PROCESS: PROCESS for mediation and/or moderation analyses.
In bruceR: Broadly Useful Convenient and Efficient R Functions
View source: R/bruceR-stats_5_advance.R
PROCESS R Documentation
PROCESS for mediation and/or moderation analyses.
Description
To perform mediation, moderation, and conditional process (moderated mediation) analyses,
people may use software like
Mplus,
SPSS "PROCESS" macro,
and SPSS "MLmed" macro.
Some R packages can also perform such analyses separately and in a complex way, including
R package "mediation",
R package "interactions",
and R package "lavaan".
Some other R packages or scripts/modules have been further developed to improve the convenience, including
jamovi module "jAMM" (by Marcello Gallucci, based on the lavaan package),
R package "processR" (by Keon-Woong Moon, not official, also based on the lavaan package),
and R script file "process.R"
(the official PROCESS R code by Andrew F. Hayes, but it is not yet an R package and has some bugs and limitations).
Here, the bruceR::PROCESS() function provides
an alternative to performing mediation/moderation analyses in R.
This function supports a total of 24 kinds of SPSS PROCESS models (Hayes, 2018)
and also supports multilevel mediation/moderation analyses.
Overall, it supports the most frequently used types of mediation, moderation,
moderated moderation (3-way interaction), and moderated mediation (conditional indirect effect) analyses
for (generalized) linear or linear mixed models.
Specifically, the bruceR::PROCESS() function
fits regression models based on the data, variable names, and a few other arguments
that users input (with no need to specify the PROCESS model number and no need to manually mean-center the variables).
The function can automatically judge the model number/type and also conduct grand-mean centering before model building
(using the bruceR::grand_mean_center() function).
This automatic grand-mean centering can be turned off by setting center=FALSE.
Note that this automatic grand-mean centering
(1) makes the results of main effects accurate for interpretation;
(2) does not change any results of model fit (it only affects the interpretation of main effects);
(3) is only conducted in "PART 1" (for an accurate estimate of main effects) but not in "PART 2" because
it is more intuitive and interpretable to use the raw values of variables for the simple-slope tests in "PART 2";
(4) is not optional to users because mean-centering should always be done when there is an interaction;
(5) is not conflicted with group-mean centering because after group-mean centering the grand mean of a variable will also be 0,
such that the automatic grand-mean centering (with mean = 0) will not change any values of the variable.
If you need to do group-mean centering, please do this before using PROCESS.
bruceR::group_mean_center() is a useful function of group-mean centering.
Remember that the automatic grand-mean centering in PROCESS never affects the values of a group-mean centered variable, which already has a grand mean of 0.
The bruceR::PROCESS() function uses:
the interactions::sim_slopes() function to
estimate simple slopes (and conditional direct effects) in moderation, moderated moderation, and moderated mediation models
(PROCESS Models 1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 58, 59, 72, 73, 75, 76).
the mediation::mediate() function to
estimate (conditional) indirect effects in (moderated) mediation models
(PROCESS Models 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 58, 59, 72, 73, 75, 76).
the lavaan::sem() function to perform serial multiple mediation analysis (PROCESS Model 6).
If you use this function in your research and report its results in your paper, please cite not only bruceR but also
the other R packages it uses internally (mediation, interactions, and/or lavaan).
Two parts of results are printed:
PART 1. Regression model summary (using bruceR::model_summary() to summarize the models)
PART 2. Mediation/moderation effect estimates (using one or a combination of the above packages and functions to estimate the effects)
To organize the PART 2 output, the results of Simple Slopes are titled in green,
whereas the results of Indirect Path are titled in blue.
Disclaimer:
Although this function is named after PROCESS, Andrew F. Hayes has no role in its design, and
its development is independent from the official SPSS PROCESS macro and "process.R" script.
Any error or limitation should be attributed to the three R packages/functions that bruceR::PROCESS() uses internally.
Moreover, as mediation analyses include random processes (i.e., bootstrap resampling or Monte Carlo simulation),
the results of mediation analyses are unlikely to be exactly the same across different software
(even if you set the same random seed in different software).
