Table 5.

Mean and Standard Deviation of the Random Intercept Dispersion Estimate $\sqrt{{\widehat{\tau }}_{00}}$ as a Function of the Number of Clusters and Cluster Size, Collapsing Over Number of Categories and Category Distribution.

Clusters/Cluster Size	Small random effect variance (τ00=0.50)			Medium random effect variance (τ00 =1.63)			Large random effect variance (τ00=8.15)
	Population $\sqrt{{\tau }_{00}}$ = 0.71			Population $\sqrt{{\tau }_{00}}$ = 1.28			Population $\sqrt{{\tau }_{00}}$ = 2.85
	Linear – REML	Logistic – PQL	Logistic – ML	Linear – REML	Logistic – PQL	Logistic – ML	Linear – REML	Logistic – PQL	Logistic – ML
25 Clusters
5 Members	0.63 (.33)	0.68 (.33)	0.66 (.35)	1.11 (.34)	1.17 (.34)	1.22 (.42)	2.28 (.57)	2.30 (.54)	2.92 (1.41)
10 Members	0.64 (.21)	0.68 (.22)	0.65 (.23)	1.11 (.25)	1.20 (.26)	1.21 (.28)	2.26 (.50)	2.45 (.49)	2.80 (.62)
20 Members	0.64 (.15)	0.68 (.16)	0.66 (.16)	1.11 (.22)	1.22 (.22)	1.21 (.23)	2.24 (.47)	2.56 (.45)	2.76 (.53)
50 Clusters
5 Members	0.64 (.23)	0.65 (.23)	0.67 (.25)	1.12 (.24)	1.14 (.24)	1.26 (.28)	2.26 (.44)	2.21 (.42)	2.87 (.57)
10 Members	0.65 (.14)	0.67 (.15)	0.68 (.16)	1.11 (.19)	1.18 (.18)	1.25 (.20)	2.45 (.40)	2.40 (.38)	2.83 (.42)
20 Members	0.65 (.11)	0.68 (.11)	0.68 (.11)	1.11 (.17)	1.21 (.15)	1.25 (.16)	2.23 (.39)	2.53 (.34)	2.81 (.36)
100 Clusters
5 Members	0.65 (.15)	0.65 (.16)	0.69 (.17)	1.11 (.18)	1.12 (.17)	1.26 (.19)	2.24 (.38)	2.16 (.37)	2.85 (.37)
10 Members	0.65 (.10)	0.67 (.10)	0.69 (.11)	1.11 (.15)	1.17 (.13)	1.26 (.14)	2.23 (.36)	2.37 (.33)	2.83 (.29)
20 Members	0.65 (.08)	0.68 (.08)	0.70 (.08)	1.11 (.14)	1.21 (.11)	1.26 (.12)	2.23 (.34)	2.52 (.28)	2.83 (.25)
200 Clusters
5 Members	0.65 (.11)	0.65 (.11)	0.70 (.12)	1.11 (.14)	1.12 (.13)	1.27 (.13)	2.23 (.34)	2.14 (.34)	2.84 (.26)
10 Members	0.65 (.08)	0.67 (.07)	0.70 (.08)	1.11 (.13)	1.17 (.10)	1.27 (.10)	2.24 (.33)	2.35 (.30)	2.85 (.20)
20 Members	0.65 (.07)	0.68 (.05)	0.70 (.05)	1.11 (.12)	1.21 (.08)	1.27 (.08)	2.23 (.32)	2.51 (.25)	2.84 (.18)

Notes. See Table 3 notes.