Table 6.

Mean and Standard Deviation of the Random Slope Dispersion Estimate $\sqrt{{\widehat{\tau }}_{11}}$ 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 (τ11=0.08)			Medium random effect variance (τ11=0.25)			Large random effect variance (τ11=1.25)
	Population $\sqrt{{\tau }_{11}}$ = 0.28			Population $\sqrt{{\tau }_{11}}$ = 0.50			Population $\sqrt{{\tau }_{11}}$ = 1.12
	Linear – REML	Logistic – PQL	Logistic – ML	Linear – REML	Logistic – PQL	Logistic – ML	Linear – REML	Logistic – PQL	Logistic – ML
25 Clusters
5 Members	0.26 (.28)	0.34 (.33)	0.37 (.31)	0.37 (.32)	0.44 (.35)	0.51 (.37)	0.82 (.39)	0.80 (.42)	1.12 (.94)
10 Members	0.24 (.20)	0.26 (.23)	0.28 (.20)	0.39 (.22)	0.42 (.25)	0.44 (.24)	0.84 (.24)	0.92 (.30)	1.05 (.36)
20 Members	0.25 (.15)	0.25 (.17)	0.24 (.14)	0.42 (.14)	0.45 (.18)	0.45 (.18)	0.85 (.19)	1.00 (.23)	1.06 (.26)
50 Clusters
5 Members	0.22 (.22)	0.26 (.25)	0.32 (.23)	0.36 (.25)	0.38 (.27)	0.48 (.28)	0.83 (.28)	0.74 (.34)	1.09 (.41)
10 Members	0.24 (.16)	0.24 (.18)	0.27 (.16)	0.40 (.16)	0.41 (.19)	0.45 (.19)	0.86 (.18)	0.91 (.22)	1.10 (.24)
20 Members	0.26 (.11)	0.24 (.13)	0.25 (.12)	0.43 (.10)	0.45 (.12)	0.47 (.13)	0.86 (.15)	1.00 (.16)	1.09 (.17)
100 Clusters
5 Members	0.21 (.18)	0.23 (.20)	0.29 (.19)	0.36 (.20)	0.35 (.22)	0.47 (.23)	0.83 (.21)	0.73 (.29)	1.10 (.28)
10 Members	0.24 (.13)	0.23 (.15)	0.26 (.14)	0.42 (.11)	0.42 (.14)	0.48 (.14)	0.85 (.15)	0.90 (.18)	1.10 (.17)
20 Members	0.27 (.08)	0.25 (.10)	0.26 (.09)	0.43 (.07)	0.46 (.08)	0.49 (.09)	0.86 (.13)	1.00 (.13)	1.11 (.12)
200 Clusters
5 Members	0.21 (.15)	0.21 (.17)	0.28 (.16)	0.37 (.15)	0.35 (.19)	0.47 (.17)	0.84 (.15)	0.73 (.26)	1.11 (.19)
10 Members	0.25 (.10)	0.23 (.12)	0.26 (.11)	0.42 (.08)	0.42 (.11)	0.49 (.10)	0.86 (.13)	0.90 (.15)	1.11 (.12)
20 Members	0.28 (.06)	0.26 (.07)	0.27 (.07)	0.44 (.06)	0.46 (.06)	0.49 (.06)	0.86 (.12)	0.99 (.11)	1.11 (.09)

Notes. See Table 3 notes.