Design matrices unite seemingly disparate statistical methods, including linear regression, ANOVA, multiple regression, ANCOVA, and generalized linear modeling.
As part of a hierarchical Bayesian modeling course that we offered this semester, we wanted our students to learn about design matrices to facilitate model specification and parameter interpretation.
Naively, I thought that I could spend a few minutes in class reviewing matrix multiplication and a design matrix for simple linear regression, and if students wanted more, they might end up on Wikipedia’s Design matrix page.
It quickly became clear that this approach was not effective, so I started to think about how students could construct their own understanding of design matrices.
About the same time, I watched a pretty incredible kung fu movie called Five Element Ninjas, and it occurred to me that the “five elements” concept could be an effective device for getting my students to think about model specification and design matrices.
Students should be able to specify design matrices for many different types of models (e.g., linear models and generalized linear models), and they should be able to interpret the parameters.
The broad idea was to get the students to think about model specification from five perspectives:
- Model specification via a design matrix
- Model specification via R syntax (e.g., the
formulaargument tolm) - Model specification via “long form” equations
- Graphical model specification
- Verbal model specification (along with an interpretation of each of the parameter estimates)
This leverages what students already know, and encourages them to connect new concepts to their existing knowledge.
In our case, the students were all students in CU Boulder’s Ecology and Evolutionary Biology graduate program.
Most of them had a strong grasp of perspective 2 (model specification in R syntax), but relatively weak understanding of the remaining perspectives.
Before we asked them to do anything, I demonstrated this five elements approach on a simple model: the model …read more
Source:: r-bloggers.com
