Table 4.

Parameter Recovery for the GPC-ML-HIRT Model With a Sample Size of 565.

Parameter	True	Bias	RMSE	ARB	Ratio	Skewness
Location
M	−0.875	0.003	0.125	0.068	1.131	−0.241
SD	1.114	0.040	0.044	0.200	0.144	0.347
Maximum	1.846	0.093	0.246	1.495	1.639	0.675
Minimum	−2.834	−0.087	0.051	0.000	0.924	−1.066
Slope
M	0.970	−0.031	0.083	0.031	1.054	0.341
SD	0.330	0.025	0.032	0.016	0.159	0.422
Maximum	1.816	−0.001	0.173	0.066	1.477	1.026
Minimum	0.412	−0.101	0.033	0.001	0.788	−0.273
Residual variance at Level 1
M	0.662	0.051	0.130	0.082	1.069	0.378
SD	0.253	0.022	0.041	0.038	0.161	0.340
Maximum	1.310	0.087	0.226	0.151	1.328	0.907
Minimum	0.417	0.024	0.072	0.035	0.850	−0.117
Residual variance at Level 2
${\mathrm{\psi }}_1$	0.361	0.030	0.118	0.082	0.880	−0.588
${\mathrm{\psi }}_2$	0.241	0.030	0.062	0.124	1.203	−0.053
${\mathrm{\psi }}_3$	0.093	0.023	0.064	0.242	1.169	1.023
Residual variance at Level 3
Intercept (β0)	0.407	0.052	0.119	0.127	0.868	0.278
Slope (β1)	0.060	0.006	0.026	0.107	1.204	1.009
Covariance	0.014	0.001	0.040	0.071	0.992	−0.724
Regression weight at Level 3
Intercept of β0	0	NA	NA	NA	NA	NA
Slope of β0	0.112	0.013	0.051	0.113	0.886	−0.164
Intercept of β1	−0.148	0.008	0.026	0.052	1.081	0.001
Slope of β1	0.010	−0.006	0.030	0.560	0.889	−0.229
Factor loading
λ1	0.807	−0.011	0.072	0.014	1.086	0.409
λ2	1.123	−0.037	0.103	0.033	1.006	0.305
λ3	1	NA	NA	NA	NA	NA

Note. The number of estimated location parameters and estimated slope parameters and the estimated Level 1 residual variances are 18, 15, and 9, respectively. GPC-ML-HIRT = generalized partial credit–multilevel higher order item response theory; True = true values; RMSE = root mean square error; ARB = absolute value of relative bias; NA = not applicable because of model constraints.