Nothing
Generate Bootstrap Estimates"
In manymome: Mediation, Moderation and Moderated-Mediation After Model Fitting
Introduction
This article is a brief illustration of how
to use do_boot() from the package
manymome
(Cheung & Cheung, 2023)
to generate bootstrap estimates for
indirect_effect() and cond_indirect_effects() to
form bootstrap confidence intervals.
Although indirect_effect() and cond_indirect_effects()
can also be used to generate bootstrap estimates
when they are called (see vignette("manymome")), there
may be situations in which users prefer generating
the bootstrap estimates first before calling indirect_effect()
and cond_indirect_effects(). do_boot() is for
this purpose.
The Workflow
The following workflow will be demonstrated;
-
Fit the model as usual.
-
Use do_boot() to generate the bootstrap estimates.
-
Call other functions (e.g, indirect_effect()
and cond_indirect_effects()) to compute the desired
effects and form bootstrap confidence intervals.
Demonstration: lavaan::sem()
Fit a Model by lavaan::sem()
The data set for illustration:
library(manymome)
dat <- data_med
head(dat)
#> x m y c1 c2
#> 1 9.931992 17.89644 20.73893 1.426513 6.103290
#> 2 8.331493 17.92150 22.91594 2.940388 3.832698
#> 3 10.327471 17.83178 22.14201 3.012678 5.770532
#> 4 11.196969 20.01750 25.05038 3.120056 4.654931
#> 5 11.887811 22.08645 28.47312 4.440018 3.959033
#> 6 8.198297 16.95198 20.73549 2.495083 3.763712
It has one predictor (x), one mediator (m),
one outcome variable (y), and two control
variables (c1 and c2).
This simple mediation model with two
control variables (c1 and c2)
will be fitted:
We first fit the model by lavaan::sem():
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit_lavaan <- sem(model = mod, data = dat,
fixed.x = FALSE,
estimator = "MLR")
summary(fit_lavaan)
#> lavaan 0.6-19 ended normally after 1 iteration
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 15
#>
#> Number of observations 100
#>
#> Model Test User Model:
#> Standard Scaled
#> Test Statistic 0.000 0.000
#> Degrees of freedom 0 0
#>
#> Parameter Estimates:
#>
#> Standard errors Sandwich
#> Information bread Observed
#> Observed information based on Hessian
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> m ~
#> x 0.935 0.075 12.437 0.000
#> c1 0.198 0.079 2.507 0.012
#> c2 -0.168 0.099 -1.703 0.089
#> y ~
#> m 0.785 0.233 3.363 0.001
#> x 0.508 0.323 1.573 0.116
#> c1 0.140 0.188 0.747 0.455
#> c2 -0.154 0.214 -0.720 0.471
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> x ~~
#> c1 0.026 0.121 0.211 0.833
#> c2 0.100 0.084 1.186 0.235
#> c1 ~~
#> c2 -0.092 0.109 -0.841 0.400
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .m 0.681 0.085 7.976 0.000
#> .y 4.030 0.580 6.944 0.000
#> x 1.102 0.150 7.338 0.000
#> c1 1.218 0.161 7.540 0.000
#> c2 0.685 0.073 9.340 0.000
Suppose we would like to use robust "sandwich"
standard errors and confidence intervals
provided by MLR for the free parameters,
but want to use percentile nonparametric
bootstrap
confidence interval for the indirect effect.
In the call above, we used estimator = "MLR"
and did not set se = "boot".
Generate Bootstrap Estimates
We can then call do_boot() on the output of
lavaan::sem() to generate the bootstrap
estimates of all free parameters and
the implied statistics, such as the variances
of m and y, which are not free parameters
but are needed to form the confidence
interval of the standardized indirect effect.
boot_out_lavaan <- do_boot(fit = fit_lavaan,
R = 500,
ncores = 1,
seed = 58491)
Usually, just three arguments are needed:
-
fit: The output of lavaan::sem().
-
R: The number of bootstrap samples. Should
be at least 2000 or even 5000 in real
research. 500 is used here just for illustration.
-
ncores: The number of CPU cores to be used
in generating bootstrap estimates in parallel
processing.
