Testing the Rasch model with the conditional likelihood ratio test: sample size requirements and bootstrap algorithms

Alexandrowicz, Rainer W.; Draxler, Clemens

doi:10.1186/s40488-016-0039-y

Journal of Statistical Distributions and Applications

Table 6 Descriptive statistics for the normal marginals case under the null hypothesis

From: Testing the Rasch model with the conditional likelihood ratio test: sample size requirements and bootstrap algorithms

	mean	%	var	%	cv	%	skew	%	kurt	%	q50	%	q90	%	q95	%	q99	%
limiting: df=4	4.00		8.00		0.71		1.41		3.00		3.36		7.78		9.49		13.28
k=5/n=100	4.11	2.7	8.46	5.8	0.71	0.1	1.42	0.7	3.04	1.2	3.45	2.8	7.98	2.6	9.79	3.2	13.66	2.9
k=5/n=250	4.04	1.0	8.19	2.4	0.71	0.2	1.43	1.4	3.14	4.7	3.39	1.0	7.86	1.0	9.60	1.2	13.43	1.2
k=5/n=500	4.02	0.6	8.09	1.2	0.71	0.0	1.42	0.3	3.04	1.2	3.37	0.4	7.82	0.5	9.53	0.4	13.34	0.5
k=5/n=750	4.01	0.3	8.04	0.5	0.71	−0.1	1.41	−0.2	2.98	−0.6	3.37	0.4	7.80	0.3	9.50	0.1	13.35	0.6
k=5/n=1000	4.02	0.4	8.05	0.6	0.71	−0.1	1.41	−0.6	2.93	−2.2	3.37	0.4	7.80	0.3	9.51	0.2	13.30	0.2
k=5/n=2500	4.00	0.1	8.03	0.4	0.71	0.1	1.44	1.8	3.16	5.2	3.35	−0.2	7.79	0.1	9.48	−0.1	13.33	0.4
k=5/n=5000	4.03	0.6	8.12	1.5	0.71	0.1	1.41	−0.2	2.98	−0.8	3.39	1.0	7.83	0.6	9.54	0.6	13.30	0.2
avg. (df=4)	4.03	0.8	8.14	1.8	0.71	0.0	1.42	0.5	3.04	1.2	3.38	0.8	7.84	0.8	9.56	0.8	13.39	0.9
limiting: df=9	9.00		18.00		0.47		0.94		1.33		8.34		14.68		16.92		21.67
k=10/n=100	9.20	2.2	18.86	4.8	0.47	0.1	0.95	0.3	1.32	−0.6	8.52	2.1	15.02	2.3	17.30	2.3	22.15	2.2
k=10/n=250	9.05	0.6	18.12	0.7	0.47	−0.2	0.92	−2.3	1.25	−5.9	8.41	0.8	14.77	0.6	16.98	0.4	21.64	−0.1
k=10/n=500	9.06	0.7	18.25	1.4	0.47	0.0	0.95	0.5	1.32	−1.2	8.38	0.4	14.78	0.7	17.01	0.5	21.86	0.9
k=10/n=750	9.02	0.3	18.16	0.9	0.47	0.2	0.95	0.5	1.42	6.8	8.37	0.3	14.72	0.2	16.95	0.2	21.67	0.0
k=10/n=1000	8.99	−0.1	17.86	−0.8	0.47	−0.3	0.94	−0.3	1.32	−1.2	8.33	−0.2	14.68	−0.0	16.88	−0.2	21.57	−0.4
k=10/n=2500	9.01	0.2	18.05	0.3	0.47	−0.0	0.95	0.8	1.39	4.4	8.38	0.4	14.68	−0.0	16.92	0.0	21.70	0.2
k=10/n=5000	9.01	0.1	18.03	0.2	0.47	0.0	0.95	0.9	1.37	3.0	8.34	−0.0	14.66	−0.2	16.96	0.2	21.71	0.2
avg. (df=9)	9.05	0.6	18.19	1.1	0.47	−0.0	0.94	0.1	1.34	0.8	8.39	0.5	14.76	0.5	17.00	0.5	21.76	0.4
limiting: df=14	14.00		28.00		0.38		0.76		0.86		13.34		21.06		23.68		29.14
k=15/n=100	14.32	2.3	29.30	4.7	0.38	0.0	0.76	0.2	0.87	1.4	13.65	2.3	21.53	2.2	24.20	2.2	29.88	2.5
k=15/n=250	14.09	0.7	28.27	1.0	0.38	−0.2	0.76	0.6	0.90	4.8	13.45	0.8	21.20	0.6	23.82	0.6	29.22	0.3
k=15/n=500	14.05	0.4	28.33	1.2	0.38	0.2	0.75	−1.1	0.82	−4.4	13.40	0.5	21.19	0.6	23.80	0.5	29.16	0.1
k=15/n=750	14.00	−0.0	27.85	−0.5	0.38	−0.2	0.73	−3.9	0.72	−15.8	13.35	0.1	21.09	0.1	23.65	−0.1	28.88	−0.9
k=15/n=1000	14.07	0.5	28.40	1.4	0.38	0.2	0.77	2.1	0.91	6.3	13.42	0.6	21.16	0.5	23.84	0.7	29.50	1.2
k=15/n=2500	14.04	0.3	28.30	1.1	0.38	0.3	0.77	2.5	0.99	15.4	13.39	0.4	21.08	0.1	23.77	0.4	29.37	0.8
k=15/n=5000	14.02	0.1	28.10	0.4	0.38	0.0	0.75	−0.6	0.83	−3.3	13.37	0.2	21.07	0.0	23.73	0.2	29.20	0.2
avg. (df=14)	14.08	0.6	28.36	1.3	0.38	0.0	0.76	−0.0	0.86	0.6	13.43	0.7	21.19	0.6	23.83	0.6	29.32	0.6

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