The Fit Of C And γ Parameter Within Logistic Model

After designing an ideal test and a model of ideal respondence from some subjects, the thesis means to compile a program for estimating the abilities of the subjects by the use of Maximum Likelihood Estimation (MLE). It tries to analyze the influences of c parameter and y parameter on the fit of various respondences from the subjects from the perspective of ability estimation. (1) First make the subjects give either right or wrong responses to the same question with different b value. When estimating the abilities of the subjects with the use of one-parameter or two-parameter Logistic model, it is found that there exists two kinds of unfits. (2) Estimate the abilities of the subjects after introducing c parameter on the basis of the two-parameter model. The first unfit can be rectified. However, the second unfit still exists and the third unfit appears. (3) Then estimate again after introducing y parameter. It is discovered that the second unfit is rectified, but the first unfit still exists and the fourth unfit appears. (4) Form Logistic four-parameter model by introducing c parameter and y parameter at the same time and estimate one more time. This model makes all kinds of unfits, including the first, second, third and fourth unfits, rectified. (5) Finally, on the assumption that the subject ability distribution is known, estimate the abilities of the subjects with the other two methods, that is, Maximum A Posterior Estimation (MAPE) and Expected A Posterior Estimation (EAPE). We can come to the conclusion that the same results can be gained when estimating the abilities with the use of the method of MLE.