-
seed: The seed for the random number
generator. To be used by set.seed().
It is recommended to set this argument
such that the results are reproducible.
Parallel processing is enabled by default,
and a text progress bar (generated by the package pbapply)
will be displayed. If ncores is omitted,
the number of cores (ncores)
to be used will be decided automatically.
Therefore, users usually do not need to
use ncores. It is set to 1 here just for
illustration.
In real research with a complicated model and
moderate to large sample size, even with
parallel processing, it may take several minutes,
or even over twenty minutes in some cases.
Nevertheless, this only need to be conducted
once in the workflow of manymome.
If bootstrapping takes an appreciable time to
run, it is recommended to save
the output using saveRDS() or save():
### Use saveRDS() ###
# Save the output
saveRDS(boot_out_lavaan, file = "boot_out_lavaan.rds")
# Load the output
boot_out_lavaan <- readRDS("boot_out_lavaan.rds")
### Use save() ###
# Save the output
save(boot_out_lavaan, file = "boot_out_lavaan.RData")
# Load the output
load("boot_out_lavaan.RData")
We recommend readRDS() although save()
is probably a more popular function.
Using the Output of do_boot() in Other Functions of manymome
When calling indirect_effect() or
cond_indirect_effects(), the
argument boot_out can be assigned the
output of do_bout(). They will then
retrieve he stored bootstrap estimates
to form the percentile bootstrap confidence
intervals, if requested.
out_lavaan <- indirect_effect(x = "x",
y = "y",
m = "m",
fit = fit_lavaan,
boot_ci = TRUE,
boot_out = boot_out_lavaan)
out_lavaan
#>
#> == Indirect Effect ==
#>
#> Path: x -> m -> y
#> Indirect Effect: 0.733
#> 95.0% Bootstrap CI: [0.270 to 1.228]
#>
#> Computation Formula:
#> (b.m~x)*(b.y~m)
#>
#> Computation:
#> (0.93469)*(0.78469)
#>
#>
#> Percentile confidence interval formed by nonparametric bootstrapping
#> with 500 bootstrap samples.
#>
#> Coefficients of Component Paths:
#> Path Coefficient
#> m~x 0.935
#> y~m 0.785
Reusing the bootstrap estimates can ensure that
all analysis with bootstrap confidence intervals
are based on the same set of bootstrap samples.
The function also supports bias-corrected (BC)
confidence interval, which can be requested
by adding boot_type = "bc" to the call
of indirect_effect(). However, authors
in some recent work do not advocate this
method (e.g., Falk & Biesanz, 2015;
Hayes, 2022; Tofighi & Kelley, 2020).
Therefore, this option is provided merely
for research purpose.
Demonstration: lm()
Fit the Model by Several Calls to lm()
Suppose we estimate the parameters using
multiple regression. We need to fit two
regression models, one predicts m and
the other predicts y:
# Fit Models
lm_m <- lm(m ~ x + c1 + c2, dat)
lm_y <- lm(y ~ m + x + c1 + c2, dat)
#
# ###### Regression: Predict m ######
summary(lm_m)
#>
#> Call:
#> lm(formula = m ~ x + c1 + c2, data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.82810 -0.56016 -0.08481 0.52524 2.09155
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.68941 0.91979 10.534 <2e-16 ***
#> x 0.93469 0.08083 11.563 <2e-16 ***
#> c1 0.19778 0.07678 2.576 0.0115 *
#> c2 -0.16841 0.10305 -1.634 0.1055
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.8425 on 96 degrees of freedom
#> Multiple R-squared: 0.5981, Adjusted R-squared: 0.5855
#> F-statistic: 47.62 on 3 and 96 DF, p-value: < 2.2e-16
#
# ###### Regression: Predict y ######
#
summary(lm_y)
#>
#> Call:
#> lm(formula = y ~ m + x + c1 + c2, data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -4.1336 -1.3365 -0.1014 1.4597 6.5470
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 4.4152 3.3016 1.337 0.18432
#> m 0.7847 0.2495 3.145 0.00222 **
#> x 0.5077 0.3057 1.661 0.10004
#> c1 0.1405 0.1941 0.724 0.47093
#> c2 -0.1544 0.2554 -0.604 0.54695
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.06 on 95 degrees of freedom
#> Multiple R-squared: 0.3576, Adjusted R-squared: 0.3305
#> F-statistic: 13.22 on 4 and 95 DF, p-value: 1.336e-08
To use do_boot(), we first combine the
regression outputs to one object using
lm2list(). The output is an
lm_list-class object.
