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. Author manuscript; available in PMC: 2018 Mar 1.
Published in final edited form as: Stat Methods Med Res. 2016 May 16;27(3):812–831. doi: 10.1177/0962280216643347

Table 3.

Results from five simulation studies. Each is based upon 1000 datasets simulated from an ordinal GLMM with five categories (C=5), with thresholds α0 = −∞ and α5 = + ∞ and I= 100 items and J= 10 raters. Random effects ui∼N(0,σu2), and vj∼N(0,σv2).

C = 5 Categories, I= 100 items, J = 10 raters
Parameter Simulation set #1
Simulation set #2
Simulation set #3
Simulation set #4
Simulation set #5
Truth Est. mean Est. S.E. (obs.) Truth Est. mean Est. S.E. (obs.) Truth Est. mean Est. S.E. (obs.) Truth Est. mean Est. S.E. (obs.) Truth Est. mean Est. S.E. (obs.)
σu2
 1   1.008 0.195 (0.202) 5   4.798 0.878 (0.867)   5   5.019 0.971 (1.063) 20 17.465 3.467 (3.324) 10   9.778 1.816 (1.866)
σv2
 5   4.555 2.221 (2.375) 1   0.910 0.423 (0.441) 20 18.654 9.631 (12.617)   5   4.442 2.059 (2.234) 10   9.057 4.243 (4.723)
α1 0 −0.006 0.673 (0.745) 0 −0.010 0.378 (0.405)   0   0.026 1.360 (1.647)   0 −0.046 0.795 (0.855)   0 −0.026 0.984 (1.083)
α2 1   0.998 0.675 (0.748) 1   0.989 0.380 (0.409)   1   1.030 1.362 (1.651)   1   0.941 0.797 (0.857)   1   0.973 0.985 (1.083)
α3 2   2.000 0.678 (0.754) 2   1.988 0.385 (0.410)   2   2.034 1.365 (1.649)   2   1.936 0.801 (0.858)   2   1.973 0.989 (1.088)
α4 3   3.005 0.684 (0.755) 3   2.988 0.394 (0.421)   3   3.036 1.370 (1.654)   3   2.931 0.807 (0.864)   3   2.982 0.994 (1.093)
ρ 0.143   0.171 0.051 (0.063) 0.714   0.714 0.051 (0.05)   0.192   0.236 0.075 (0.094)   0.769   0.766 0.067 (0.069)   0.476   0.514 0.099 (0.111)
var(ρ) 0.002   0.004 0.003   0.003   0.0049   0.0088   0.005   0.005   0.0115   0.0123
κm 0.035   0.043 0.014 (0.017) 0.264   0.267 0.032 (0.038)   0.048   0.062 0.023 (0.029)   0.306   0.312 0.050 (0.059)   0.141   0.162 0.042 (0.050)
var(κm) 0.0002   0.0002 (0.0003) 0.001   0.001 (0.001)   0.0004   0.0006 (0.0008)   0.0029   0.0025 (0.0035)   0.0018   0.0018 (0.0025)
κma 0.091   0.110 0.033 (0.041) 0.506   0.508 0.046 (0.050)   0.123   0.153 0.050 (0.062)   0.559   0.560 0.066 (0.068)   0.316   0.347 0.075 (0.084)
var(κma) 0.001   0.0011 (0.0017) 0.002   0.002 (0.002)   0.002   0.003 (0.004)   0.005   0.004 (0.005)   0.0060   0.006 (0.007)