Table 2. Simulation results of the null distribution of LRTS.

Sample size	Proportions	Empirical type I error rate*					KS-Test P-value
		0.975 Level	0.10 Level	0.05 Level	0.025 Level	0.01 Level
200	(0.25, 0.25, 0.25, 0.25)	0.979	0.103	0.045	0.015	0.007	0.81
500	(0.25, 0.25, 0.25, 0.25)	0.971	0.097	0.052	0.021	0.013	0.79
200	(0.1, 0.2, 0.3, 0.4)	0.977	0.106	0.046	0.020	0.005	0.34
500	(0.1, 0.2, 0.3, 0.4)	0.982	0.109	0.060	0.028	0.011	0.41

Based on 1000 replications for each settings.