June 14, 2015
June 14, 2015
June 17, 2015
Educational Research and Methods
26.280.1 - 26.280.12
Exploration of the Multiple‐Institution Database for Investigating Engineering Longitudinal Development through Hierarchal Linear Models (HLMs) and clustering The MIDFIELD database includes complete student records of twelve institutions offering engineering degrees in the United States with a total student record of more than 1,000,000. These institutions enroll more than twelve percent of the nation’s total engineering students at any given time. While researchers have explored MIDFIELD using regression analysis, thus far only single‐level methodologies have been used. Hierarchical Linear Models, (sometimes called multi‐level models, nested models, or generalized mixed models,) provide a unique interpretive tool to probe a database such as MIDFIELD. Unlike ANOVA analysis variants, HLMs allow for robust analysis of incomplete data sets. For instance, in the case of a database of student grades, ANOVA methods require complete (or duplicate) recording of grades at each interval used for analysis. In other words, if one student has a missing grade for one semester, then that student cannot be used in the analysis. HLMs do not require completeness for strict convergence. More importantly, HLMs retain the nested structure of the data itself through the analysis. This aforementioned nested data structure may not necessarily be known a priori. Techniques of cluster analysis can be used to identify the presence of particular partitions in an arbitrary data set. The utilization of such methods can be paired with HLMs to provide a powerful, data driven framework for analyzing this phenomenon. In an expansion of a previous study, we focus MIDFIELD upon first‐ and second‐ year courses undertaken by most core curricula for our analysis: introductory physics; calculus; chemistry; computer languages; statics; and others. We then use a form of the null model in HLM in order analyze student grades. The null method allows us to glean an understanding of the variation of section grade distribution in these required courses through the construction of intercorrelation coefficients (ICCs) and through discussion of standard HLM regression coefficients. The work performed here, coupled with previous work, lead to a new MIDFIELD discussion of what grade distribution variations are observed at each of the partner institutions. We will be able to determine what effect the percentage of engineers enrolled in these first‐ and second‐year courses have been on section grade distribution. The effect of course size on grade distribution can also be studied. Finally, by employing the techniques of mixture modeling to examine clustering within our data and measures derived from information theory, we relate these results on section grade to fundamental outcomes in MIDFIELD, specifically graduation rates.
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