folds. Model-error correlations range from 0.54 to 0.97. In Kitchenham, the human estimate dominates: equal weighting raises mean test log-MAE from 0.239 to 0.455, a loss that remains significant under a corrected resampled t-test with Holm adjustment, whereas the simplex rule limits the increase to 0.250. In Desharnais, China, and Maxwell, every rule lowers mean log-MAE (by 1.3 to 8.6%) and BG with…