Simple-to-use functions for fitting linear models by regression or structural equation modeling and testing indirect effects, using just one function.
Usage
q_mediation(
x,
y,
m = NULL,
cov = NULL,
data = NULL,
boot_ci = TRUE,
level = 0.95,
R = 100,
seed = NULL,
ci_type = c("boot", "mc"),
boot_type = c("perc", "bc"),
model = NULL,
fit_method = c("lm", "regression", "sem", "lavaan"),
missing = "fiml",
fixed.x = TRUE,
sem_args = list(),
na.action = "na.pass",
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
progress = TRUE
)
q_simple_mediation(
x,
y,
m = NULL,
cov = NULL,
data = NULL,
boot_ci = TRUE,
level = 0.95,
R = 100,
seed = NULL,
ci_type = c("boot", "mc"),
boot_type = c("perc", "bc"),
fit_method = c("lm", "regression", "sem", "lavaan"),
missing = "fiml",
fixed.x = TRUE,
sem_args = list(),
na.action = "na.pass",
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
progress = TRUE
)
q_serial_mediation(
x,
y,
m = NULL,
cov = NULL,
data = NULL,
boot_ci = TRUE,
level = 0.95,
R = 100,
seed = NULL,
ci_type = c("boot", "mc"),
boot_type = c("perc", "bc"),
fit_method = c("lm", "regression", "sem", "lavaan"),
missing = "fiml",
fixed.x = TRUE,
sem_args = list(),
na.action = "na.pass",
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
progress = TRUE
)
q_parallel_mediation(
x,
y,
m = NULL,
cov = NULL,
data = NULL,
boot_ci = TRUE,
level = 0.95,
R = 100,
seed = NULL,
ci_type = c("boot", "mc"),
boot_type = c("perc", "bc"),
fit_method = c("lm", "regression", "sem", "lavaan"),
missing = "fiml",
fixed.x = TRUE,
sem_args = list(),
na.action = "na.pass",
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
progress = TRUE
)
# S3 method for class 'q_mediation'
print(
x,
digits = 4,
annotation = TRUE,
pvalue = TRUE,
pvalue_digits = 4,
se = TRUE,
for_each_path = FALSE,
se_ci = TRUE,
wrap_computation = TRUE,
lm_ci = TRUE,
lm_beta = TRUE,
lm_ci_level = 0.95,
sem_style = c("lm", "lavaan"),
...
)Arguments
- x
For
q_mediation(),q_simple_mediation(),q_serial_mediation(), andq_parallel_mediation(), it is the name of the predictor. For theprintmethod of these functions,xis the output of these functions.- y
The name of the outcome.
- m
A character vector of the name(s) of the mediator(s). For a simple mediation model, it must has only one name. For serial and parallel mediation models, it can have one or more names. For a serial mediation models, the direction of the paths go from the first names to the last names. For example,
c("m1", "m3", "m4")denoted that the path ism1 -> m3 -> m4.- cov
The names of the covariates, if any. If it is a character vector, then the outcome (
y) and all mediators (m) regress on all the covariates. If it is a named list of character vectors, then the covariates in an element predict only the variable with the name of this element. For example,list(m1 = "c1", dv = c("c2", "c3"))indicates thatc1predicts"m1", whilec2andc3predicts"dv". Default isNULL, no covariates.- data
The data frame. Note that listwise deletion will be used and only cases with no missing data on all variables in the model (e.g.,
x,m,yandcov) will be retained.- boot_ci
Logical. Whether bootstrap confidence interval will be formed. Default is
TRUE.- level
The level of confidence of the confidence interval. Default is .95 (for 95% confidence intervals).
- R
The number of bootstrap samples. Default is 100. Should be set to 5000 or at least 10000.
