• Learning how to produce point-range regression plots
• Understanding marginal effects
• Plotting marginal effects

• Straightforward visualizations of the regression coefficients tables

• Visual display invites comparison, so better standardize

• Relationship between life expectancy and democratic index, assuming linear relationship

mod1 = lm(life_exp ~ dem_index, data = countries)
coef(mod1)

## (Intercept)   dem_index 
##   67.191591    1.621479

• A country with additional point of democratic index has, on average, 1.6 years higher life expectancy

• Relationship between life expectancy and democratic index, but the relationship can be parabolic and also can differ based on whether the country has a post soviet history or not.

m2 = lm(life_exp ~ poly(dem_index, 2) * postsoviet,
          data = countries[!is.na(countries$dem_index),])
coef(m2)

##                       (Intercept)               poly(dem_index, 2)1 
##                         80.981531                          8.327868 
##               poly(dem_index, 2)2                     postsovietyes 
##                         -3.296518                         -1.995878 
## poly(dem_index, 2)1:postsovietyes poly(dem_index, 2)2:postsovietyes 
##                          5.085355                         12.699062

• Help, how can I interpret this?

• Once variables are transformed, there are interactions, quadratic terms, splines, etc., interpreting relationships between them using coefficients tables becomes difficult
• Solution: visual interpretation using marginal effects

• Marginal effect = expected value of the dependent variable for given values of selected independent variable while other independent variables are held constant (preferably at some reasonable value such as mean)

ggpredict(m2, terms = c("dem_index [4,6,8]", "postsoviet [yes]"))

## # Predicted values of life_exp
## 
## dem_index | Predicted |         95% CI
## --------------------------------------
##         4 |     79.87 | [75.00, 84.74]
##         6 |     76.25 | [75.34, 77.15]
##         8 |     78.62 | [77.55, 79.69]

• The plot contains the exact same information as the table of regression coefficients, but is actually interpretable

• We can also plot just one variable one, while holding the others constant
• The following plot shows the difference in expected life expectancy for countries with average democratic index

• Question: How is this plot different from displaying simply group means, i.e. mean life expectancy for the postsoviet vs. non-postsoviet?

• ggeffects package computes marginal effects and returns ggplot2 friendly data frames

• The ggeffects offers three basic functions:

  • ggpredict - based on the base predict() function, works on almost any model
  • ggeffects - based on the effects package, similar to ggpredict, but handles categorical variables differently
  • ggemeans - based on the emeans package, mostly for contrasts

• The package works for a variety of models not covered in this course
  • generalized linear models
  • (generalized) mixed models
  • bayesian models
  • survival models
  • and many more

And that is pretty cool!