Usage
PROCESS(
data,
y = "",
x = "",
meds = c(),
mods = c(),
covs = c(),
clusters = c(),
hlm.re.m = "",
hlm.re.y = "",
hlm.type = c("1-1-1", "2-1-1", "2-2-1"),
med.type = c("parallel", "serial"),
mod.type = c("2-way", "3-way"),
mod.path = c("x-y", "x-m", "m-y", "all"),
cov.path = c("y", "m", "both"),
mod1.val = NULL,
mod2.val = NULL,
ci = c("boot", "bc.boot", "bca.boot", "mcmc"),
nsim = 100,
seed = NULL,
center = TRUE,
std = FALSE,
digits = 3,
file = NULL
)
Arguments
data
Data frame.
y, x
Variable name of outcome (Y) and predictor (X).
It supports both continuous (numeric) and dichotomous (factor) variables.
meds
Variable name(s) of mediator(s) (M).
Use c() to combine multiple mediators.
It supports both continuous (numeric) and dichotomous (factor) variables.
It allows an infinite number of mediators in parallel
or 2~4 mediators in serial.
* Order matters when med.type="serial"
(PROCESS Model 6: serial mediation).
mods
Variable name(s) of 0~2 moderator(s) (W).
Use c() to combine multiple moderators.
It supports all types of variables:
continuous (numeric), dichotomous (factor), and multicategorical (factor).
* Order matters when mod.type="3-way"
(PROCESS Models 3, 5.3, 11, 12, 18, 19, 72, and 73).
** Do not set this argument when med.type="serial"
(PROCESS Model 6).
covs
Variable name(s) of covariate(s) (i.e., control variables).
Use c() to combine multiple covariates.
It supports all types of (and an infinite number of) variables.
clusters
HLM (multilevel) cluster(s):
e.g., "School", c("Prov", "City"), c("Sub", "Item").
hlm.re.m, hlm.re.y
HLM (multilevel) random effect term of M model and Y model.
By default, it converts clusters to lme4 syntax of random intercepts:
e.g., "(1 | School)" or "(1 | Sub) + (1 | Item)".
You may specify these arguments to include more complex terms:
e.g., random slopes "(X | School)", or 3-level random effects "(1 | Prov/City)".
hlm.type
HLM (multilevel) mediation type (levels of "X-M-Y"):
"1-1-1" (default),
"2-1-1" (indeed the same as "1-1-1" in a mixed model),
or "2-2-1" (currently not fully supported, as limited by the mediation package).
In most cases, no need to set this argument.
med.type
Type of mediator:
"parallel" (default) or "serial"
(only relevant to PROCESS Model 6).
Partial matches of "p" or "s" also work.
In most cases, no need to set this argument.
mod.type
Type of moderator:
"2-way" (default) or "3-way"
(relevant to PROCESS Models 3, 5.3, 11, 12, 18, 19, 72, and 73).
Partial matches of "2" or "3" also work.
mod.path
Which path(s) do the moderator(s) influence?
"x-y", "x-m", "m-y", or any combination of them
(use c() to combine), or "all" (i.e., all of them).
No default value.
cov.path
Which path(s) do the control variable(s) influence?
"y", "m", or "both" (default).
mod1.val, mod2.val
By default (NULL), it uses
Mean +/- SD of a continuous moderator (numeric) or
all levels of a dichotomous/multicategorical moderator (factor) to
perform simple slope analyses and/or conditional mediation analyses.
You may manually specify a vector of certain values: e.g.,
mod1.val=c(1, 3, 5) or mod1.val=c("A", "B", "C").
ci
Method for estimating the standard error (SE) and
95% confidence interval (CI) of indirect effect(s).
Defaults to "boot" for (generalized) linear models or
"mcmc" for (generalized) linear mixed models (i.e., multilevel models).
"boot"Percentile Bootstrap
"bc.boot"Bias-Corrected Percentile Bootstrap
"bca.boot"Bias-Corrected and Accelerated (BCa) Percentile Bootstrap
"mcmc"Markov Chain Monte Carlo (Quasi-Bayesian)
* Note that these methods never apply to the estimates of simple slopes.
You should not report the 95% CIs of simple slopes as Bootstrap or Monte Carlo CIs,
because they are just standard CIs without any resampling method.
nsim
Number of simulation samples (bootstrap resampling or Monte Carlo simulation)
for estimating SE and 95% CI. Defaults to 100 for running examples faster.
