. Author manuscript; available in PMC: 2012 Dec 1.

Published in final edited form as: Psychol Methods. 2011 Oct 31;16(4):373–390. doi: 10.1037/a0025813

Table 3.

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

Categories	Small random effect variance (τ₀₀=0.50)			Medium random effect variance (τ₀₀=1.63)			Large random effect variance (τ₀₀ =8.15)
	Population $\sqrt{τ_{00}}$ = 0.71			Population $\sqrt{τ_{00}}$ = 1.28			Population $\sqrt{τ_{00}}$ = 2.85

	Linear – REML	Logistic – PQL	Logistic – ML	Linear – REML	Logistic – PQL	Logistic – ML	Linear – REML	Logistic – PQL	Logistic – ML
2	0.57 (.16)	0.63 (.19)	0.69 (.23)	0.94 (.16)	1.07 (.20)	1.26 (.28)	1.75 (.26)	1.95 (.32)	2.91 (.97)
3	0.63 (.16)	0.66 (.17)	0.68 (.19)	1.07 (.17)	1.16 (.19)	1.25 (.22)	2.10 (.27)	2.27 (.33)	2.84 (.46)
5	0.67 (.16)	0.69 (.15)	0.68 (.16)	1.17 (.17)	1.21 (.18)	1.25 (.19)	2.42 (.27)	2.52 (.32)	2.81 (.39)
7	0.69 (.15)	0.69 (.15)	0.68 (.15)	1.21 (.18)	1.23 (.17)	1.24 (.19)	2.54 (.31)	2.62 (.32)	2.81 (.36)

Notes. Standard deviation of estimates presented in parentheses. REML=Restricted Maximum Likelihood; ML= Maximum Likelihood; PQL= Penalized Quasi-Likelihood.