- seed
The seed for the random number generator. Default is
NULL. Should nearly always be set to an integer to make the results reproducible.- ci_type
Can be
"boot"for nonparametric bootstrapping or"mc"for Monte Carlo. Iffit_methodis"regression"or"lm", then only"boot"is supported.- boot_type
The type of the bootstrap confidence intervals. Default is
"perc", percentile confidence interval. Set"bc"for bias-corrected confidence interval. Ignored ifci_typeis not"boot".- model
The type of model. For
q_mediation(), it can be"simple"(simple mediation model),"serial"(serial mediation model), or"parallel"(parallel mediation model). It is recommended to call the corresponding wrappers directly (q_simple_mediation(),q_serial_mediation(), andq_parallel_mediation()) instead of callq_mediation().- fit_method
How the model is to be fitted. If set to
"lm"or"regression", linear regression will be used (fitted bystats::lm()). If set to"sem"or"lavaan", structural equation modeling will be used and the model will be fitted bylavaan::sem(). Default is"lm".- missing
If
fit_methodis set to"sem"or"lavaan", this argument determine how missing data is handled. The default value is"fiml"and full information maximum likelihood will be used to handle missing data. Please refer to lavaan::lavOptions for other options.- fixed.x
If
fit_methodis set to"sem"or"lavaan", this determines whether the observed predictors ("x" variables, including control variables) are treated as fixed variables or random variables. Default isTRUE, to mimic the same implicit setting in regression fitted bystats::lm().- sem_args
If
fit_methodis set to"sem"or"lavaan", this is a named list of arguments to be passed tolavaan::sem(). Arguments listed here will not overridemissingandfixed.x.- na.action
How missing data is handled. Used only when
fit_methodis set to"sem"or"lavaan". If"na.pass", the default, then all data will be passed tolavaan, and full information maximum likelihood (fiml) will be used to handle missing data. If"na.omit", then listwise deletion will be used.- parallel
If
TRUE, default, parallel processing will be used when doing bootstrapping.- ncores
Integer. The number of CPU cores to use when
parallelisTRUE. Default is the number of non-logical cores minus one (one minimum). Will raise an error if greater than the number of cores detected byparallel::detectCores(). Ifncoresis set, it will overridemake_cluster_argsindo_boot().- progress
Logical. Display progress or not.
- digits
Number of digits to display. Default is 4.
- annotation
Logical. Whether the annotation after the table of effects is to be printed. Default is
TRUE.- pvalue
Logical. If
TRUE, asymmetric p-values based on bootstrapping will be printed if available. Default isTRUE.- pvalue_digits
Number of decimal places to display for the p-values. Default is 4.
- se
Logical. If
TRUEand confidence intervals are available, the standard errors of the estimates are also printed. They are simply the standard deviations of the bootstrap estimates. Default isTRUE.- for_each_path
Logical. If
TRUE, each of the paths will be printed individually, using theprint-method of the output ofindirect_effect(). Default isFALSE.- se_ci
Logical. If
TRUEand confidence interval has not been computed, the function will try to compute them from stored standard error if the original standard error is to be used. Ignored if confidence interval has already been computed. Default isTRUE.- wrap_computation
Logical. If
TRUE, the default, long computational symbols and values will be wrapped to fit to the screen width.- lm_ci
If
TRUE, when printing the regression results ofstats::lm(), confidence interval based on t statistic and standard error will be computed and added to the output. Default isTRUE.- lm_beta
If
TRUE, when printing the regression results ofstats::lm(), standardized coefficients are computed and included in the printout. Only numeric variables will be computed, and any derived terms, such as product terms, will be formed after standardization. Default isTRUE.- lm_ci_level
The level of confidence of the confidence interval. Ignored if
lm_ciis notTRUE.- sem_style
How the for the model is to be printed if the model is fitted by structural equation modeling (using
lavaan). Default is"lm"and the results will be printed in a style similar to that ofsummary()output ofstats::lm(). If"lavaan", the results will be printed in usuallavaanstyle.- ...
Other arguments. If
for_each_pathisTRUE, they will be passed to the print method of the output ofindirect_effect(). Ignored otherwise.
Value
The function q_mediation() returns
a q_mediation class object, with
its print method.
The function q_simple_mediation() returns
a q_simple_mediation class object, which
is a subclass of q_mediation.
The function q_serial_mediation() returns
a q_serial_mediation class object, which
is a subclass of q_mediation.
The function q_parallel_mediation() returns
a q_parallel_mediation class object, which
is a subclass of q_mediation.
Details
The family of "q" (quick) functions are for testing mediation effects in common models. These functions do the following in one single call:
Fit the linear models.
Compute and test all the indirect effects.
