Research Article
Random Forests in Count Data Modelling: An Analysis of the Influence of Data Features and Overdispersion on Regression Performance
Table 3
Effect of overdispersion on the RF optimal size of the sample to draw.
| Data types | Variance-to-mean relationship | sample size | N = 50 (%) | N = 250 (%) | N = 1250 (%) | | | | | | | | | | | | | | | | | | | | | | | | |
| Categorical | Linear | 0.55 | 56 | 46 | 56 | 30 | 49 | 31 | 63 | 71 | 59 | 27 | 37 | 39 | 89 | 89 | 74 | 34 | 39 | 43 | 0.632 | 18 | 30 | 18 | 24 | 17 | 24 | 19 | 12 | 26 | 32 | 25 | 27 | 10 | 9 | 22 | 27 | 25 | 25 | 0.7 | 13 | 11 | 14 | 21 | 16 | 23 | 11 | 12 | 6 | 22 | 16 | 21 | 1 | 2 | 4 | 23 | 21 | 16 | 0.8 | 13 | 13 | 12 | 25 | 18 | 22 | 7 | 5 | 9 | 19 | 22 | 13 | 0 | 0 | 0 | 16 | 15 | 16 | Quadratic | 0.55 | 57 | 62 | 57 | 40 | 36 | 37 | 58 | 68 | 62 | 41 | 38 | 37 | 79 | 70 | 86 | 46 | 36 | 43 | 0.632 | 21 | 13 | 21 | 21 | 25 | 30 | 28 | 19 | 23 | 27 | 18 | 25 | 19 | 26 | 10 | 19 | 32 | 26 | 0.7 | 12 | 12 | 10 | 19 | 22 | 13 | 9 | 8 | 12 | 17 | 22 | 20 | 1 | 4 | 0 | 23 | 15 | 17 | 0.8 | 10 | 13 | 12 | 20 | 17 | 20 | 5 | 5 | 3 | 15 | 22 | 18 | 1 | 0 | 4 | 12 | 17 | 14 |
| 25% of predictors are quantitative | Linear | 0.55 | 100 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 100 | 100 | 0 | 100 | 100 | 0 | 100 | 0 | 100 | 0 | 0.632 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 100 | 0 | 0 | 0.7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0.8 | 0 | 100 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | Quadratic | 0.55 | 100 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 100 | 100 | 0 | 100 | 100 | 0 | 0 | 100 | 100 | 100 | 0.632 | 0 | 0 | 0 | 100 | 0 | 0 | 100 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0.7 | 0 | 100 | 0 | 0 | 100 | 100 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 |
| 50% of predictors are quantitative | Linear | 0.55 | 100 | 100 | 100 | 100 | 0 | 100 | 0 | 100 | 100 | 0 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 0 | 0.632 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 100 | 100 | 0 | 100 | 0.7 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 100 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0.8 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | Quadratic | 0.55 | 0 | 100 | 0 | 0 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 100 | 0.632 | 100 | 0 | 100 | 0 | 100 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0.7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0.8 | 0 | 0 | 0 | 100 | 0 | 100 | 0 | 0 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 100 | 0 | 0 |
| 75% of predictors are quantitative | Linear | 0.55 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 100 | 100 | 0 | 100 | 0 | 0 | 0.632 | 100 | 100 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 100 | 0 | 0 | 100 | 0 | 0 | 0 | 0.7 | 0 | 0 | 100 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 100 | 100 | 0.8 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | Quadratic | 0.55 | 0 | 0 | 100 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 100 | 100 | 0 | 100 | 0 | 0 | 100 | 0.632 | 0 | 100 | 0 | 100 | 0 | 100 | 0 | 100 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 100 | 100 | 0 | 0.7 | 100 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0.8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Quantitative | Linear | 0.55 | 100 | 0 | 100 | 100 | 0 | 0 | 100 | 100 | 100 | 100 | 0 | 100 | 0 | 100 | 100 | 0 | 100 | 100 | 0.632 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.7 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0.8 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | Quadratic | 0.55 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 100 | 0 | 100 | 0 | 0 | 100 | 100 | 100 | 0 | 100 | 100 | 0.632 | 0 | 100 | 0 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.7 | 0 | 0 | 0 | 100 | 0 | 100 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.8 | 100 | 0 | 0 | 0 | 100 | 0 | 0 | 0 | 0 | 0 | 100 | 100 | 0 | 0 | 0 | 100 | 0 | 0 |
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