The Effect of Small Sample Size on Measurement Equivalence of Psychometric Questionnaires in MIMIC Model: A Simulation Study

Table 2

The mean of Type I error rates and power of MIMIC model for detecting medium uniform-DIF in 5-item scale.

	Distributions for θ	3 categories		5 categories		7 categories		Distributions for θ	3 categories		5 categories		7 categories
		Power	Alpha	Power	Alpha	Power	Alpha		Power	Alpha	Power	Alpha	Power	Alpha
R100/F100	R: N (0, 1); F: Beta (1, 4)	0.637	0.086	0.688	0.065	0.755	0.057	R: N (0, 1); F: Beta (0.5, 4)	0.615	0.061	0.711	0.057	0.719	0.064
R200/F100		0.701	0.051	0.800	0.061	0.837	0.041		0.699	0.085	0.812	0.076	0.853	0.064
R300/F100		0.750	0.057	0.857	0.052	0.861	0.055		0.747	0.080	0.837	0.064	0.876	0.070
R400/F100		0.794	0.062	0.866	0.047	0.886	0.046		0.786	0.069	0.855	0.056	0.890	0.060
R500/F100		0.784	0.065	0.889	0.056	0.917	0.057		0.789	0.075	0.886	0.069	0.901	0.041
R100/F100	R: N (0, 1); F: Beta (4, 1)	0.638	0.058	0.698	0.059	0.759	0.060	R: N (0, 1); F: Beta (4, 0.5)	0.658	0.063	0.744	0.061	0.790	0.058
R200/F100		0.748	0.059	0.845	0.064	0.874	0.055		0.779	0.075	0.833	0.074	0.873	0.072
R300/F100		0.809	0.063	0.884	0.060	0.887	0.064		0.801	0.057	0.874	0.060	0.905	0.058
R400/F100		0.831	0.044	0.871	0.047	0.916	0.058		0.808	0.069	0.894	0.059	0.911	0.072
R500/F100		0.819	0.053	0.910	0.060	0.922	0.040		0.846	0.064	0.910	0.059	0.926	0.056
R100/F100	R: Beta (1, 4); F: Beta (1, 4)	0.616	0.053	0.725	0.050	0.710	0.057	R: Beta (0.5, 4); F: Beta (0.5, 4)	0.612	0.045	0.690	0.063	0.723	0.067
R200/F100		0.729	0.047	0.820	0.056	0.866	0.069		0.738	0.050	0.825	0.056	0.832	0.054
R300/F100		0.752	0.046	0.858	0.046	0.860	0.048		0.757	0.046	0.852	0.057	0.876	0.046
R400/F100		0.775	0.057	0.875	0.050	0.877	0.051		0.775	0.051	0.862	0.053	0.882	0.039
R500/F100		0.815	0.050	0.883	0.046	0.899	0.035		0.785	0.044	0.878	0.050	0.895	0.042
R100/F100	R: Beta (4, 1); F: Beta (4, 1)	0.639	0.049	0.731	0.061	0.750	0.057	R: Beta (4, 0.5); F: Beta (4, 0.5)	0.663	0.044	0.743	0.044	0.772	0.062
R200/F100		0.761	0.053	0.842	0.057	0.870	0.066		0.754	0.054	0.865	0.063	0.848	0.041
R300/F100		0.775	0.053	0.893	0.050	0.886	0.046		0.811	0.057	0.902	0.058	0.905	0.057
R400/F100		0.802	0.048	0.888	0.055	0.907	0.050		0.805	0.057	0.907	0.046	0.923	0.039
R500/F100		0.833	0.051	0.895	0.059	0.938	0.045		0.845	0.046	0.908	0.053	0.933	0.047
R100/F100	R:Beta (1, 4); F: Beta (4, 1)	0.608	0.073	0.723	0.054	0.739	0.069	R: Beta (0.5, 4); F: Beta (4, 0.5)	0.650	0.089	0.709	0.070	0.735	0.080
R200/F100		0.748	0.069	0.835	0.060	0.869	0.070		0.738	0.115	0.848	0.079	0.836	0.062
R300/F100		0.767	0.071	0.856	0.072	0.871	0.058		0.779	0.120	0.868	0.084	0.900	0.074
R400/F100		0.778	0.083	0.875	0.079	0.897	0.075		0.784	0.114	0.866	0.084	0.902	0.058
R500/F100		0.836	0.077	0.877	0.074	0.920	0.055		0.809	0.101	0.878	0.092	0.909	0.084
R100/F100	R: Beta (4, 1); F: Beta (1, 4)	0.582	0.054	0.685	0.073	0.711	0.071	R: Beta (4, 0.5); F: Beta (0.5, 4)	0.587	0.078	0.654	0.080	0.699	0.080
R200/F100		0.708	0.085	0.803	0.074	0.839	0.074		0.685	0.100	0.769	0.084	0.803	0.062
R300/F100		0.724	0.075	0.845	0.062	0.868	0.055		0.716	0.103	0.819	0.106	0.853	0.070
R400/F100		0.754	0.091	0.858	0.062	0.881	0.050		0.728	0.119	0.854	0.082	0.857	0.070
R500/F100		0.763	0.087	0.872	0.073	0.902	0.050		0.744	0.131	0.849	0.096	0.885	0.069
R100/F100	R: N (0, 1); F: N (0, 1)	0.609	0.058	0.708	0.055	0.770	0.066
R200/F100		0.705	0.052	0.828	0.049	0.855	0.053
R300/F100		0.785	0.060	0.852	0.057	0.896	0.048
R400/F100		0.830	0.045	0.878	0.067	0.895	0.043
R500/F100		0.803	0.060	0.881	0.062	0.900	0.046