Table 5: The mean of Type I error rates and power of MIMIC model for detecting severe uniform-DIF in 10-item scale.

Distributions for θ3 categories5 categories7 categoriesDistributions for θ3 categories5 categories7 categories
PowerAlphaPowerAlphaPowerAlphaPowerAlphaPowerAlphaPowerAlpha

R100/F100R: N (0, 1)
F: Beta (1, 4)
0.9750.0510.9980.0711.0000.051R: N (0, 1)
F: Beta (0.5, 4)
0.9690.0660.9970.0610.9990.060
R200/F1000.9910.0541.0000.0751.0000.0550.9860.0790.9980.0651.0000.069
R300/F1000.9920.0520.9990.0541.0000.0530.9920.0850.9990.0621.0000.051
R400/F1000.9970.0561.0000.0540.9990.0530.9900.0611.0000.0731.0000.065
R500/F1000.9930.0621.0000.0431.0000.0610.9900.0711.0000.0711.0000.050

R100/F100R: N (0, 1)
F: Beta (4, 1)
0.9890.0530.9980.0640.9990.049R: N (0, 1)
F: Beta (4, 0.5)
0.9970.0571.0000.0620.9990.062
R200/F1000.9980.0501.0000.0651.0000.0571.0000.0651.0000.0691.0000.074
R300/F1001.0000.0561.0000.0621.0000.0541.0000.0651.0000.0571.0000.061
R400/F1000.9990.0621.0000.0541.0000.0561.0000.0801.0000.0681.0000.077
R500/F1001.0000.0611.0000.0491.0000.0501.0000.0561.0000.0601.0000.063

R100/F100R: Beta (1, 4)
F: Beta (1, 4)
0.9910.0580.9970.0510.9980.059R: Beta (0.5, 4)
F: Beta (0.5, 4)
0.9770.0590.9950.0480.9970.061
R200/F1000.9890.0440.9990.0621.0000.0510.9910.0531.0000.0490.9990.053
R300/F1000.9980.0481.0000.0510.9990.0540.9940.0501.0000.0490.9990.057
R400/F1000.9940.0501.0000.0571.0000.0450.9910.0441.0000.0521.0000.055
R500/F1000.9980.0681.0000.0641.0000.0590.9960.0430.9990.0431.0000.048

R100/F100R: Beta (4, 1)
F: Beta (4, 1)
0.9920.0670.9980.0491.0000.057R: Beta (4, 0.5)
F: Beta (4, 0.5)
0.9980.0531.0000.0541.0000.049
R200/F1001.0000.0431.0000.0561.0000.0560.9990.0571.0000.0611.0000.051
R300/F1000.9980.0371.0000.0531.0000.0480.9980.0541.0000.0531.0000.053
R400/F1000.9970.0541.0000.0461.0000.0420.9970.0461.0000.0531.0000.043
R500/F1001.0000.0561.0000.0651.0000.0640.9980.0500.9990.0631.0000.046

R100/F100R: Beta (1, 4)
F: Beta (4, 1)
0.9970.0590.9960.0631.0000.065R: Beta (0.5, 4)
F: Beta (4, 0.5)
0.9960.0861.0000.0781.0000.066
R200/F1001.0000.0781.0000.0701.0000.0650.9990.1271.0000.0831.0000.092
R300/F1001.0000.0761.0000.0561.0000.0541.0000.1211.0000.0811.0000.081
R400/F1000.9990.0811.0000.0661.0000.0591.0000.1101.0000.0801.0000.084
R500/F1001.0000.0941.0000.0791.0000.0741.0000.1141.0000.0921.0000.079

R100/F100R: Beta (4, 1)
F: Beta (1, 4)
0.9780.0870.9940.0520.9990.056R: Beta (4, 0.5)
F: Beta (0.5, 4)
0.9550.0940.9890.0800.9950.063
R200/F1000.9790.0660.9970.0641.0000.0600.9730.0990.9970.0760.9990.072
R300/F1000.9880.0550.9990.0681.0000.0610.9770.1320.9970.0970.9980.082
R400/F1000.9840.0800.9980.0751.0000.0550.9720.1350.9990.0801.0000.085
R500/F1000.9900.0930.9980.0791.0000.0750.9840.1080.9990.0831.0000.072

R100/F100R: N (0, 1)
F: N (0, 1)
0.9930.0520.9980.0561.0000.059
R200/F1000.9960.0560.9990.0541.0000.050
R300/F1000.9980.0551.0000.0481.0000.057
R400/F1000.9970.0491.0000.0611.0000.045
R500/F1000.9960.0521.0000.0591.0000.056