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

Table 4

The mean of Type I error rates and power of MIMIC model for detecting medium uniform-DIF in 10-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)	0.665	0.051	0.740	0.072	0.780	0.052	R: N (0, 1); F: Beta (0.5, 4)	0.671	0.068	0.768	0.061	0.803	0.062
R200/F100		0.777	0.054	0.884	0.074	0.885	0.055		0.777	0.079	0.883	0.066	0.881	0.068
R300/F100		0.827	0.050	0.894	0.054	0.927	0.053		0.817	0.084	0.894	0.062	0.920	0.051
R400/F100		0.833	0.056	0.911	0.054	0.937	0.053		0.832	0.061	0.913	0.073	0.946	0.066
R500/F100		0.842	0.062	0.929	0.043	0.949	0.061		0.839	0.072	0.930	0.071	0.950	0.050
R100/F100	R: N (0, 1); F: Beta (4, 1)	0.710	0.053	0.776	0.065	0.790	0.049	R: N (0, 1); F: Beta (4, 0.5)	0.743	0.058	0.789	0.061	0.829	0.062
R200/F100		0.823	0.049	0.901	0.066	0.902	0.057		0.840	0.065	0.888	0.069	0.917	0.074
R300/F100		0.857	0.056	0.907	0.062	0.938	0.054		0.868	0.065	0.914	0.058	0.937	0.061
R400/F100		0.877	0.061	0.925	0.054	0.949	0.058		0.867	0.081	0.947	0.068	0.952	0.077
R500/F100		0.901	0.060	0.946	0.049	0.956	0.05		0.906	0.056	0.940	0.059	0.966	0.063
R100/F100	R: Beta (1, 4); F: Beta (1, 4)	0.708	0.058	0.756	0.051	0.807	0.058	R: Beta (0.5, 4); F: Beta (0.5, 4)	0.673	0.059	0.780	0.048	0.812	0.062
R200/F100		0.793	0.042	0.870	0.062	0.880	0.052		0.786	0.053	0.862	0.049	0.881	0.053
R300/F100		0.837	0.047	0.929	0.050	0.929	0.054		0.837	0.049	0.891	0.049	0.913	0.057
R400/F100		0.841	0.050	0.911	0.057	0.925	0.044		0.833	0.045	0.921	0.052	0.938	0.055
R500/F100		0.879	0.068	0.934	0.064	0.958	0.059		0.853	0.043	0.919	0.043	0.940	0.048
R100/F100	R: Beta (4, 1); F: Beta (4, 1)	0.701	0.067	0.783	0.051	0.825	0.057	R: Beta (4, 0.5); F: Beta (4, 0.5)	0.703	0.052	0.788	0.053	0.835	0.048
R200/F100		0.806	0.044	0.882	0.056	0.917	0.056		0.824	0.059	0.896	0.061	0.909	0.052
R300/F100		0.868	0.037	0.934	0.053	0.929	0.048		0.879	0.054	0.926	0.053	0.931	0.053
R400/F100		0.847	0.055	0.931	0.046	0.948	0.042		0.879	0.047	0.940	0.053	0.962	0.043
R500/F100		0.889	0.056	0.935	0.065	0.961	0.064		0.886	0.050	0.948	0.064	0.958	0.046
R100/F100	R: Beta (1, 4); F: Beta (4, 1)	0.701	0.060	0.754	0.064	0.813	0.064	R: Beta (0.5, 4); F: Beta (4, 0.5)	0.687	0.086	0.773	0.077	0.815	0.066
R200/F100		0.809	0.076	0.871	0.071	0.893	0.065		0.813	0.127	0.880	0.083	0.893	0.092
R300/F100		0.857	0.075	0.928	0.057	0.932	0.053		0.842	0.121	0.908	0.081	0.924	0.081
R400/F100		0.833	0.081	0.920	0.066	0.940	0.058		0.845	0.109	0.929	0.080	0.946	0.084
R500/F100		0.896	0.094	0.923	0.080	0.954	0.074		0.872	0.113	0.936	0.092	0.959	0.079
R100/F100	R: Beta (4, 1); F: Beta (1, 4)	0.680	0.088	0.739	0.053	0.798	0.054	R: Beta (4, 0.5); F: Beta (0.5, 4)	0.627	0.095	0.707	0.078	0.779	0.063
R200/F100		0.755	0.068	0.849	0.063	0.865	0.06		0.738	0.098	0.816	0.075	0.860	0.073
R300/F100		0.793	0.056	0.910	0.067	0.915	0.061		0.802	0.133	0.871	0.096	0.891	0.082
R400/F100		0.799	0.079	0.903	0.076	0.913	0.055		0.797	0.135	0.883	0.081	0.906	0.086
R500/F100		0.842	0.093	0.917	0.080	0.939	0.075		0.816	0.108	0.890	0.083	0.917	0.072
R100/F100	R: N (0, 1); F: N (0, 1)	0.696	0.052	0.786	0.054	0.817	0.058
R200/F100		0.785	0.055	0.855	0.054	0.900	0.05
R300/F100		0.860	0.054	0.910	0.048	0.926	0.057
R400/F100		0.869	0.050	0.929	0.062	0.954	0.045
R500/F100		0.870	0.052	0.922	0.059	0.971	0.055