Table 2.

Parameter Recovery for the Linear Higher-Order Mixture Rasch Model With a Sample Size of 2,000.

Test length	20				30
Class	Majority		Minority		Majority		Minority
Criterion	Bias	RMSE	Bias	RMSE	Bias	RMSE	Bias	RMSE
Parameter
Difficulty
Test 1
Mean	0.007	0.088	0.007	0.120	0.004	0.083	0.004	0.101
SD	0.024	0.013	0.016	0.022	0.015	0.011	0.020	0.015
Test 2
Mean	0.007	0.088	0.007	0.113	−0.002	0.080	−0.002	0.103
SD	0.023	0.014	0.022	0.024	0.019	0.014	0.024	0.025
Test 3
Mean	0.006	0.081	0.006	0.117	0.002	0.080	0.002	0.100
SD	0.016	0.013	0.020	0.023	0.013	0.011	0.019	0.015
Test 4
Mean	−0.001	0.086	−0.001	0.115	0.005	0.082	0.005	0.104
SD	0.023	0.015	0.020	0.018	0.015	0.014	0.019	0.015
Test 5
Mean	0.001	0.084	0.001	0.116	0.003	0.082	0.003	0.102
SD	0.016	0.015	0.022	0.023	0.017	0.012	0.016	0.018
Second-order
${\overline{\mathrm{\theta }}}^{(2)}$	—	—	0.001	0.082	—	—	0.009	0.067
${\mathrm{Var}(\mathrm{\theta }}^{(2)})$	—	—	−0.009	0.096	—	—	−0.008	0.082
Loading
β1	0.011	0.037	—	—	0.006	0.025	—	—
β2	0.005	0.029	—	—	0.000	0.032	—	—
β3	−0.001	0.022	—	—	0.003	0.039	—	—
β4	0.002	0.026	—	—	−0.001	0.023	—	—
β5	−0.003	0.034	—	—	0.002	0.026	—	—
Residual
Mean	0.003	0.047	0.001	0.067	−0.004	0.044	0.016	0.058
SD	0.006	0.007	0.015	0.010	0.004	0.007	0.014	0.016

Note. RMSE = root mean square error; Second-order = second-order latent trait; Loading = factor loading; Residual = residual variance; — = not applicable because of model constraints.