| Summary: | Mokken (1971) 提出兩個無母數反應試題理論模型，包含單調同質性模型(MHM)和雙重單調同質性模型(DMM)，Grayson (1988) 和Huynh (1994)說明並證明出在單調同質性模型架構之下，受試者二元反應試題的回答總分與受試者的潛在特質具有MLR(monotone likelihood ratio)的性質，因此也具有SOM(stochastic ordering of the manifest variable)及SOL(stochastic ordering of the latent trait)這兩個隨機排序(stochastic ordering)的特性。另外，Mokken (1971) 也提到在Mokken量表下，受試者的試題回答總分與受試者的潛在特質有高度相關。然而這些好的特性都僅只於理論上的說法，實務的應用上並沒有實際的數字可作為使用者的參考依據。本研究將利用模擬實驗的方式，就上述議題作探討。
模擬結果顯示，未加權的時候，使用答題總分來排序受試者的潛在特質或藉由受試者的潛在特質來預估其答題總分之正確率都會隨著鑑別參數的增加而增加，前者正確率約有七成以上，後者正確率則大約有八成以上；受試者的潛在特質與其答題總分的相關係數也隨著鑑別參數增加而增加，大約介於0.50與0.80之間。
=== Mokken (1971) proposed two Nonparametric Item Response Theory Models, the Monotone Homogeneity Model (MHM) and the Double Monotonicity Model (DMM). Under MHM, Grayson (1988) and Huynh (1994) showed that the unweighted total score for dichotomous items has monotone likelihood ratio (MLR) in the latent trait θ, which in turn implies two stochastic ordering (SO) properties, namely SOM (stochastic ordering of the manifest variable) and SOL (stochastic ordering of the latent trait). In addition, Mokken (1971) also mentioned that the total score were highly correlated with the latent trait for subjects. However, these properties are only theoretical arguments, and there are no actual figures that can serve as a guideline for practitioners regarding how good the properties are. We hence try to answer some of the questions through simulation experiments in this study.
Simulation results show that the accuracy rate of using unweighted total score to rank the latent trait of subjects and the accuracy rate of using the latent trait to predict the total score for subjects will increase with the discrimination parameters. The former is about more than 70%, while the latter is about more than 80%. The correlation coefficients between the total score and the latent trait of subjects will also increase with the discrimination parameters, ranging between 0.50 and 0.80.
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