They are easy-to-use and are suitable for common models with mediators. For now, there are "q" functions for these models:
A simple mediation: One predictor (
x), one mediator (m), one outcome (y), and optionally some control variables (covariates) (q_simple_mediation())A serial mediation model: One predictor (
x), one or more mediators (m), one outcome (y), and optionally some control variables (covariates). The mediators positioned sequentially betweenxandy(q_serial_mediation()):x -> m1 -> m2 -> ... -> y
A parallel mediation model: One predictor (
x), one or more mediators (m), one outcome (y), and optionally some control variables (covariates). The mediators positioned in parallel betweenxandy(q_parallel_mediation()):x -> m1 -> yx -> m2 -> y...
An arbitrary mediation model: One predictor (
x), one or more mediators (m), one outcome (y), and optionally some control variables (covariates). The mediators positioned in an arbitrary form betweenxandy, as long as there are no feedback loops (q_mediation()). For example:x -> m1m1 -> m21 -> ym1 -> m22 -> y...
Users only need to specify the x,
m, and y variables, and covariates
or control variables, if any (by cov),
and the functions will automatically
identify all indirect effects and
total effects.
Note that they are not intended to
be flexible. For more complex models,
it is recommended to fit the models
manually, either by structural
equation modelling (e.g.,
lavaan::sem()) or by regression
analysis using stats::lm() or
lmhelprs::many_lm(). See
https://sfcheung.github.io/manymome/articles/med_lm.html
for an illustration on how to compute
and test indirect effects for an
arbitrary mediation model.
Specifying a Model of an Arbitrary Form
If a custom model is to be estimated,
instead of setting model to a name
of the form ("simple","serial",
or "parallel"), set model to the paths between xandy`. It can
take one of the following two forms:
A character vector, each element a
string of a path, with variable names
connected by "->" (the spaces are
optional):
c("x -> m11 -> m12 -> y",
"x -> m2 -> y")A list of character vectors, each vector is a vector of names representing a path, going from the first element to the last element:
list(c("x", "m11, "m12", "y"),
c("x", "m2", "y")The two forms above specify the same model.
Paths not included are fixed to zero (i.e., does not "exist" in the model). A path can be specified more than once if this can enhance readability. For example:
c("x1 -> m1 -> m21 -> y1",
"x1 -> m1 -> m22 -> y1")The path "x1 -> m1" appears twice,
to indicate two different pathways from
x1 to y1.
Workflow
The coefficients of the model can be
estimated by one of these two
methods: OLS (ordinary least squares)
regression (setting fit_method to
"regression" or "lm"), or path
analysis (SEM, structural equation
modeling, by setting fit_method to
"sem" or "lavaan").
Regression
This is the workflow of the "q" functions when estimating the coefficients by regression:
Do listwise deletion based on all the variables used in the models.
Generate the regression models based on the variables specified.
Fit all the models by OLS regression using
stats::lm().Call
all_indirect_paths()to identify all indirect paths.Call
many_indirect_effects()to compute all indirect effects and form their confidence intervals.Call
total_indirect_effect()to compute the total indirect effect.Return all the results for printing.
The output of the "q" functions have
a print method for
printing all the major results.
Path Analysis
This is the workflow of the "q" functions when estimating the coefficients by path analysis (SEM):
By default, cases with missing data only on the mediators and the outcome variable will be retained, and full information maximum likelihood (FIML) will be used to estimate the coefficients. (Controlled by
missing, default to"fiml") usinglavaan::sem().Generate the SEM (
lavaan) model syntax based on the model specified.Fit the model by path analysis using
lavaan::sem().Call
all_indirect_paths()to identify all indirect paths.Call
many_indirect_effects()to compute all indirect effects and form their confidence intervals.Call
total_indirect_effect()to compute the total indirect effect.Return all the results for printing.
Testing the Indirect Effects
Two methods are available for testing
the indirect effects: nonparametric
bootstrap confidence intervals
(ci_type set to "boot") and
Monte Carlo confidence intervals
(ci_type set to "mc").
If the coefficients are estimated by OLS regression, only nonparametric bootstrap confidence intervals are supported.
If the coefficients are estimated by path analysis (SEM), then both methods are supported.
Printing the Results
The output of the "q" functions have
a print method for
printing all the major results.