In formal analyses, however, nsim=1000 (or larger) is strongly suggested!
seed
Random seed for obtaining reproducible results.
Defaults to NULL.
You may set to any number you prefer
(e.g., seed=1234, just an uncountable number).
* Note that all mediation models include random processes
(i.e., bootstrap resampling or Monte Carlo simulation).
To get exactly the same results between runs, you need to set a random seed.
However, even if you set the same seed number, it is unlikely to
get exactly the same results across different R packages
(e.g., lavaan vs. mediation)
and software (e.g., SPSS, Mplus, R, jamovi).
center
Centering numeric (continuous) predictors? Defaults to TRUE (suggested).
std
Standardizing variables to get standardized coefficients? Defaults to FALSE.
If TRUE, it will standardize all numeric (continuous) variables
before building regression models.
However, it is not suggested to set std=TRUE for generalized linear (mixed) models.
digits
Number of decimal places of output. Defaults to 3.
file
File name of MS Word (.doc).
Currently, only regression model summary can be saved.
Details
For more details and illustrations, see
PROCESS-bruceR-SPSS (PDF and Markdown files).
Value
Invisibly return a list of results:
process.idPROCESS model number.
process.typePROCESS model type.
model.m"Mediator" (M) models (a list of multiple models).
model.y"Outcome" (Y) model.
resultsEffect estimates and other results (unnamed list object).
References
Hayes, A. F. (2018). Introduction to mediation, moderation,
and conditional process analysis (second edition):
A regression-based approach. Guilford Press.
Yzerbyt, V., Muller, D., Batailler, C., & Judd, C. M. (2018).
New recommendations for testing indirect effects in mediational models:
The need to report and test component paths.
Journal of Personality and Social Psychology, 115(6), 929–943.
See Also
lavaan_summary
model_summary
med_summary
Examples
#### NOTE ####
## In the following examples, I set nsim=100 to save time.
## In formal analyses, nsim=1000 (or larger) is suggested!
#### Demo Data ####
# ?mediation::student
data = mediation::student %>%
dplyr::select(SCH_ID, free, smorale, pared, income,
gender, work, attachment, fight, late, score)
names(data)[2:3] = c("SCH_free", "SCH_morale")
names(data)[4:7] = c("parent_edu", "family_inc", "gender", "partjob")
data$gender01 = 1 - data$gender # 0 = female, 1 = male
# dichotomous X: as.factor()
data$gender = factor(data$gender01, levels=0:1, labels=c("Female", "Male"))
# dichotomous Y: as.factor()
data$pass = as.factor(ifelse(data$score>=50, 1, 0))
#### Descriptive Statistics and Correlation Analyses ####
Freq(data$gender)
Freq(data$pass)
Describe(data) # file="xxx.doc"
Corr(data[,4:11]) # file="xxx.doc"
#### PROCESS Analyses ####
## Model 1 ##
PROCESS(data, y="score", x="late", mods="gender") # continuous Y
PROCESS(data, y="pass", x="late", mods="gender") # dichotomous Y
# (multilevel moderation)
PROCESS(data, y="score", x="late", mods="gender", # continuous Y (LMM)
clusters="SCH_ID")
PROCESS(data, y="pass", x="late", mods="gender", # dichotomous Y (GLMM)
clusters="SCH_ID")
# (Johnson-Neyman (J-N) interval and plot)
PROCESS(data, y="score", x="gender", mods="late") -> P
P$results[[1]]$jn[[1]] # Johnson-Neyman interval
P$results[[1]]$jn[[1]]$plot # Johnson-Neyman plot (ggplot object)
GLM_summary(P$model.y) # detailed results of regression
# (allows multicategorical moderator)
d = airquality
d$Month = as.factor(d$Month) # moderator: factor with levels "5"~"9"
PROCESS(d, y="Temp", x="Solar.R", mods="Month")
## Model 2 ##
PROCESS(data, y="score", x="late",
mods=c("gender", "family_inc"),
mod.type="2-way") # or omit "mod.type", default is "2-way"
## Model 3 ##
PROCESS(data, y="score", x="late",
mods=c("gender", "family_inc"),
mod.type="3-way")
PROCESS(data, y="pass", x="gender",
mods=c("late", "family_inc"),
mod1.val=c(1, 3, 5), # moderator 1: late
mod2.val=seq(1, 15, 2), # moderator 2: family_inc
mod.type="3-way")
## Model 4 ##
PROCESS(data, y="score", x="parent_edu",
meds="family_inc", covs="gender",
ci="boot", nsim=100, seed=1)
# (allows an infinite number of multiple mediators in parallel)
PROCESS(data, y="score", x="parent_edu",
meds=c("family_inc", "late"),
