Publication-ready moderations with simple slopes in R

Getting started

Let’s first load the demo data. This data set comes with base R (meaning you have it too and can directly type this command into your R console).

head(mtcars)

##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

Load the rempsyc package:

library(rempsyc)

Note: If you haven’t installed this package yet, you will need to install it via the following command: install.packages("rempsyc"). Furthermore, you may be asked to install the following packages if you haven’t installed them already (you may decide to install them all now to avoid interrupting your workflow if you wish to follow this tutorial from beginning to end):

pkgs <- c("effectsize", "flextable", "interactions")
install_if_not_installed(pkgs)

For moderations and simple slopes, we usually want to standardize (or at least center) our variables.

mtcars2 <- lapply(mtcars, scale) |> as.data.frame()

Simple moderation: nice_mod

moderations <- nice_mod(
  data = mtcars2,
  response = "mpg",
  predictor = "gear",
  moderator = "wt"
)
moderations

##   Dependent Variable Predictor df           B          t            p
## 1                mpg      gear 28 -0.08718042 -0.7982999 4.314156e-01
## 2                mpg        wt 28 -0.94959988 -8.6037724 2.383144e-09
## 3                mpg   gear:wt 28 -0.23559962 -2.1551077 3.989970e-02
##           sr2     CI_lower   CI_upper
## 1 0.004805465 0.0000000000 0.02702141
## 2 0.558188818 0.3142326391 0.80214500
## 3 0.035022025 0.0003502202 0.09723370

If we want it to look nice

(my_table <- nice_table(moderations, highlight = TRUE))

Note: The sr2 (semi-partial correlation squared, also known as delta R-square) allows us to quantify the unique contribution (proportion of variance explained) of an independent variable on the dependent variable, over and above the other variables in the model. sr2 is often considered a better indicator of the practical relevance of a variable.

# Open in Word
print(my_table, preview = "docx")

# Save in Word
flextable::save_as_docx(my_table, path = "moderations.docx")

Simple slopes: nice_slopes

You might have heard about “simple slopes” before. But what does that mean? Essentially, this means looking at the strength (regression coefficient) and significance of the slope, when subsetting for observations that are high, low, or average on a variable, typically the moderating variable. A bit further down, this will get clearer by looking at the plot of the interaction, which shows one slope for observations that are high on the wt (moderating) variable, a second slope for those that are low, and a third slope for those that are average.

Let’s extract the simple slopes now, including the sr2.

slopes <- nice_slopes(
  data = mtcars2,
  response = "mpg",
  predictor = "gear",
  moderator = "wt"
)
slopes

##   Dependent Variable Predictor (+/-1 SD) df           B          t          p
## 1                mpg       gear (LOW-wt) 28  0.14841920  1.0767040 0.29080233
## 2                mpg      gear (MEAN-wt) 28 -0.08718042 -0.7982999 0.43141565
## 3                mpg      gear (HIGH-wt) 28 -0.32278004 -1.9035367 0.06729622
##           sr2 CI_lower   CI_upper
## 1 0.008741702        0 0.03886052
## 2 0.004805465        0 0.02702141
## 3 0.027322839        0 0.08179662

nice_table(slopes, highlight = TRUE)

In this specific case, the interaction is significant but none of the simple slopes. This means that although the two slopes are significantly different from each other, taken individually, the slopes aren’t significantly different from a straight line.

The neat thing is that you can add as many dependent variables at once as you want.

# Moderations
nice_mod(
  data = mtcars2,
  response = c("mpg", "disp", "hp"),
  predictor = "gear",
  moderator = "wt"
) |>
  nice_table(highlight = TRUE)

# Simple slopes
nice_slopes(
  data = mtcars2,
  response = c("mpg", "disp", "hp"),
  predictor = "gear",
  moderator = "wt"
) |>
  nice_table(highlight = TRUE)

Pro tip: Both the nice_mod() and nice_slopes() functions take the same argument, so you can just copy-paste the first and change the function call to save time!

Special cases

nice_mod(
  data = mtcars2,
  response = "mpg",
  predictor = "gear",
  moderator = "wt",
  covariates = c("am", "vs")
) |>
  nice_table(highlight = TRUE)

nice_slopes(
  data = mtcars2,
  response = "mpg",
  predictor = "gear",
  moderator = "wt",
  covariates = c("am", "vs")
) |>
  nice_table(highlight = TRUE)

# First need to define model for plot function
mod <- lm(mpg ~ gear * wt + am + vs, data = mtcars2)

# Plot the model
library(interactions)
interact_plot(mod, pred = "gear", modx = "wt", interval = TRUE)

mtcars2$am <- mtcars$am

nice_mod(
  response = "mpg",
  predictor = "gear",
  moderator = "disp",
  moderator2 = "am",
  data = mtcars2
) |>
  nice_table(highlight = TRUE)

nice_slopes(
  data = mtcars2,
  response = "mpg",
  predictor = "gear",
  moderator = "disp",
  moderator2 = "am"
) |>
  nice_table(highlight = TRUE)

Complex models: nice_lm

For more complicated models not supported by nice_mod, one can define the model in the traditional way and feed it to nice_lm and nice_lm_slopes instead. They support multiple lm models as well.

model1 <- lm(mpg ~ cyl + wt * hp, mtcars2)
model2 <- lm(qsec ~ disp + drat * carb, mtcars2)
my.models <- list(model1, model2)
nice_lm(my.models) |>
  nice_table(highlight = TRUE)

model1 <- lm(mpg ~ gear * wt, mtcars2)
model2 <- lm(disp ~ gear * wt, mtcars2)
my.models <- list(model1, model2)
nice_lm_slopes(my.models, predictor = "gear", moderator = "wt") |>
  nice_table(highlight = TRUE)