
Publication-ready moderations with simple slopes in R
Rémi Thériault
February 8, 2022
Source:vignettes/moderation.Rmd
moderation.Rmd
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:
Note: If you haven’t installed this package yet, you will need to install it via the following command:
install.packages("rempsyc")
.
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))
Dependent Variable |
Predictor |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear |
28 |
-0.09 |
-0.80 |
.431 |
.00 |
[0.00, 0.03] |
wt |
28 |
-0.95 |
-8.60 |
< .001*** |
.56 |
[0.31, 0.80] |
|
gear × wt |
28 |
-0.24 |
-2.16 |
.040* |
.04 |
[0.00, 0.10] |
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.
Save table to Word
Let’s save it to word for use in a publication (optional).
flextable::save_as_docx(my_table, path = "moderations.docx")
Simple slopes: nice_slopes
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)
Dependent Variable |
Predictor (+/-1 SD) |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear (LOW-wt) |
28 |
0.15 |
1.08 |
.291 |
.01 |
[0.00, 0.04] |
gear (MEAN-wt) |
28 |
-0.09 |
-0.80 |
.431 |
.00 |
[0.00, 0.03] |
|
gear (HIGH-wt) |
28 |
-0.32 |
-1.90 |
.067 |
.03 |
[0.00, 0.08] |
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)
Dependent Variable |
Predictor |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear |
28 |
-0.09 |
-0.80 |
.431 |
.00 |
[0.00, 0.03] |
wt |
28 |
-0.95 |
-8.60 |
< .001*** |
.56 |
[0.31, 0.80] |
|
gear × wt |
28 |
-0.24 |
-2.16 |
.040* |
.04 |
[0.00, 0.10] |
|
disp |
gear |
28 |
-0.07 |
-0.70 |
.492 |
.00 |
[0.00, 0.02] |
wt |
28 |
0.83 |
7.67 |
< .001*** |
.43 |
[0.19, 0.67] |
|
gear × wt |
28 |
-0.09 |
-0.81 |
.422 |
.00 |
[0.00, 0.03] |
|
hp |
gear |
28 |
0.42 |
2.65 |
.013* |
.11 |
[0.00, 0.27] |
wt |
28 |
0.93 |
5.75 |
< .001*** |
.53 |
[0.29, 0.77] |
|
gear × wt |
28 |
0.15 |
0.96 |
.346 |
.01 |
[0.00, 0.07] |
# Simple slopes
nice_slopes(data = mtcars2,
response = c("mpg", "disp", "hp"),
predictor = "gear",
moderator = "wt") |>
nice_table(highlight = TRUE)
Dependent Variable |
Predictor (+/-1 SD) |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear (LOW-wt) |
28 |
0.15 |
1.08 |
.291 |
.01 |
[0.00, 0.04] |
gear (MEAN-wt) |
28 |
-0.09 |
-0.80 |
.431 |
.00 |
[0.00, 0.03] |
|
gear (HIGH-wt) |
28 |
-0.32 |
-1.90 |
.067 |
.03 |
[0.00, 0.08] |
|
disp |
gear (LOW-wt) |
28 |
0.01 |
0.09 |
.926 |
.00 |
[0.00, 0.00] |
gear (MEAN-wt) |
28 |
-0.07 |
-0.70 |
.492 |
.00 |
[0.00, 0.02] |
|
gear (HIGH-wt) |
28 |
-0.16 |
-0.97 |
.339 |
.01 |
[0.00, 0.03] |
|
hp |
gear (LOW-wt) |
28 |
0.27 |
1.34 |
.190 |
.03 |
[0.00, 0.11] |
gear (MEAN-wt) |
28 |
0.42 |
2.65 |
.013* |
.11 |
[0.00, 0.27] |
|
gear (HIGH-wt) |
28 |
0.58 |
2.33 |
.027* |
.09 |
[0.00, 0.22] |
Pro tip: Both the
nice_mod()
andnice_slopes()
functions take the same argument, so you can just copy-paste the first and change the function call to save time!
Special cases
Covariates
You can also have more complicated models, like with added covariates.
Moderations
nice_mod(data = mtcars2,
response = "mpg",
predictor = "gear",
moderator = "wt",
covariates = c("am", "vs")) |>
nice_table(highlight = TRUE)
Dependent Variable |
Predictor |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear |
26 |
-0.11 |
-0.88 |
.388 |
.00 |
[0.00, 0.02] |
wt |
26 |
-0.70 |
-5.07 |
< .001*** |
.15 |
[0.02, 0.28] |
|
am |
26 |
0.13 |
0.86 |
.399 |
.00 |
[0.00, 0.02] |
|
vs |
26 |
0.32 |
3.24 |
.003** |
.06 |
[0.00, 0.14] |
|
gear × wt |
26 |
-0.25 |
-2.56 |
.017* |
.04 |
[0.00, 0.09] |
Simple slopes
nice_slopes(data = mtcars2,
response = "mpg",
predictor = "gear",
moderator = "wt",
covariates = c("am", "vs")) |>
nice_table(highlight = TRUE)
Dependent Variable |
Predictor (+/-1 SD) |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear (LOW-wt) |
26 |
0.14 |
0.89 |
.383 |
.00 |
[0.00, 0.02] |
gear (MEAN-wt) |
26 |
-0.11 |
-0.88 |
.388 |
.00 |
[0.00, 0.02] |
|
gear (HIGH-wt) |
26 |
-0.36 |
-2.25 |
.033* |
.03 |
[0.00, 0.08] |
In this case, only the third row is significant, which means that
those who are high on the wt
variable (above one standard
deviation) have significantly lower mpg
the higher their
gear. We can plot this in the more traditional way:
# 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)
Note: If you haven’t installed this package yet, you will need to install it via the following command:
install.packages(interactions)
. Furthermore, know that this plot can be heavily customized with available arguments for publication purposes, but I won’t be going into these details here.