Notes
Flexibility
The "q" functions are designed to be
easy to use. They are not designed to
be flexible. For maximum flexibility,
fit the models manually and call
functions such as
indirect_effect() separately. See
https://sfcheung.github.io/manymome/articles/med_lm.html
for illustrations.
Monte Carlo Confidence Intervals
We do not recommend using Monte Carlo confidence intervals for models fitted by regression because the covariances between parameter estimates are assumed to be zero, which may not be the case in some models. Therefore, the "q" functions do not support Monte Carlo confidence intervals if OLS regression is used.
Methods (by generic)
print(q_mediation): Theprintmethod of the outputs ofq_mediation(),q_simple_mediation(),q_serial_mediation(), andq_parallel_mediation().
Functions
q_mediation(): The general "q" function for common mediation models. Not to be used directly.q_simple_mediation(): A wrapper ofq_mediation()for simple mediation models (a model with only one mediator).q_serial_mediation(): A wrapper ofq_mediation()for serial mediation models.q_parallel_mediation(): A wrapper ofq_mediation()for parallel mediation models.
See also
lmhelprs::many_lm() for
fitting several regression models
using model syntax,
indirect_effect() for computing and
testing a specific path,
all_indirect_paths() for
identifying all paths in a model,
many_indirect_effects() for
computing and testing indirect
effects along several paths, and
total_indirect_effect() for
computing and testing the total
indirect effects.
Examples
# ===== A user-specified mediation model
# Set R to 5000 or 10000 in real studies
# Remove 'parallel' or set it to TRUE for faster bootstrapping
# Remove 'progress' or set it to TRUE to see a progress bar
out <- q_mediation(x = "x1",
y = "y1",
model = c("x1 -> m11 -> m2 -> y1",
"x1 -> m12 -> m2 -> y1"),
cov = c("c2", "c1"),
data = data_med_complicated,
R = 40,
seed = 1234,
parallel = FALSE,
progress = FALSE)
# Suppressed printing of p-values due to the small R
# Remove `pvalue = FALSE` when R is large
print(out,
pvalue = FALSE)
#>
#> =============== User-Specified Model ===============
#>
#> Call:
#>
#> q_mediation(x = "x1", y = "y1", cov = c("c2", "c1"), data = data_med_complicated,
#> R = 40, seed = 1234, model = c("x1 -> m11 -> m2 -> y1", "x1 -> m12 -> m2 -> y1"),
#> parallel = FALSE, progress = FALSE)
#>
#> ===================================================
#> | Basic Information |
#> ===================================================
#>
#> Predictor(x): x1
#> Outcome(y): y1
#> Mediator(s)(m):
#> Model: User-Specified Model
#>
#> The regression models fitted:
#>
#> m11 ~ x1 + c2 + c1
#> m2 ~ m11 + m12 + c2 + c1
#> y1 ~ m2 + c2 + c1
#> m12 ~ x1 + c2 + c1
#>
#> The number of cases included: 100
#>
#> ===================================================
#> | Regression Results |
#> ===================================================
#>
#>
#> Model:
#> m11 ~ x1 + c2 + c1
#>
#> Estimate CI.lo CI.hi betaS Std. Error t value Pr(>|t|) Sig
#> (Intercept) 1.8800 -0.4966 4.2566 -0.0000 1.1973 1.5702 0.1197
#> x1 0.3543 0.1777 0.5309 0.3830 0.0890 3.9819 0.0001 ***
#> c2 -0.0948 -0.2677 0.0781 -0.1020 0.0871 -1.0881 0.2793
#> c1 0.0756 -0.1230 0.2741 0.0722 0.1000 0.7555 0.4518
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> - BetaS are standardized coefficients with (a) only numeric variables
#> standardized and (b) product terms formed after standardization.
#> Variable(s) standardized is/are: m11, x1, c2, c1
#> - CI.lo and CI.hi are the 95.0% confidence levels of 'Estimate'
#> computed from the t values and standard errors.
