IRT中Logistic模型的c、γ参数对能力估计的改善

C and γ Parameters in Logistic Model Improve the Ability of Estimation within IRT

设计一个理想测验和被试作答情况，在单、双参数模型下进行能力估计，存在第一、二未契合现象；增加c参数后进行能力估计，则能有效纠正第一未契合现象，仍然存在第二未契合现象，同时存在第三未契合现象；增加γ参数后进行能力估计，则能有效纠正第二未契合现象，仍然存在第一未契合现象，同时存在第四未契合现象；同时增加c、γ参数后进行能力估计，则能有效纠正第一、二、三、四未契合现象。最后概述了c、γ参数的测量含义。

In the past years， c parameter was viewed as guessing parameter， and what it means remains unclear for the IRT researchers. The four-parameter logistic model was given little attention， and not applied in the practice. In this thesis the authors examined the meaning of c and γ parameters in logistic model by proposing that c and γ parameters would improve the ability of estimation when the subjects make responses on items of different b value.After designing an ideal test and responses from subjects that can give either right or wrong responses to one extra item with varying degrees of difficulty， we compile a program for estimating the abilities of subjects with method of Maximum Likelihood Estimation (MLE). It analyzes the influences of c parameter and γ parameter on agreement of the abilities and various responses drawn from the subjects.(1) When estimating the abilities of the subjects within one-parameter or two-parameter logistic model， two kinds of disagreement existed. (2) Estimating the abilities of the subjects after introducing c parameter on the basis of a two-parameter model， the first disagreement could be rectified. However， the second disagreement remained and a third disagreement appeared. (3) Estimating the abilities of the subjects again after introducing γ parameter， it was discovered that the second disagreement was rectified， but the first disagreement still existed and a fourth disagreement appeared. (4) Forming four-parameter Logistic model by introducing c parameter and γ parameter simultaneously and estimating the abilities one more time， the model rectified all four disagreements，.In future research， the present findings need to be replicated in other conditions: (1) when the subjects make responses to two or more items of different b value; (2) on the assumption that the subject’s ability distribution has been known， estimating the abilities of the subjects with the other two methods--Maximum A Posterior Estimation (MAPE) and Expected A Posterior Estimation (EAPE).To summarize， C parameter is the probability of guessing that all the subjects make right response to the item that item difficulty is larger than the ability of subjects， and adding c parameter can improve the ability estimation in such case. γ parameter is the probability of mistakes that all subjects make wrong response to the item which difficulty is less than the ability of subjects， and adding γ parameter can improve the ability estimation in that case. And so， the four-parameter logistic model is advocated.