Three-way interaction
Let’s make a three-way interaction for example.
Note that for the simple slopes, for now, the second moderator needs to be a dichotomic variable (and the first moderator a continuous variable). We’ll reset the am variable for this purpose for now.
mtcars2$am <- mtcars$am
Moderations
nice_mod(response = "mpg",
predictor = "gear",
moderator = "disp",
moderator2 = "am",
data = mtcars2) |>
nice_table(highlight = TRUE)
Dependent Variable |
Predictor |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear |
24 |
-0.43 |
-0.68 |
.500 |
.00 |
[0.00, 0.02] |
disp |
24 |
-3.04 |
-3.16 |
.004** |
.06 |
[0.00, 0.14] |
|
am |
24 |
-0.21 |
-0.35 |
.731 |
.00 |
[0.00, 0.01] |
|
gear × disp |
24 |
-1.09 |
-1.09 |
.287 |
.01 |
[0.00, 0.03] |
|
gear × am |
24 |
1.34 |
2.41 |
.024* |
.04 |
[0.00, 0.09] |
|
disp × am |
24 |
-0.07 |
-0.08 |
.936 |
.00 |
[0.00, 0.00] |
|
gear × disp × am |
24 |
1.90 |
2.21 |
.037* |
.03 |
[0.00, 0.08] |
Simple slopes
nice_slopes(data = mtcars2,
response = "mpg",
predictor = "gear",
moderator = "disp",
moderator2 = "am") |>
nice_table(highlight = TRUE)
Dependent Variable |
am |
Predictor (+/-1 SD) |
df |
β |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|---|
mpg |
0.00 |
gear (LOW-disp) |
24 |
1.11 |
1.57 |
.131 |
.02 |
[0.00, 0.05] |
0.00 |
gear (MEAN-disp) |
24 |
-1.53 |
-1.49 |
.148 |
.01 |
[0.00, 0.05] |
|
0.00 |
gear (HIGH-disp) |
24 |
-4.16 |
-1.56 |
.131 |
.02 |
[0.00, 0.05] |
|
1.00 |
gear (LOW-disp) |
24 |
-0.00 |
-0.01 |
.990 |
.00 |
[0.00, 0.00] |
|
1.00 |
gear (MEAN-disp) |
24 |
1.17 |
2.59 |
.016* |
.04 |
[0.00, 0.10] |
|
1.00 |
gear (HIGH-disp) |
24 |
2.34 |
2.71 |
.012* |
.05 |
[0.00, 0.11] |
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.
nice_lm
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)
Dependent Variable |
Predictor |
df |
b |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
cyl |
27 |
-0.11 |
-0.72 |
.479 |
.00 |
[0.00, 0.01] |
wt |
27 |
-0.62 |
-5.70 |
< .001*** |
.14 |
[0.02, 0.25] |
|
hp |
27 |
-0.29 |
-2.40 |
.023* |
.02 |
[0.00, 0.06] |
|
wt × hp |
27 |
0.29 |
3.23 |
.003** |
.04 |
[0.00, 0.10] |
|
qsec |
disp |
27 |
-0.43 |
-1.97 |
.059 |
.07 |
[0.00, 0.20] |
drat |
27 |
-0.33 |
-1.53 |
.138 |
.04 |
[0.00, 0.14] |
|
carb |
27 |
-0.51 |
-3.32 |
.003** |
.20 |
[0.00, 0.41] |
|
drat × carb |
27 |
-0.23 |
-1.08 |
.289 |
.02 |
[0.00, 0.09] |
The same applies to simple slopes, this time we use the
nice_lm_slopes
function. It supports multiple
lm
models as well, but the predictor and moderator need to
be the same for these models (the dependent variable can change).
nice_lm_slopes
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)
Dependent Variable |
Predictor (+/-1 SD) |
df |
b |
t |
p |
sr2 |
95% CI |
---|---|---|---|---|---|---|---|
mpg |
gear (LOW-wt) |
28 |
0.15 |
1.08 |
.291 |
.01 |
[0.00, 0.04] |
gear (MEAN-wt) |
28 |
-0.09 |
-0.80 |
.431 |
.00 |
[0.00, 0.03] |
|
gear (HIGH-wt) |
28 |
-0.32 |
-1.90 |
.067 |
.03 |
[0.00, 0.08] |
|
disp |
gear (LOW-wt) |
28 |
0.01 |
0.09 |
.926 |
.00 |
[0.00, 0.00] |
gear (MEAN-wt) |
28 |
-0.07 |
-0.70 |
.492 |
.00 |
[0.00, 0.02] |
|
gear (HIGH-wt) |
28 |
-0.16 |
-0.97 |
.339 |
.01 |
[0.00, 0.03] |
Thanks for checking in
Make sure to check out this page again if you use the code after a time or if you encounter errors, as I periodically update or improve the code. Feel free to contact me for comments, questions, or requests to improve this function at https://github.com/rempsyc/rempsyc/issues. See all tutorials here: https://remi-theriault.com/tutorials.