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