#> R-square = 0.166. Adjusted R-square = 0.140. F(3, 96) = 6.367, p < .001
#>
#> Model:
#> m2 ~ m11 + m12 + c2 + c1
#>
#> Estimate CI.lo CI.hi betaS Std. Error t value Pr(>|t|) Sig
#> (Intercept) 9.0428 6.6202 11.4653 -0.0000 1.2203 7.4104 0.0000 ***
#> m11 0.0170 -0.1790 0.2131 0.0191 0.0988 0.1726 0.8634
#> m12 -0.0224 -0.2106 0.1658 -0.0291 0.0948 -0.2361 0.8139
#> c2 -0.0525 -0.2402 0.1351 -0.0633 0.0945 -0.5558 0.5797
#> c1 -0.1042 -0.2976 0.0893 -0.1115 0.0974 -1.0690 0.2878
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> - BetaS are standardized coefficients with (a) only numeric variables
#> standardized and (b) product terms formed after standardization.
#> Variable(s) standardized is/are: m2, m11, m12, c2, c1
#> - CI.lo and CI.hi are the 95.0% confidence levels of 'Estimate'
#> computed from the t values and standard errors.
#> R-square = 0.016. Adjusted R-square = -0.025. F(4, 95) = 0.398, p = 0.810
#>
#> Model:
#> y1 ~ m2 + c2 + c1
#>
#> Estimate CI.lo CI.hi betaS Std. Error t value Pr(>|t|) Sig
#> (Intercept) 9.5114 6.7500 12.2728 -0.0000 1.3911 6.8371 0.0000 ***
#> m2 -0.4364 -0.6499 -0.2228 -0.3775 0.1076 -4.0564 0.0001 ***
#> c2 -0.1677 -0.3437 0.0083 -0.1748 0.0887 -1.8909 0.0617 .
#> c1 0.0982 -0.1010 0.2975 0.0909 0.1004 0.9786 0.3303
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> - BetaS are standardized coefficients with (a) only numeric variables
#> standardized and (b) product terms formed after standardization.
#> Variable(s) standardized is/are: y1, m2, c2, c1
#> - CI.lo and CI.hi are the 95.0% confidence levels of 'Estimate'
#> computed from the t values and standard errors.
#> R-square = 0.182. Adjusted R-square = 0.156. F(3, 96) = 7.104, p < .001
#>
#> Model:
#> m12 ~ x1 + c2 + c1
#>
#> Estimate CI.lo CI.hi betaS Std. Error t value Pr(>|t|) Sig
#> (Intercept) 8.6694 5.9999 11.3389 0.0000 1.3449 6.4464 0.0000 ***
#> x1 -0.0474 -0.2457 0.1510 -0.0441 0.0999 -0.4741 0.6365
#> c2 -0.4609 -0.6552 -0.2667 -0.4275 0.0978 -4.7112 0.0000 ***
#> c1 0.2317 0.0087 0.4548 0.1908 0.1124 2.0623 0.0419 *
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> - BetaS are standardized coefficients with (a) only numeric variables
#> standardized and (b) product terms formed after standardization.
#> Variable(s) standardized is/are: m12, x1, c2, c1
#> - CI.lo and CI.hi are the 95.0% confidence levels of 'Estimate'
#> computed from the t values and standard errors.
#> R-square = 0.219. Adjusted R-square = 0.195. F(3, 96) = 8.976, p < .001
#>
#> ===================================================
#> | Indirect Effect Results |
#> ===================================================
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) ==
#>
#> ind CI.lo CI.hi Sig SE
#> x1 -> m11 -> m2 -> y1 -0.0026 -0.0527 0.0799 0.0235
#> x1 -> m12 -> m2 -> y1 -0.0005 -0.0077 0.0082 0.0031
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - The 'ind' column shows the indirect effect(s).
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) (x-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x1 -> m11 -> m2 -> y1 -0.0029 -0.0579 0.0777 0.0251
#> x1 -> m12 -> m2 -> y1 -0.0005 -0.0081 0.0081 0.0034
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The partially standardized indirect effect(s).
#> - x-variable(s) standardized.
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) (y-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x1 -> m11 -> m2 -> y1 -0.0025 -0.0506 0.0717 0.0219
#> x1 -> m12 -> m2 -> y1 -0.0004 -0.0068 0.0079 0.0030
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The partially standardized indirect effect(s).
#> - y-variable(s) standardized.
