Table 1.

Root (integrated) mean square errors for eigenvalues and eigenfunctions in simulations. Simulation settings vary according to sample size (n = 100, 200, 300) and the number of grid points per function (N = 3, 6, 9, 12). In simulations, the first four principal components (PC) at both levels were compared to their underlying true counterparts. Root mean square errors and root integrated mean square errors are used to measure estimation accuracy for eigenvalues and eigenfunctions, respectively.

n	N	Eigenvalues				Eigenfunctions
		PC 1	PC 2	PC 3	PC 4	PC 1	PC 2	PC 3	PC 4
Level 1
100	3	0.25	0.39	0.69	1.16	0.45	0.66	1.03	1.07
100	6	0.29	0.36	0.76	1.26	0.56	0.81	1.00	1.21
100	9	0.19	0.25	0.35	0.48	0.38	0.54	0.83	0.98
100	12	0.21	0.26	0.36	0.54	0.42	0.66	0.85	1.08
200	3	0.18	0.22	0.26	0.36	0.34	0.48	0.73	0.92
200	6	0.19	0.23	0.30	0.41	0.35	0.56	0.76	0.97
300	3	0.17	0.20	0.23	0.31	0.32	0.46	0.66	0.87
Level 2
100	3	0.14	0.18	0.28	0.36	0.25	0.37	0.67	0.90
100	6	0.15	0.21	0.30	0.42	0.31	0.51	0.71	0.95
100	9	0.15	0.23	0.45	0.64	0.27	0.39	0.81	0.98
100	12	0.17	0.25	0.37	0.64	0.36	0.62	0.83	1.06
200	3	0.12	0.16	0.39	0.50	0.21	0.30	0.67	0.90
200	6	0.14	0.22	0.32	0.51	0.30	0.53	0.74	0.97
300	3	0.09	0.10	0.16	0.20	0.15	0.21	0.33	0.51