Table 1.

Empirical type I errors (%) for comparing three methods under different scenarios for Poisson response for the simulation study.

	First scenario (β1 = 0)						Second scenario (β1 = 1)
Sample Size	μ = 0.5			μ = 1			β0 = 0.5				β0 = 1
	Vuong	Naive	New	Vuong	Naive	New	Vuong1	Vuong2	Naive	New	Vuong1	Vuong2	Naive	New
50	0.09	0.05	3.82	0.13	0.60	4.81	0.03	12.84	0.40	4.13	0	26.27	0.50	4.59
100	0.02	0.06	3.95	0.05	0.53	4.64	0.03	13.75	0.40	3.68	0	26.82	0.49	4.94
200	0.05	0.03	4.42	0.05	0.45	4.55	0.01	13.05	0.29	4.06	0	24.64	0.49	4.48
500	0.08	0.06	4.47	0.04	0.49	4.77	0.03	11.14	0.49	4.78	0	21.49	0.73	4.86
1000	0.03	0.03	4.43	0.04	0.54	4.51	0.03	10.02	0.52	4.74	0	17.60	0.65	5.34

Note: In the second scenario, “Vuong1” and “Vuong2” are for the Vuong tests with the alternative zero-inflated Poisson models (3.10) and (3.11), respectively.