fit_lm <- lm2list(lm_m, lm_y)
fit_lm
#>
#> The model(s):
#> m ~ x + c1 + c2
#> y ~ m + x + c1 + c2
Generate Bootstrap Estimates
We can now use do_boot() as described
above, using the output of lm2list()
instead of the output of lavaan::sem():
boot_out_lm <- do_boot(fit = fit_lm,
R = 500,
seed = 98715,
ncores = 1)
Like working on the outputs of lavaan::lavaan(),
parallel processing is also used by default.
ncores is the number of CPU cores to
be used. Because
the output may not be saved, it is
recommended to set the seed of the random
number generation using seed, set
to 98715 in the above example. The seed can
be any integer within the range allowed
in R, see set.seed(). Setting the seed
ensures that the same R set of bootstrap
samples will be generated every time.
Using the Output of do_boot() in Other Functions of manymome
When calling indirect_effect() or
cond_indirect_effects(), we cab set the
argument boot_out to the output of
do_bout():
out_lm <- indirect_effect(x = "x",
y = "y",
m = "m",
fit = fit_lm,
boot_ci = TRUE,
boot_out = boot_out_lm)
out_lm
#>
#> == Indirect Effect ==
#>
#> Path: x -> m -> y
#> Indirect Effect: 0.733
#> 95.0% Bootstrap CI: [0.292 to 1.201]
#>
#> Computation Formula:
#> (b.m~x)*(b.y~m)
#>
#> Computation:
#> (0.93469)*(0.78469)
#>
#>
#> Percentile confidence interval formed by nonparametric bootstrapping
#> with 500 bootstrap samples.
#>
#> Coefficients of Component Paths:
#> Path Coefficient
#> m~x 0.935
#> y~m 0.785
As long as users are aware of the potential
problem with bias-corrected (BC) bootstrap
confidence interval (see the references
cited above), boot_type = "bc" can be
used to request BC bootstrap confidence
interval instead of the default percentile
bootstrap confidence interval.
The Structure of the Output
Models Fitted by lavaan::sem()
The output of do_boot() in this case
is an object of the class boot_out,
which is a list of R lists, each with
three elements: est, implied_stats,
and ok.
This is the content of est of the first list:
boot_out_lavaan[[1]]$est
#> lhs op rhs est
#> 1 m ~ x 0.828
#> 2 m ~ c1 0.224
#> 3 m ~ c2 -0.231
#> 4 y ~ m 1.257
#> 5 y ~ x 0.089
#> 6 y ~ c1 -0.118
#> 7 y ~ c2 -0.632
#> 8 m ~~ m 0.571
#> 9 y ~~ y 4.317
#> 10 x ~~ x 1.207
#> 11 x ~~ c1 0.146
#> 12 x ~~ c2 0.115
#> 13 c1 ~~ c1 1.331
#> 14 c1 ~~ c2 0.153
#> 15 c2 ~~ c2 0.688
#> 16 m r2 m 0.618
#> 17 y r2 y 0.396
The content is just the first four columns of
the output of lavaan::parameterEstimates().
Note that only fixed and free parameters are used
so other rows, if any, are not used even if present.
This is the content of implied_stats of the
first list:
boot_out_lavaan[[1]]$implied_stats
#> $cov
#> m y x c1 c2
#> m 1.497
#> y 1.944 7.150
#> x 1.006 1.281 1.207
#> c1 0.383 0.241 0.146 1.331
#> c2 -0.030 -0.480 0.115 0.153 0.688
#>
#> $mean
#> numeric(0)
#>
#> $mean_lv
#> numeric(0)
It has three elements. cov is the implied
variances and covariances of all variables.
