Typical approaches to assessing students' understanding of the engineering design process (EDP) include performance assessments that are time-consuming to score. It is also possible to use multiple-choice (MC) items to assess the EDP, but researchers and practitioners often view the diagnostic value of this assessment format as limited. However, through the use of distractor analysis, it is possible to glean additional insights into student conceptualizations of complex concepts. Using an EDP assessment based on MC items, this study illustrates the value of distractor analysis for exploring students' understanding of the EDP. Specifically, we analyzed 128 seventh grade students' responses to 20 MC items using a distractor analysis technique based on Rasch measurement theory. Our results indicated that students with different levels of achievement have substantively different conceptualizations of the EDP, where there were different probabilities for selecting various answer choices among students with low, medium, and high relative achievement. We also observed statistically significant differences (p < 0.05) in student achievement on several items when we analyzed the data separately by teacher. For these items, we observed different patterns of answer choice probabilities in each classroom. Qualitative results from student interviews corroborated many of the results from the distractor analyses. Together, these results indicated that distractor analysis is a useful approach to explore students' conceptualization of the EDP, and that this technique provides insight into differences in student achievement across subgroups. We discuss the results in terms of their implications for research and practice.

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In this paper, a hidden Markov model for modelling matrix-variate time series data is developed. It relies on matrix-variate distribution and presents a promising alternative to the existing methods. Simulation study is carefully conducted and uses benchmark tests with pre-specified overlapping values. Compared with the existing methods, the proposed model demonstrates rather high accuracy in state classification. Results suggest that such an approach is indeed competitive. Interesting applications are presented for real-life data illustration.

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