covs=c("gender", "partjob"),
ci="boot", nsim=100, seed=1)
# (multilevel mediation)
PROCESS(data, y="score", x="SCH_free",
meds="late", clusters="SCH_ID",
ci="mcmc", nsim=100, seed=1)
## Model 6 ##
PROCESS(data, y="score", x="parent_edu",
meds=c("family_inc", "late"),
covs=c("gender", "partjob"),
med.type="serial",
ci="boot", nsim=100, seed=1)
## Model 8 ##
PROCESS(data, y="score", x="fight",
meds="late",
mods="gender",
mod.path=c("x-m", "x-y"),
ci="boot", nsim=100, seed=1)
## For more examples and details, see the "note" subfolder at:
## https://github.com/psychbruce/bruceR/tree/main/note
bruceR documentation built on June 22, 2024, 12:26 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
View source: R/bruceR-stats_5_advance.R
| PROCESS | R Documentation |
PROCESS for mediation and/or moderation analyses.
Description
To perform mediation, moderation, and conditional process (moderated mediation) analyses,
people may use software like
Mplus,
SPSS "PROCESS" macro,
and SPSS "MLmed" macro.
Some R packages can also perform such analyses separately and in a complex way, including
R package "mediation",
R package "interactions",
and R package "lavaan".
Some other R packages or scripts/modules have been further developed to improve the convenience, including
jamovi module "jAMM" (by Marcello Gallucci, based on the lavaan package),
R package "processR" (by Keon-Woong Moon, not official, also based on the lavaan package),
and R script file "process.R"
(the official PROCESS R code by Andrew F. Hayes, but it is not yet an R package and has some bugs and limitations).
Here, the bruceR::PROCESS() function provides
an alternative to performing mediation/moderation analyses in R.
This function supports a total of 24 kinds of SPSS PROCESS models (Hayes, 2018)
and also supports multilevel mediation/moderation analyses.
Overall, it supports the most frequently used types of mediation, moderation,
moderated moderation (3-way interaction), and moderated mediation (conditional indirect effect) analyses
for (generalized) linear or linear mixed models.
Specifically, the bruceR::PROCESS() function
fits regression models based on the data, variable names, and a few other arguments
that users input (with no need to specify the PROCESS model number and no need to manually mean-center the variables).
The function can automatically judge the model number/type and also conduct grand-mean centering before model building
(using the bruceR::grand_mean_center() function).
This automatic grand-mean centering can be turned off by setting center=FALSE.
Note that this automatic grand-mean centering (1) makes the results of main effects accurate for interpretation; (2) does not change any results of model fit (it only affects the interpretation of main effects); (3) is only conducted in "PART 1" (for an accurate estimate of main effects) but not in "PART 2" because it is more intuitive and interpretable to use the raw values of variables for the simple-slope tests in "PART 2"; (4) is not optional to users because mean-centering should always be done when there is an interaction; (5) is not conflicted with group-mean centering because after group-mean centering the grand mean of a variable will also be 0, such that the automatic grand-mean centering (with mean = 0) will not change any values of the variable.
If you need to do group-mean centering, please do this before using PROCESS.
bruceR::group_mean_center() is a useful function of group-mean centering.
Remember that the automatic grand-mean centering in PROCESS never affects the values of a group-mean centered variable, which already has a grand mean of 0.
The bruceR::PROCESS() function uses:
the
interactions::sim_slopes()function to estimate simple slopes (and conditional direct effects) in moderation, moderated moderation, and moderated mediation models (PROCESS Models 1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 58, 59, 72, 73, 75, 76).the
mediation::mediate()function to estimate (conditional) indirect effects in (moderated) mediation models (PROCESS Models 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 58, 59, 72, 73, 75, 76).the
lavaan::sem()function to perform serial multiple mediation analysis (PROCESS Model 6).
