試題作答反應序列具轉移機率之測驗分析新模式

如全民英檢類之測驗，當試題作答反應序列為序列相關時，現有之測驗分析模式均有所不足，隱藏式馬可夫模式為處理序列相關之有效模式，正廣泛應用於測驗析以外之諸多不同領域，劉湘川於二○○三年考慮將其應用於序列相關之測驗分析，唯該模式之各時間點之「符號機率矩陣」與「轉移機率矩陣」均須相同，適用範圍常有限，劉湘川(2004)因而提出上述兩種機率矩陣均可變動之「廣義隱藏式馬可夫模型」，及其專有之參數估計法，劉湘川(2005a)進而提出「廣義隱藏式馬可夫式」與參數型「試題反應理論模式」之整合模式，則兼可分析個別受試能力及全體受試情況，劉湘川(2005b)進而再提出「廣義隱藏式馬可夫模式」與無參數型「試題反應理論模式」之整合模式，則進而與試題順序理論分析模式或試題關聯結構分析合應用，改進既有測驗分析模式之缺失與不足，更有效地應用於一般化具轉移機率係之測驗分析，且有更廣闊應用發展空間。本文簡介其系列模式之發展與應用。

關鍵字

隱藏式馬可夫模型HMM ；廣義隱藏式馬可夫模型GHMM ；核平滑化無參數試題反應理論模式KN-IRT ；試題順序理論IOT ；試題關聯結構分析IRS

並列摘要

So far our testing models have not dealt with item response sequences with serial correlation. Hidden Markov Models (HMMs) are a frequently used tool for time series data. They are used in numerous applications. It can represent probability over sequences of observations. Using HMMs to analyze item response sequences with transition probability was considered by Hsiang-Chuan Liu in 2003. Unfortunately, They are not always adequate to treat the general item response sequences, since the observation symbol probability matrices and the state transition probability matrices of HMMs are both fixed. Hsiang-Chuan Liu (2004) proposed a set of generalized Hidden Markov Models (GHMMs) with varying observation symbol probability matrices and state transition probability matrices and gave appropriate methods for parameters estimation. Further, Hsiang-Chuan Liu (2005a) proposed the mixing parametric item response theory models based on GHMM Models. The abilities of examinee can also be analyzed by those mixing models. Hsiang-Chuan Liu (2005b) also proposed the mixing kernel smoothing nonparametric item response theory model (KN-IRT) based on GHMM Model. Those mixing models can analyze not only the abilities of examinee but also the ordering relations between the items or the item relational structure by connecting the Item Ordering Theory model (IOT) or the Item Relational Structure model (TRS). Some developments and applications of the new testing models are briefly reviewed in this paper.

並列關鍵字

Generalized Hidden Markov Model GHMM ； Kernel Smoothing Nonparametric IRT KN-IRT ； Item Ordering Theory IOT ； Item Relational Structure IRS

參考文獻

劉湘川(2004)。廣義隱藏式馬可夫模型應用於測驗分析之研究。測驗統計年刊。12，1-22。

劉湘川(2003)。高階相關比累進加權核平滑化試題選項分析綜合模式。測驗統計年刊。10，197-218。

劉湘川(2005)。基於GHMM之KN-IRT混合模式及其估計。測驗統計年刊。13(上)，11-23。

劉湘川(2003)。核平滑化試題與選項分析模式之條件最大概似數值估計。測驗統計年刊。11，17-40。

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試題作答反應序列具轉移機率之測驗分析新模式

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