Incorporating Response Time to Analyze Test Data with Mixture Structural Equation Modeling

利用結構方程混合模型分析具反應時間的測驗資料

過去的研究顯示，試題作答的反應時間可以幫助了解考生們不同的測驗作答行 為，特別是考慮反應時間所建構的Rasch 混合模型（MRM-RT），利用兩個潛在類 別來刻劃及區辨快速猜測或真實作答之受試者，比起單純只考慮認真作答的受試者 模型，更符合實際的測驗資料。本研究將此MRM-RT 模型放在結構方程混合模型 的架構下，同時對試題的反應時間及測驗作答反應的資料進行分析，如此一來可以 很容易地增加MRM-RT 模型中的潛在類別個數，並且對此模型做參數估計。由模 擬結果顯示，MRM-RT 在試題的參數估計及描述受試者的應試行為上，表現皆優 於Rasch 混合模型。也發現使用穩健標準誤之最大概似估計所花費的時間，遠少於 使用蒙特卡羅馬爾可夫鏈的貝氏估計。因此，採用此架構之作法對研究者來說，將 可以更容易地獲得MRM-RT的參數估計。

Item response time has been shown valuable in identifying different test behavior of the test takers. In particular， the mixture Rasch model with response time components (MRM-RT) has suggested that a two-class solution representing rapid-guessers and solution behavior examinees could empirically fit the test data better than a one-class solution. In this study， we embed such a simultaneous analysis of item responses and response time into the mixture structural equation model framework， which in turn facilitates the estimation of the model with another additional class. Our simulation results indicate that the MRM-RT outperforms the mixture Rasch model in yielding more accurate item parameter estimates as well as describing better the test-taking behavior. The study shows that maximum likelihood estimation with robust standard errors takes much less time than using Monte Carlo Markov Chains for Bayesian estimation. Therefore， the estimation of MRM-RT is more accessible to researchers.