擴展試題反應模型於分析評等量尺關係

Abstract

本研究發展了一種用於分析對兩兩關係進行評級（rating relational data）的試題反應模型（item response theory model）。本研究假設此種資料是發送者（sender）使用小的量尺數目對與接受者的關係（receiver）進行評級。因此，我們將此網路資料定義為是由發送者和接收者建構的有向網路（directed networks）。該模型是基於評等量尺模型（rating scale model）並結合潛在空間模型（latent space model）構建的。本研究所提出之模型，將發送者和接收者投射在一維的潛在量尺上討論兩兩間的互惠關係（reciprocity），並同時在低維度量空間上比較個體間的同質性（homophily）。該模型是在貝氏框架（Bayesian framework）下建立的，並使用馬可夫鏈蒙特卡羅方法（Markov chain Monte Carlo methods）來逼近全條件後驗分佈（full conditional posterior distributions）。模擬研究顯示模型參數得到了滿意的估計。該模型的有效性已透過實徵研究得到證明，並且還表現出令人滿意的恢復完整網路（complete networks）的能力。

This study developed a new item response theory model for rating relational data. The relational data is assumed to be rated using a rating scale with a small ordinal number. Thus, the network data is supposed to be directed networks constructed by senders and receivers. The model is built based on the rating scale model and incorporated with a latent space model. In the proposed model, senders and receivers are supposed to be compared on a one-dimensional scale for dyadic relationships and be compared on a low-dimensional metric space for homophily. The model is built under a Bayesian framework, and Markov chain Monte Carlo methods are used to approximate the full conditional posterior distributions. The simulation study demonstrates that the model parameters are satisfactorily recovered. The model's applicability has been proven by implementing it with empirical data, and it also exhibits a satisfactory ability to recover completed networks.