What is my model telling me?
How can I tell other people?
September 2021
Graphics for inference
Principles
- Graphs tell stories better than tables do
- Use graphs to illustrate comparisons
- Be careful about units
Distinguish between (scientific) variables and (statistical) parameters
Keep P values in their place
Show data if it doesn’t interfere
Smoking data
Smoking data
Smoking data
Smoking inference
- Different units Bad
Smoking inference
Smoking inference
- Would P values add anything here?
Comparing effects on different response variables
- Put response variables on same scale:
- Standardize
- Logs
- Proportions
Shape of response
Standard prediction plot
Marginal prediction plot
Combined
Variables vs. parameters
- A coefficient plot is most useful when each variable corresponds to a single statistical parameter
- Binary predictor
- Linear predictor
- More detailed shape information should be preferred when there is more than one parameter for a single logical variable
- More than two categories
- Splines and polynomials
No standard approach
- There are many different ways to try to capture marginal effects of a single variable
- Particularly if it’s associated with more than one parameter
- JD likes to calculate from the model “center”
- This is the average value from each predictor column of the model matrix
- Relatively stable
- A bit divorced from physical reality
Prediction plots
P values
- We use variable-level P values as a standard for whether the overall pattern associated with a given variable is significant
- This is not super-easy to interpret
- But it is also not super-easy to think of a better alternative
Interactions
Scales and transformations
Your model will often involve an original scale (where the data are collected) and a link scale (where the linear predictor lives)
- Which scale should you use for:
- Calculations?
- Displaying numbers to users?
- Graphing?