Table II.

Simulation results for the probit generalized linear mixed model and model-based kappa statistic κ_m based upon 100 data sets for I = 50 and J = 50 using two different sets of parameter values $\mathit{\theta }=(\eta ,\beta ,{\sigma }_u^2,{\sigma }_v^2{\sigma }_{v_1}^1,{\rho }_v)$.

Parameter	True value	Model (a)	Model (b)	Model (c)
(ii) η =3, ${\sigma }_{u_0}^2={\sigma }_{v_0}^2={\sigma }_{v_1}^2=1$
η	3	2.95 (0.25)	3.05 (0.41)	3.02 (0.41)
β	0.5	—	0.51 (0.40)	0.42 (0.08)
${\sigma }_u^2$	1	1.00 (0.37)	1.05 (0.30)	0.76 (0.30)
${\sigma }_v^2$	1	1.09 (0.38)	1.14 (0.36)	1.3 (0.52)
${\sigma }_{v_1}^2$	1	—	—	1.25 (0.94)
ρv	0.25	—	—	−0.004 (0.002)
κ		0.09 (0.04)
κm		0.21 (0.05)
(ii) η = 3, ${\sigma }_{u_0}^2={\sigma }_{v_0}^2={\sigma }_{v_1}^2=5$
η	3	2.93 (0.33)	2.87 (0.49)	2.71 (0.29)
β	0.5	—	0.45 (0.56)	0.54 (0.31)
${\sigma }_u^2$	5	5.00 (1.12)	4.44 (1.04)	3.99 (0.56)
${\sigma }_v^2$	5	5.39 (1.51)	4.34 (0.51)	4.44 (1.59)
${\sigma }_{v_1}^2$	5	—	—	5.21 (3.25)
ρv	0.25	—	—	0.003 (0.01)
κ		0.24 (0.06)
κm		0.29 (0.05)

The three models fitted are: (a) Φ⁻¹(p_ij) = η+u_i+v_j, (b) Φ⁻¹(p_ij) = η+βx_j+u_i+v_j and (c) Φ⁻¹(p_ij) = η+βx_j+u_i+v_j+z₂v_1j; x_i ~ Bin(1,0.5), z₂ ~ Bin(1,0.5). Cohen’s kappa = κ and model-based kappa = κ_m. Mean parameter estimates are presented with associated standard errors in parentheses.