MANE 6313
Week 6, Module G
Student Learning Outcome
- Select an appropriate experimental design with one or more factors,
- Select an appropriate model with one or more factors,
- Evaluate statistical analyses of experimental designs,
- Assess the model adequacy of any experimental design, and
- Interpret model results.
Module Learning Outcome
Judging models for factorial designs.
Resources for the Week 6, Module G micro-lecture are:
Judging Models
Fitting the correct regression model can be as much art as it is a science.
- Parsimonious model
- Hierarchical Model
- Example Problem
Parsimonious Model
A parsimonious model is a model that achieves a desired level of goodness of fit using as few explanatory variables as possible
Source: https://www.statology.org/parsimonious-model/
- Occam's Razor states that the simplest explanation is most likely the right one
- Statistical Reasons:
- Parsimonious models are easier to interpret and understand
- Parsimonious models tend to have more predictive ability
- Parsimonious models are less likely to be impacted by multicollinearity
Hierarchical Model
In the world of linear models, a hierarchical model contains all lower-order terms that comprise the higher-order terms that also appear in the model. For example, a model that includes the interaction term ABC is hierarchical if includes these terms: A, B, C, AB, AC, and B*C
Example Problem
Consider two replicates of a factorial design with the following factors.
| Factor | Levels |
|---|---|
| A | 25,100 |
| B | 1,7 |
| C | 8,12,16 |
| D | .1,.15,.2 |
| E | 20,80 |