Statistics 744, McMaster University

Graphics for inference

• What is my fodel telling me?

• How can I tell other people?

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?