If you use this function in your research and report its results in your paper, please cite not only bruceR but also
the other R packages it uses internally (mediation, interactions, and/or lavaan).
Two parts of results are printed:
PART 1. Regression model summary (using bruceR::model_summary() to summarize the models)
PART 2. Mediation/moderation effect estimates (using one or a combination of the above packages and functions to estimate the effects)
To organize the PART 2 output, the results of Simple Slopes are titled in green, whereas the results of Indirect Path are titled in blue.
Disclaimer:
Although this function is named after PROCESS, Andrew F. Hayes has no role in its design, and
its development is independent from the official SPSS PROCESS macro and "process.R" script.
Any error or limitation should be attributed to the three R packages/functions that bruceR::PROCESS() uses internally.
Moreover, as mediation analyses include random processes (i.e., bootstrap resampling or Monte Carlo simulation),
the results of mediation analyses are unlikely to be exactly the same across different software
(even if you set the same random seed in different software).
Usage
PROCESS(
data,
y = "",
x = "",
meds = c(),
mods = c(),
covs = c(),
clusters = c(),
hlm.re.m = "",
hlm.re.y = "",
hlm.type = c("1-1-1", "2-1-1", "2-2-1"),
med.type = c("parallel", "serial"),
mod.type = c("2-way", "3-way"),
mod.path = c("x-y", "x-m", "m-y", "all"),
cov.path = c("y", "m", "both"),
mod1.val = NULL,
mod2.val = NULL,
ci = c("boot", "bc.boot", "bca.boot", "mcmc"),
nsim = 100,
seed = NULL,
center = TRUE,
std = FALSE,
digits = 3,
file = NULL
)
Arguments
data |
Data frame. |
y, x |
Variable name of outcome (Y) and predictor (X). It supports both continuous (numeric) and dichotomous (factor) variables. |
meds |
Variable name(s) of mediator(s) (M).
Use It supports both continuous (numeric) and dichotomous (factor) variables. It allows an infinite number of mediators in parallel or 2~4 mediators in serial. * Order matters when |
mods |
Variable name(s) of 0~2 moderator(s) (W).
Use It supports all types of variables: continuous (numeric), dichotomous (factor), and multicategorical (factor). * Order matters when ** Do not set this argument when |
covs |
Variable name(s) of covariate(s) (i.e., control variables).
Use |
clusters |
HLM (multilevel) cluster(s):
e.g., |
hlm.re.m, hlm.re.y |
HLM (multilevel) random effect term of M model and Y model.
By default, it converts You may specify these arguments to include more complex terms:
e.g., random slopes |
hlm.type |
HLM (multilevel) mediation type (levels of "X-M-Y"):
|
med.type |
Type of mediator:
|
mod.type |
Type of moderator:
|
mod.path |
Which path(s) do the moderator(s) influence?
|
cov.path |
Which path(s) do the control variable(s) influence?
|
mod1.val, mod2.val |
By default ( |
ci |
Method for estimating the standard error (SE) and
95% confidence interval (CI) of indirect effect(s).
Defaults to
* Note that these methods never apply to the estimates of simple slopes. You should not report the 95% CIs of simple slopes as Bootstrap or Monte Carlo CIs, because they are just standard CIs without any resampling method. |
nsim |
Number of simulation samples (bootstrap resampling or Monte Carlo simulation)
for estimating SE and 95% CI. Defaults to |
seed |
Random seed for obtaining reproducible results.
Defaults to * Note that all mediation models include random processes
(i.e., bootstrap resampling or Monte Carlo simulation).
To get exactly the same results between runs, you need to set a random seed.
However, even if you set the same seed number, it is unlikely to
get exactly the same results across different R packages
(e.g., |
center |
Centering numeric (continuous) predictors? Defaults to |
std |
Standardizing variables to get standardized coefficients? Defaults to |
digits |
Number of decimal places of output. Defaults to |
file |
File name of MS Word ( |
Details
For more details and illustrations, see PROCESS-bruceR-SPSS (PDF and Markdown files).