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) (Both x-variable(s) and y-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x1 -> m11 -> m2 -> y1 -0.0028 -0.0556 0.0697 0.0235
#> x1 -> m12 -> m2 -> y1 -0.0005 -0.0072 0.0085 0.0033
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The standardized indirect effect(s).
#>
# ===== Simple mediation
# Set R to 5000 or 10000 in real studies
# Remove 'parallel' or set it to TRUE for faster bootstrapping
# Remove 'progress' or set it to TRUE to see a progress bar
out <- q_simple_mediation(x = "x",
y = "y",
m = "m",
cov = c("c2", "c1"),
data = data_med,
R = 40,
seed = 1234,
parallel = FALSE,
progress = FALSE)
# Suppressed printing of p-values due to the small R
# Remove `pvalue = FALSE` when R is large
print(out,
pvalue = FALSE)
#>
#> =============== Simple Mediation Model ===============
#>
#> Call:
#>
#> q_simple_mediation(x = "x", y = "y", m = "m", cov = c("c2", "c1"),
#> data = data_med, R = 40, seed = 1234, parallel = FALSE, progress = FALSE)
#>
#> ===================================================
#> | Basic Information |
#> ===================================================
#>
#> Predictor(x): x
#> Outcome(y): y
#> Mediator(s)(m): m
#> Model: Simple Mediation Model
#>
#> The regression models fitted:
#>
#> m ~ x + c2 + c1
#> y ~ m + x + c2 + c1
#>
#> The number of cases included: 100
#>
#> ===================================================
#> | Regression Results |
#> ===================================================
#>
#>
#> Model:
#> m ~ x + c2 + c1
#>
#> Estimate CI.lo CI.hi betaS Std. Error t value Pr(>|t|) Sig
#> (Intercept) 9.6894 7.8636 11.5152 0.0000 0.9198 10.5344 0.0000 ***
#> x 0.9347 0.7742 1.0951 0.7536 0.0808 11.5632 0.0000 ***
#> c2 -0.1684 -0.3730 0.0361 -0.1070 0.1030 -1.6343 0.1055
#> c1 0.1978 0.0454 0.3502 0.1676 0.0768 2.5759 0.0115 *
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> - BetaS are standardized coefficients with (a) only numeric variables
#> standardized and (b) product terms formed after standardization.
#> Variable(s) standardized is/are: m, x, c2, c1
#> - CI.lo and CI.hi are the 95.0% confidence levels of 'Estimate'
#> computed from the t values and standard errors.
#> R-square = 0.598. Adjusted R-square = 0.586. F(3, 96) = 47.622, p < .001
#>
#> Model:
#> y ~ m + x + c2 + c1
#>
#> Estimate CI.lo CI.hi betaS Std. Error t value Pr(>|t|) Sig
#> (Intercept) 4.4152 -2.1393 10.9698 0.0000 3.3016 1.3373 0.1843
#> m 0.7847 0.2894 1.2800 0.4079 0.2495 3.1450 0.0022 **
#> x 0.5077 -0.0992 1.1145 0.2128 0.3057 1.6608 0.1000
#> c2 -0.1544 -0.6614 0.3526 -0.0510 0.2554 -0.6045 0.5470
#> c1 0.1405 -0.2448 0.5258 0.0619 0.1941 0.7239 0.4709
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> - BetaS are standardized coefficients with (a) only numeric variables
#> standardized and (b) product terms formed after standardization.
#> Variable(s) standardized is/are: y, m, x, c2, c1
#> - CI.lo and CI.hi are the 95.0% confidence levels of 'Estimate'
#> computed from the t values and standard errors.
#> R-square = 0.358. Adjusted R-square = 0.331. F(4, 95) = 13.220, p < .001
#>
#> ===================================================
#> | Indirect Effect Results |
#> ===================================================
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) ==
#>
#> ind CI.lo CI.hi Sig SE
#> x -> m -> y 0.7334 0.3239 1.4906 Sig 0.3025
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - The 'ind' column shows the indirect effect(s).
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) (x-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x -> m -> y 0.7739 0.3221 1.5004 Sig 0.3159
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The partially standardized indirect effect(s).
#> - x-variable(s) standardized.
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) (y-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x -> m -> y 0.2914 0.1382 0.5426 Sig 0.1107
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The partially standardized indirect effect(s).
#> - y-variable(s) standardized.
