英文詞彙測驗試題反應模型之建構與檢定

Abstract

本研究旨在針對英文詞彙測驗考慮其題組架構，提出一套能夠解決其題目之間存在相依性問題的模型。目前常用於分析此測驗的模型為Rasch模型，但是在Rasch模型的假設之下，卻忽略了同題組題目因為使用共同選項而存在著相依性的問題，而本論文所提出的新模型，目標即在改善此問題。本文利用模擬研究比較新模型與IRT模型的估計，以確認估計方式的有效性、忽略題組間相依性所造成的結果以及確認M_3統計量用於檢測適配度之可行性；除此之外，我們也藉由AIC、BIC比較新模型與IRT模型在分析實徵資料上的優劣，並進一步利用M_3檢定新模型在分析實徵資料上適配度的表現。

主要的研究結果有三個，第一、建構出新的模型；第二、以模擬實驗確認了參數估計的有效性與適配度檢定方式的可行性；第三、在實徵資料中呈現出新的二參數模型在估計與適配度上優於Rasch、2PL與單參數的新模型。

The Vocabulary Levels Test (VLT) is a tool to measure the learner’s word knowledge required for reading in English. Although Rasch model has been applied to analyze VLT, it is likely that ignorance of the dependency structure among items within a cluster in the matching format might cause bias on the estimation of item or person parameters. The purpose of this study is to propose a new model for VLT while taking into account the multiple matching format of the test. The maximum likelihood estimates of the parameters in the VLT-sequence model (VSM) are shown effectively obtained and the validity of a goodness-of-fit index based on limited information within each cluster of items is established for VSM. In the simulation studies, we investigate the effect of ignoring the dependency structure of items by comparing the estimation results from the proposed VSM models and from IRT models such as Rasch and the two-parameter logistic (2PL) models. This study has achieved the three-fold purpose: (a) to build a VSM model, (b) to facilitate the estimation and goodness-of-fit indices of both the Rasch-VSM and 2PL-VSM, and (c) to illustrate the usefulness of VSM by showing the superior of 2PL-VSM over IRT models and Rasch-VSM in fitting the actual 3000-level VLT data.