Table 4.

Mean and Standard Deviation of the Random Slope Dispersion Estimate $\sqrt{{\widehat{\tau }}_{11}}$ as a Function of the Number of Categories, Collapsing Over Number of Clusters, Cluster Size and Category Distribution

Categories	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
2	0.23 (.16)	0.21 (.20)	0.31 (.23)	0.35 (.17)	0.32 (.22)	0.49 (.27)	0.68 (.19)	0.64 (.30)	1.14 (.63)
3	0.23 (.16)	0.24 (.19)	0.28 (.18)	0.38 (.17)	0.39 (.19)	0.47 (.20)	0.79 (.18)	0.83 (.25)	1.09 (.30)
5	0.25 (.16)	0.26 (.18)	0.27 (.16)	0.42 (.17)	0.45 (.18)	0.47 (.17)	0.91 (.18)	.97 (.20)	1.08 (.24)
7	0.25 (.16)	0.27 (.18)	0.27 (.15)	0.44 (.17)	0.48 (.17)	0.47 (.17)	0.95 (.18)	1.02 (.19)	1.08 (.21)

Notes. See Table 3 notes.