Statistically Modelling Effects of Dynamic Processes on Outcomes: An Example of Discourse Sequences and Group Solutions
Keywords:Time, multilevel modelling, hierarchicaly linear modelling, mathematical proof, sequential analysis.
Learning analysts often consider whether learning processes across time are related 1) to one another or 2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation -> correct, new idea) during its problem solving related to its group solution? I show how to address these issues with 1) a higher-level outcome regression and 2) a lower-level process regression, applying both to 3,234 turns of talk by 80 students working in 20 groups to solve an algebra problem. The easy-to-use, outcome-level analysis of group solution score has the following problems: multicollinearity, possibly low statistical power, cannot test for links among sequence components, and cannot model outcomes at multiple levels. The complex, process-level analysis for turns of talk overcomes these shortcomings with multilevel analysis, vector auto-regression, and outcome-level regression residuals. These results suggest a combined procedure. First, run an outcome-level analysis. If the results are significant, then the outcome-level results suffice. Otherwise, non-significant results might reflect multicollinearity, which then requires a process-level analysis. This procedure can help test a comprehensive model of how learning processes or their temporal sequences are related to learning outcomes at the turn-, time period-, individual-, group-, class-, and school-levels.
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