. Author manuscript; available in PMC: 2010 Dec 1.

Published in final edited form as: Psychol Methods. 2009 Dec;14(4):301–322. doi: 10.1037/a0016972

Table 4.

Empirical bias (×1,000) and coverage rate (%) of 95% credible interval of Bayesian estimates of the covariance between α_j and β_j. N₁ and N₂ denote the sample size of the first-level units and second-level units, respectively. Numbers in the parentheses are coverage rates.

	α = β = 0.3			α = β = 0.6

N₁	σ_{α_j}_{β_j} = −0.113	σ_{α_j}_{β_j} = 0	σ_{α_j}_{β_j} = 0.113	σ_{α_j}_{β_j} = −0.113	σ_{α_j}_{β_j} = 0	σ_{α_j}_{β_j} = 0.113
	N₂ = 25
4	−23 (79.5)	2 (88.7)	−23 (79.5)	18 (80.3)	0 (86.9)	−20 (81.1)
8	−9 (90.3)	3 (76.3)	10 (90.9)	−8 (89.5)	−2 (74.6)	7 (88.9)
16	−13 (92.6)	−2 (87.2)	11 (91.7)	−12 (92.7)	1 (89.0)	12 (91.4)
	N₂ = 50
4	2 (87.8)	0 (73.9)	1 (89.9)	−2 (89.6)	−2 (74.9)	4 (89.2)
8	−14 (91.9)	0 (85.4)	12 (92.2)	−12 (91.9)	−1 (88.2)	12 (92.0)
16	−6 (92.5)	0 (92.3)	6 (93.8)	−7 (93.7)	0 (92.9)	7 (92.9)
	N₂ = 100
4	−11 (92.5)	0 (80.7)	12 (91.7)	−11 (92.5)	−3 (80.0)	11 (91.5)
8	−10 (91.5)	−2 (91.9)	9 (91.9)	−10 (93.1)	0 (95.2)	9 (91.1)
16	−3 (94.5)	0 (94.1)	2 (94.7)	−2 (94.7)	0 (94.5)	3 (95.5)