Value
Invisibly return a list of results:
process.idPROCESS model number.
process.typePROCESS model type.
model.m"Mediator" (M) models (a list of multiple models).
model.y"Outcome" (Y) model.
resultsEffect estimates and other results (unnamed list object).
References
Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis (second edition): A regression-based approach. Guilford Press.
Yzerbyt, V., Muller, D., Batailler, C., & Judd, C. M. (2018). New recommendations for testing indirect effects in mediational models: The need to report and test component paths. Journal of Personality and Social Psychology, 115(6), 929–943.
See Also
lavaan_summary
model_summary
med_summary
Examples
#### NOTE ####
## In the following examples, I set nsim=100 to save time.
## In formal analyses, nsim=1000 (or larger) is suggested!
#### Demo Data ####
# ?mediation::student
data = mediation::student %>%
dplyr::select(SCH_ID, free, smorale, pared, income,
gender, work, attachment, fight, late, score)
names(data)[2:3] = c("SCH_free", "SCH_morale")
names(data)[4:7] = c("parent_edu", "family_inc", "gender", "partjob")
data$gender01 = 1 - data$gender # 0 = female, 1 = male
# dichotomous X: as.factor()
data$gender = factor(data$gender01, levels=0:1, labels=c("Female", "Male"))
# dichotomous Y: as.factor()
data$pass = as.factor(ifelse(data$score>=50, 1, 0))
#### Descriptive Statistics and Correlation Analyses ####
Freq(data$gender)
Freq(data$pass)
Describe(data) # file="xxx.doc"
Corr(data[,4:11]) # file="xxx.doc"
#### PROCESS Analyses ####
## Model 1 ##
PROCESS(data, y="score", x="late", mods="gender") # continuous Y
PROCESS(data, y="pass", x="late", mods="gender") # dichotomous Y
# (multilevel moderation)
PROCESS(data, y="score", x="late", mods="gender", # continuous Y (LMM)
clusters="SCH_ID")
PROCESS(data, y="pass", x="late", mods="gender", # dichotomous Y (GLMM)
clusters="SCH_ID")
# (Johnson-Neyman (J-N) interval and plot)
PROCESS(data, y="score", x="gender", mods="late") -> P
P$results[[1]]$jn[[1]] # Johnson-Neyman interval
P$results[[1]]$jn[[1]]$plot # Johnson-Neyman plot (ggplot object)
GLM_summary(P$model.y) # detailed results of regression
# (allows multicategorical moderator)
d = airquality
d$Month = as.factor(d$Month) # moderator: factor with levels "5"~"9"
PROCESS(d, y="Temp", x="Solar.R", mods="Month")
## Model 2 ##
PROCESS(data, y="score", x="late",
mods=c("gender", "family_inc"),
mod.type="2-way") # or omit "mod.type", default is "2-way"
## Model 3 ##
PROCESS(data, y="score", x="late",
mods=c("gender", "family_inc"),
mod.type="3-way")
PROCESS(data, y="pass", x="gender",
mods=c("late", "family_inc"),
mod1.val=c(1, 3, 5), # moderator 1: late
mod2.val=seq(1, 15, 2), # moderator 2: family_inc
mod.type="3-way")
## Model 4 ##
PROCESS(data, y="score", x="parent_edu",
meds="family_inc", covs="gender",
ci="boot", nsim=100, seed=1)
# (allows an infinite number of multiple mediators in parallel)
PROCESS(data, y="score", x="parent_edu",
meds=c("family_inc", "late"),
covs=c("gender", "partjob"),
ci="boot", nsim=100, seed=1)
# (multilevel mediation)
PROCESS(data, y="score", x="SCH_free",
meds="late", clusters="SCH_ID",
ci="mcmc", nsim=100, seed=1)
## Model 6 ##
PROCESS(data, y="score", x="parent_edu",
meds=c("family_inc", "late"),
covs=c("gender", "partjob"),
med.type="serial",
ci="boot", nsim=100, seed=1)
## Model 8 ##
PROCESS(data, y="score", x="fight",
meds="late",
mods="gender",
mod.path=c("x-m", "x-y"),
ci="boot", nsim=100, seed=1)
## For more examples and details, see the "note" subfolder at:
## https://github.com/psychbruce/bruceR/tree/main/note
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