`sim_slopes`

conducts a simple slopes analysis for the purposes of
understanding two- and three-way interaction effects in linear regression.

## Usage

```
sim_slopes(
model,
pred,
modx,
mod2 = NULL,
modx.values = NULL,
mod2.values = NULL,
centered = "all",
data = NULL,
cond.int = FALSE,
johnson_neyman = TRUE,
jnplot = FALSE,
jnalpha = 0.05,
robust = FALSE,
digits = getOption("jtools-digits", default = 2),
pvals = TRUE,
confint = FALSE,
ci.width = 0.95,
cluster = NULL,
modx.labels = NULL,
mod2.labels = NULL,
v.cov = NULL,
v.cov.args = NULL,
...
)
```

## Arguments

- model
A regression model. The function is tested with

`lm`

,`glm`

,`svyglm`

,`merMod`

,`rq`

,`brmsfit`

,`stanreg`

models. Models from other classes may work as well but are not officially supported. The model should include the interaction of interest.- pred
The name of the predictor variable involved in the interaction. This can be a bare name or string. Note that it is evaluated using

`rlang`

, so programmers can use the`!!`

syntax to pass variables instead of the verbatim names.- modx
The name of the moderator variable involved in the interaction. This can be a bare name or string. The same

`rlang`

proviso applies as with`pred`

.- mod2
Optional. The name of the second moderator variable involved in the interaction. This can be a bare name or string. The same

`rlang`

proviso applies as with`pred`

.- modx.values
For which values of the moderator should lines be plotted? There are two basic options:

A vector of values (e.g.,

`c(1, 2, 3)`

)A single argument asking to calculate a set of values. See details below.

Default is

`NULL`

. If`NULL`

(or`mean-plus-minus`

), then the customary +/- 1 standard deviation from the mean as well as the mean itself are used for continuous moderators. If`"plus-minus"`

, plots lines when the moderator is at +/- 1 standard deviation without the mean. You may also choose`"terciles"`

to split the data into equally-sized groups and choose the point at the mean of each of those groups.If the moderator is a factor variable and

`modx.values`

is`NULL`

, each level of the factor is included. You may specify any subset of the factor levels (e.g.,`c("Level 1", "Level 3")`

) as long as there is more than 1. The levels will be plotted in the order you provide them, so this can be used to reorder levels as well.- mod2.values
For which values of the second moderator should the plot be facetted by? That is, there will be a separate plot for each level of this moderator. Defaults are the same as

`modx.values`

.- centered
A vector of quoted variable names that are to be mean-centered. If

`"all"`

, all non-focal predictors as well as the`pred`

variable are centered. You may instead pass a character vector of variables to center. User can also use "none" to base all predictions on variables set at 0. The response variable,`modx`

, and`mod2`

variables are never centered.- data
Optional, default is NULL. You may provide the data used to fit the model. This can be a better way to get mean values for centering and can be crucial for models with variable transformations in the formula (e.g.,

`log(x)`

) or polynomial terms (e.g.,`poly(x, 2)`

). You will see a warning if the function detects problems that would likely be solved by providing the data with this argument and the function will attempt to retrieve the original data from the global environment.- cond.int
Should conditional intercepts be printed in addition to the slopes? Default is

`FALSE`

.- johnson_neyman
Should the Johnson-Neyman interval be calculated? Default is

`TRUE`

. This can be performed separately with`johnson_neyman`

.- jnplot
Should the Johnson-Neyman interval be plotted as well? Default is

`FALSE`

.- jnalpha
What should the alpha level be for the Johnson-Neyman interval? Default is .05, which corresponds to a 95% confidence interval.

- robust
Should robust standard errors be used to find confidence intervals for supported models? Default is FALSE, but you should specify the type of sandwich standard errors if you'd like to use them (i.e.,

`"HC0"`

,`"HC1"`

, and so on). If`TRUE`

, defaults to`"HC3"`

standard errors.- digits
An integer specifying the number of digits past the decimal to report in the output. Default is 2. You can change the default number of digits for all jtools functions with

`options("jtools-digits" = digits)`

where digits is the desired number.- pvals
Show p values? If

`FALSE`

, these are not printed. Default is`TRUE`

.- confint
Show confidence intervals instead of standard errors? Default is

`FALSE`

.- ci.width
A number between 0 and 1 that signifies the width of the desired confidence interval. Default is

`.95`

, which corresponds to a 95% confidence interval. Ignored if`confint = FALSE`

.- cluster
For clustered standard errors, provide the column name of the cluster variable in the input data frame (as a string). Alternately, provide a vector of clusters.

- modx.labels
A character vector of labels for each level of the moderator values, provided in the same order as the

`modx.values`

argument. If`NULL`

, the values themselves are used as labels unless`modx,values`

is also`NULL`

. In that case, "+1 SD" and "-1 SD" are used.- mod2.labels
A character vector of labels for each level of the 2nd moderator values, provided in the same order as the

`mod2.values`

argument. If`NULL`

, the values themselves are used as labels unless`mod2.values`

is also`NULL`

. In that case, "+1 SD" and "-1 SD" are used.- v.cov
A function to calculate variances for the model. Examples could be

`sandwich::vcovPC()`

.- v.cov.args
A list of arguments for the

`v.cov`

function. For whichever argument should be the fitted model, put`"model"`

.- ...
Arguments passed to

`johnson_neyman`

and`summ`

.

