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題名 | The Comparison of Maximum Likelihood Estimation and Expected a Posteriori in CAT Using the Graded Response Model=應用等級反應模式之電腦適性測驗中最大概似法與貝氏期望後驗法之比較 |
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作者 | 陳思光; Chen, Ssu-kuang; |
期刊 | 國教學報 |
出版日期 | 20071200 |
卷期 | 19 2007.12[民96.12] |
頁次 | 頁339-371 |
分類號 | 521.3 |
語文 | eng |
關鍵詞 | 等級反應模式; 電腦適性測驗; 最大概似法; 貝氏期望後驗法; Graded response model; Computerized adaptive tests; Maximum likelihood estimation; Expected a posteriori; CAT; MLE; EAP; |
中文摘要 | 本研究之目的是在應用等級反應模式 (Samejima, 1969) 之電腦適性測驗中,於不同的題庫下對最大概似法(MLE)與貝氏期望後驗法 (EAP) 進行比較。其中 EAP 所採用之事前能力分佈包括均態、常態和負向偏態。本研究使用易、中、難三種題庫,而每一題庫均含 72 題五項目等級反應試題。首先利用模擬研究方法產生受試者對此三種題庫的試題反應,並進行 10 次重複抽樣以避免抽樣誤差。再以 SAS 程式模擬電腦適性測驗及答完全部試題之過程。本研究結果建議MLE、採用均態事前能力分佈之 EAP 及採用常態事前能力分佈之 EAP 在訊息量足夠的量尺下表現差不多。採用常態事前能力分佈之 EAP 在量尺兩端有估計值縮向中間的問題。然而此現象可藉由提供足夠的訊息量來彌補。本研究結果亦建議 EAP 計算中勿採用不合適的事前能力分佈。 |
英文摘要 | The purpose of this research is to compare maximum likelihood estimation (MLE) and expected a posteriori estimation (EAP) under different item pool conditions in polytomous computerized adaptive tests (CATs) based on the graded response model (Samejima, 1969). The impact of various priors (uniform, normal, and negatively skewed distribution) adopted in the EAP calculation was especially examined. In the study, three types of item pools (easy, medium, and difficult), each containing 72 five-category graded response items were employed. Simulated response data were generated to reflect examinees’ responses to the three types of items. In order to prevent the erroneous results from sampling errors, ten replications were conducted. A SAS program was used to simulate the CAT and full scale process in the study. The result suggests that MLE, EAP with uniform, and EAP with normal prior perform equally well at the region of the trait continumm where item information is provided. EAP with normal prior has the problem of shrinkage toward the center of the trait continumm. However, the magnitude of the shrinkage is reduced if sufficient information is provided at the extreme ends of trait continumm. The study also suggests that improper priors should not be used with the EAP estimation method. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。