#>
#> ----------------------------------------------------------------
#>
#> == Indirect Effect(s) (Both x-variable(s) and y-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x -> m -> y 0.3074 0.1372 0.5846 Sig 0.1160
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The standardized indirect effect(s).
#>
#> ===================================================
#> | Direct Effect Results |
#> ===================================================
#>
#> ----------------------------------------------------------------
#>
#> == Effect(s) ==
#>
#> ind CI.lo CI.hi Sig SE
#> x -> y 0.5077 -0.4633 1.0643 0.4065
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - The 'ind' column shows the effect(s).
#>
#> ----------------------------------------------------------------
#>
#> == Effect(s) (x-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x -> y 0.5357 -0.4732 1.0294 0.4140
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The partially standardized effect(s).
#> - x-variable(s) standardized.
#>
#> ----------------------------------------------------------------
#>
#> == Effect(s) (y-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x -> y 0.2017 -0.1787 0.4199 0.1637
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The partially standardized effect(s).
#> - y-variable(s) standardized.
#>
#> ----------------------------------------------------------------
#>
#> == Effect(s) (Both x-variable(s) and y-variable(s) Standardized) ==
#>
#> std CI.lo CI.hi Sig SE
#> x -> y 0.2128 -0.1827 0.4068 0.1666
#>
#> - [CI.lo to CI.hi] are 95.0% percentile confidence intervals by
#> nonparametric bootstrapping with 40 samples.
#> - [SE] are standard errors.
#> - std: The standardized effect(s).
#>
#> ===================================================
#> | Notes |
#> ===================================================
#>
#> - For reference, the bootstrap confidence interval (and bootstrap
#> p-value, if requested) of the (unstandardized) direct effect is also
#> reported. The bootstrap p-value and the OLS t-statistc p-value can be
#> different.
#> - For the direct effects with either 'x'-variable or 'y'-variable, or
#> both, standardized, it is recommended to use the bootstrap confidence
#> intervals, which take into account the sampling error of the sample
#> standard deviations.
# # Different control variables for m and y
# out <- q_simple_mediation(x = "x",
# y = "y",
# m = "m",
# cov = list(m = "c1",
# y = c("c1", "c2")),
# data = data_med,
# R = 100,
# seed = 1234,
# parallel = FALSE,
# progress = FALSE)
# out
# ===== Serial mediation
# Set R to 5000 or 10000 in real studies
# Remove 'parallel' or set it to TRUE for faster bootstrapping
# Remove 'progress' or set it to TRUE to see a progress bar
# out <- q_serial_mediation(x = "x",
# y = "y",
# m = c("m1", "m2"),
# cov = c("c2", "c1"),
# data = data_serial,
# R = 40,
# seed = 1234,
# parallel = FALSE,
# progress = FALSE)
# # Suppressed printing of p-values due to the small R
# # Remove `pvalue = FALSE` when R is large
# print(out,
# pvalue = FALSE)
# # Different control variables for m and y
# out <- q_serial_mediation(x = "x",
# y = "y",
# m = c("m1", "m2"),
# cov = list(m1 = "c1",
# m2 = c("c2", "c1"),
# y = "c2"),
# data = data_serial,
# R = 100,
# seed = 1234,
# parallel = FALSE,
# progress = FALSE)
# out
# ===== Parallel mediation
# Set R to 5000 or 10000 in real studies
# Remove 'parallel' or set it to TRUE for faster bootstrapping
# Remove 'progress' or set it to TRUE to see a progress bar
# out <- q_parallel_mediation(x = "x",
# y = "y",
# m = c("m1", "m2"),
# cov = c("c2", "c1"),
# data = data_parallel,
# R = 40,
# seed = 1234,
# parallel = FALSE,
# progress = FALSE)
# # Suppressed printing of p-values due to the small R
# # Remove `pvalue = FALSE` when R is large
# print(out,
# pvalue = FALSE)
# # Different control variables for m and y
# out <- q_parallel_mediation(x = "x",
# y = "y",
# m = c("m1", "m2"),
# cov = list(m1 = "c1",
# m2 = c("c2", "c1"),
# y = "c2"),
# data = data_parallel,
# R = 100,
# seed = 1234,
# parallel = FALSE,
# progress = FALSE)
# out