臺灣博碩士論文加值系統

作答時間已被證明能夠辨別不同測試行為的考生以及混合試題反應理論
模型已經提出了探索試題資料的反應模式。在近其的文獻中，混合Rasch 模
型(mixture Rasch model, MRM) 加入試題反應時間(mixture Rasch model with response
time components, MRM-RT) 透過資料分析顯示將作答行為分成兩類行為
- 快速猜題、確實作答，比只有一類的作答行為- 確實作答，模型適配度較佳。
然而，MRM-RT 無法解釋在快速猜測類中一些成員在作答時間要比同一類的成
員少的很多。因此，可能要多加入一類群- 作答快速，幫助解釋資料。
在這項研究中，我們試題反應和作答時間同時嵌入到混合的結構方程模型
的分析框架，並多加入快速反應類群以促進模型分析，並重新分析數據。由模
擬結果顯示，MRM-RT 的表現較優於MRM。具體來說，研究顯示MRM-RT 具
有較好的收斂速度，得到更準確的參數估計，更好地描述應試行為，並允許評
估測量潛在類群的不變性。此外，穩健標準誤差的最大似然估計比利用蒙特卡
羅馬爾可夫鏈貝式估計需要花費的時間極少，使得MRM-RT 更容易研究估計。

Item response time has been shown valuable in identifying different test behavior
of the test takers and mixtures of item response models have been proposed
to explore response patterns in test data. In recent literature, a mixture
Rasch model with response time components (MRM-RT) showed that a two-class
solution representing rapid-guessers and solution behavior examinees fit the test
data better than a one-class solution. However, the two-class MRM-RT could not
account for the much less response time of some members in the rapid-guessing
class of the test data. Thus, the inclusion of an additional class of fast respondents,
might be necessary to fulfill the assumption of conditional independence
of item responses and response time given the latent class.
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 facilitated the estimation of a three-class model with the fast responders
class added, and reanalyze the empirical test data. Our simulation results indicated
that the MRM-RT performed better than the mixture Rasch model alone.
Specifically, it showed that MRM-RT has better convergence rate, yield more
accurate item parameter estimates, describe better the test-taking behavior, and
allow for assessing measurement invariance across latent classes as well. In addition,
Maximum Likelihood estimation with robust standard errors takes much
less time than using Monte Carlo Markov Chains for Bayesian estimation and
therefore makes the estimation of MRM-RT more accessible to researchers.

1 Introduction 7
2 Model 11
2.1 MRM-RT in Mixture SEM . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Mixture Rasch Model . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Mixture Response Time Model . . . . . . . . . . . . . . . . . . 12
2.1.3 MRM-RT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Simulation Studies 20
3.1 Data Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Applied Data Analysis 36
4.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 Discussion 47
6 Conclusion 49

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