## Value

A list object with the following components:

- slopes
A table of coefficients for the focal predictor at each value of the moderator

- ints
A table of coefficients for the intercept at each value of the moderator

- modx.values
The values of the moderator used in the analysis

- mods
A list containing each regression model created to estimate the conditional coefficients.

- jn
If

`johnson_neyman = TRUE`

, a list of`johnson_neyman`

objects from`johnson_neyman`

. These contain the values of the interval and the plots. If a 2-way interaction, the list will be of lengthOtherwise, there will be 1

`johnson_neyman`

object for each value of the 2nd moderator for 3-way interactions.

## Details

This allows the user to perform a simple slopes analysis for the purpose of probing interaction effects in a linear regression. Two- and three-way interactions are supported, though one should be warned that three-way interactions are not easy to interpret in this way.

For more about Johnson-Neyman intervals, see `johnson_neyman`

.

The function is tested with `lm`

, `glm`

, `svyglm`

, and `merMod`

inputs.
Others may work as well, but are not tested. In all but the linear model
case, be aware that not all the assumptions applied to simple slopes
analysis apply.

## References

Bauer, D. J., & Curran, P. J. (2005). Probing interactions in fixed and
multilevel regression: Inferential and graphical techniques.
*Multivariate Behavioral Research*, *40*(3), 373-400.
doi: 10.1207/s15327906mbr4003_5

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). *Applied
multiple regression/correlation analyses for the behavioral sciences* (3rd
ed.). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

## See also

`interact_plot`

accepts similar syntax and will plot the
results with `ggplot`

.

`testSlopes`

performs a hypothesis test of
differences and provides Johnson-Neyman intervals.

`simpleSlope`

performs a similar analysis.

Other interaction tools:
`johnson_neyman()`

,
`probe_interaction()`

,
`sim_margins()`

## Author

Jacob Long jacob.long@sc.edu

## Examples

```
# Using a fitted model as formula input
fiti <- lm(Income ~ Frost + Murder * Illiteracy,
data = as.data.frame(state.x77))
sim_slopes(model = fiti, pred = Murder, modx = Illiteracy)
#> JOHNSON-NEYMAN INTERVAL
#>
#> When Illiteracy is OUTSIDE the interval [0.68, 2.20], the slope of
#> Murder is p < .05.
#>
#> Note: The range of observed values of Illiteracy is [0.50, 2.80]
#>
#> SIMPLE SLOPES ANALYSIS
#>
#> Slope of Murder when Illiteracy = 0.5604669 (- 1 SD):
#>
#> Est. S.E. t val. p
#> ------- ------- -------- ------
#> 78.99 34.81 2.27 0.03
#>
#> Slope of Murder when Illiteracy = 1.1700000 (Mean):
#>
#> Est. S.E. t val. p
#> ------ ------- -------- ------
#> 8.36 29.24 0.29 0.78
#>
#> Slope of Murder when Illiteracy = 1.7795331 (+ 1 SD):
#>
#> Est. S.E. t val. p
#> -------- ------- -------- ------
#> -62.28 41.49 -1.50 0.14
#>
# With svyglm
if (requireNamespace("survey")) {
library(survey)
data(api)
dstrat <- svydesign(id = ~1, strata = ~stype, weights = ~pw,
data = apistrat, fpc = ~fpc)
regmodel <- svyglm(api00 ~ ell * meals, design = dstrat)
sim_slopes(regmodel, pred = ell, modx = meals)
# 3-way with survey and factor input
regmodel <- svyglm(api00 ~ ell * meals * sch.wide, design = dstrat)
sim_slopes(regmodel, pred = ell, modx = meals, mod2 = sch.wide)
}
#> ██████████████████████ While sch.wide (2nd moderator) = No █████████████████████
#>
#> JOHNSON-NEYMAN INTERVAL
#>
#> The Johnson-Neyman interval could not be found. Is the p value for your
#> interaction term below the specified alpha?
#>
#> SIMPLE SLOPES ANALYSIS
#>
#> Slope of ell when meals = 18.72139 (- 1 SD):
#>
#> Est. S.E. t val. p
#> ------- ------ -------- ------
#> -3.51 1.99 -1.76 0.08
#>
#> Slope of ell when meals = 48.22427 (Mean):
#>
#> Est. S.E. t val. p
#> ------- ------ -------- ------
#> -1.98 1.25 -1.58 0.11
#>
#> Slope of ell when meals = 77.72716 (+ 1 SD):
#>
#> Est. S.E. t val. p
#> ------- ------ -------- ------
#> -0.45 1.23 -0.37 0.71
#>
#> █████████████████████ While sch.wide (2nd moderator) = Yes █████████████████████
#>
#> JOHNSON-NEYMAN INTERVAL
#>
#> The Johnson-Neyman interval could not be found. Is the p value for your
#> interaction term below the specified alpha?
#>
#> SIMPLE SLOPES ANALYSIS
#>
#> Slope of ell when meals = 18.72139 (- 1 SD):
#>
#> Est. S.E. t val. p
#> ------- ------ -------- ------
#> -0.93 0.83 -1.12 0.26
#>
#> Slope of ell when meals = 48.22427 (Mean):
#>
#> Est. S.E. t val. p
#> ------- ------ -------- ------
#> -0.62 0.56 -1.12 0.26
#>
#> Slope of ell when meals = 77.72716 (+ 1 SD):
#>
#> Est. S.E. t val. p
#> ------- ------ -------- ------
#> -0.32 0.38 -0.84 0.40
#>
```