1 Example dataset

The dataset for this example contains standardized test scores on reading, writing, math, science, and social studies. There are also binary indicators (e.g., hisci) that encode whether someone received a high score on a given test. We also want to compute centered versions of each variable to aid interpretation in moderation-related models.

Following Hayes, I will use the convention \(X\) for independent variable/predictor, \(M\) for mediator, \(W\) for moderator, and \(Y\) for outcome.

df <- read_csv("mediation_data.csv")

## Parsed with column specification:
## cols(
##   id = col_double(),
##   female = col_double(),
##   ses = col_double(),
##   prog = col_double(),
##   read = col_double(),
##   write = col_double(),
##   math = col_double(),
##   science = col_double(),
##   socst = col_double(),
##   honors = col_double(),
##   awards = col_double(),
##   cid = col_double(),
##   hiread = col_double(),
##   hiwrite = col_double(),
##   hisci = col_double(),
##   himath = col_double()
## )

df <- df %>% mutate_at(vars(read, write, math, science, socst), funs(c=scale))

## Warning: funs() is soft deprecated as of dplyr 0.8.0
## please use list() instead
## 
## # Before:
## funs(name = f(.)
## 
## # After: 
## list(name = ~f(.))
## This warning is displayed once per session.

2 Moderation with a continuous moderator

Hayes Process model 1

Does the relationship between performance on reading (\(Y\)) and social studies (\(X\)) tests depend on math ability (\(W\))?