Table 1.

(a) – (b). Results from six simulation studies in each table for the proposed measure of agreement ${\kappa }_m$ and its standard error $se({\widehat{\kappa }}_m)$. Each simulation study is based upon 1000 simulated datasets with C = 5 categories. Two sample sizes are examined (I = 100, J = 10) and (I = 250, J = 100) and random effect parameters in (a) ${\sigma }_{u_0}^2=1,{\sigma }_{v_0}^2=5,{\rho }_{v0v1}=0$and in (b) ${\sigma }_{u_0}^2=5,{\sigma }_{v_0}^2=1,{\rho }_{v0v1}=0.$

(a). Number of Categories C = 5; True parameters ( ${\sigma }_{u_0}^2=1,{\sigma }_{v_0}^2=5,{\rho }_{u0u1}={\rho }_{v0v1}=0$)
Model	True ${\kappa }_m$	I = 100 J = 10	I = 250 J = 100
		Mean ${\widehat{\kappa }}_m$ (S.E.)	Mean ${\widehat{\kappa }}_m$ (S.E.)
Overall	0.035	0.036 (0.007)	0.036 (0.005)
Model (a)
xj = 0	0.035	0.037 (0.007)	0.035 (0.004)
xj = 1	0.032	0.034 (0.006)	0.032 (0.004)
xj = 0, xj′ = 1	0.033	0.036 (0.006)	0.032 (0.004)
Model (b)
xi = 0	0.035	0.035 (0.004)	0.035 (0.004)
xi = 1	0.050	0.051 (0.006)	0.050 (0.006)
Model (c)
xi = 0, xj = 0	0.035	0.037 (0.006)	0.035 (0.004)
xi = 0, xj = 1	0.032	0.034 (0.006)	0.032 (0.004)
xi = 1, xj = 0	0.050	0.052 (0.009)	0.050 (0.006)
xi = 1, xj = 1	0.046	0.049 (0.008)	0.046 (0.006)

(b). Number of Categories C = 5; True parameters ( ${\sigma }_{u_0}^2=5,{\sigma }_{v_0}^2=1,{\rho }_{u0u1}={\rho }_{v0v1}=0$)
Model	True ${\kappa }_m$	I = 100 J = 10	I = 250 J = 100
		Mean ${\widehat{\kappa }}_m$ (S.E.)	Mean ${\widehat{\kappa }}_m$ (S.E.)
Overall	0.264	0.262 (0.022)	0.262 (0.015)
Model (a)
xj = 0	0.264	0.261 (0.026)	0.263 (0.018)
xj = 1	0.233	0.232 (0.027)	0.233 (0.018)
xj = 0, xj′ = 1	0.248	0.260 (0.027)	0.262 (0.017)
Model (b)
xi = 0	0.264	0.261 (0.017)	0.261 (0.017)
xi = 1	0.277	0.275 (0.017)	0.275 (0.017)
Model (c)
xi = 0, xj = 0	0.264	0.263 (0.026)	0.263 (0.017)
xi = 0, xj = 1	0.233	0.234 (0.026)	0.233 (0.017)
xi = 1, xj = 0	0.277	0.276 (0.026)	0.277 (0.017)
xi = 1, xj = 1	0.246	0.247 (0.026)	0.247 (0.017)