If a model has latent variables, they will
be included too. The other elements,
mean and mean_lv, are the implied
means of the observed variables and
the latent variables (if any), respectively.
They are of zero length if mean structure is
not in the fitted model.
The last element, ok, denotes whether
the solution in a bootstrap sample is
admissible or not (determined by
lavaan::lavInspect() with
what = "post.check"). If not admissible,
it will not be used in forming confidence
intervals.
Models Fitted by lm()
The output of do_boot() using the
outputs of lm() is identical to
that using the output of lavaan::sem(). It is an object of the
class boot_out,
which is a list of R lists, each with
two elements: est and implied_stats.
This is the content of est of the first list:
boot_out_lm[[1]]$est
#> lhs op rhs est
#> 1 m ~ x 0.9583396
#> 2 m ~ c1 0.2808811
#> 3 m ~ c2 -0.3040130
#> 4 m ~1 9.9351030
#> 5 y ~ m 0.3986059
#> 6 y ~ x 0.5626298
#> 7 y ~ c1 0.5010449
#> 8 y ~ c2 -0.3614863
#> 9 y ~1 11.7212742
The content is similar in structure
to the output of lavaan::parameterEstimates().
However, the estimates are the estimates
based on lm().
This is the content of implied_stats of the
first list:
boot_out_lm[[1]]$implied_stats
#> $cov
#> m x c1 c2 y
#> m 1.7489520 0.99463099 0.32168750 -0.15480736 1.4738922
#> x 0.9946310 1.03034065 0.04418569 0.01709202 0.9921266
#> c1 0.3216875 0.04418569 1.13244802 0.12743087 0.6744295
#> c2 -0.1548074 0.01709202 0.12743087 0.68082701 -0.2343517
#> y 1.4738922 0.99212663 0.67442949 -0.23435172 5.4383227
#>
#> $mean
#> m x c1 c2 y
#> 18.487194 9.848009 2.329366 5.065314 23.967238
It has two elements. cov is the
variances and covariances of all variables.
Unlike the output based on lavaan::sem(),
the content is just the sample variances
and covariances of the variables in each
bootstrap sample, generated using cov().
The other element,
mean, stores sample means of all variables
in each bootstrap sample.
Further Information
For further information on do_boot(),
please refer to its help page.
References
Cheung, S. F., & Cheung, S.-H. (2023). manymome: An R
package for computing the indirect effects, conditional
effects, and conditional indirect effects, standardized or
unstandardized, and their bootstrap confidence intervals,
in many (though not all) models. Behavior Research Methods.
https://doi.org/10.3758/s13428-023-02224-z
Falk, C. F., & Biesanz, J. C. (2015). Inference and interval estimation methods for indirect effects with latent variable models. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 24--38. https://doi.org/10.1080/10705511.2014.935266
Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (Third Edition). The Guilford Press.
Tofighi, D., & Kelley, K. (2020). Indirect effects in sequential mediation models: Evaluating methods for hypothesis testing and confidence interval formation. Multivariate Behavioral Research, 55(2), 188--210. https://doi.org/10.1080/00273171.2019.1618545
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Introduction
This article is a brief illustration of how
to use do_boot() from the package
manymome
(Cheung & Cheung, 2023)
to generate bootstrap estimates for
indirect_effect() and cond_indirect_effects() to
form bootstrap confidence intervals.
Although indirect_effect() and cond_indirect_effects()
can also be used to generate bootstrap estimates
when they are called (see vignette("manymome")), there
may be situations in which users prefer generating
the bootstrap estimates first before calling indirect_effect()
and cond_indirect_effects(). do_boot() is for
this purpose.
The Workflow
The following workflow will be demonstrated;
-
Fit the model as usual.
-
Use
do_boot()to generate the bootstrap estimates. -
Call other functions (e.g,
indirect_effect()andcond_indirect_effects()) to compute the desired effects and form bootstrap confidence intervals.
Demonstration: lavaan::sem()
Fit a Model by lavaan::sem()
The data set for illustration:
library(manymome) dat <- data_med head(dat) #> x m y c1 c2 #> 1 9.931992 17.89644 20.73893 1.426513 6.103290 #> 2 8.331493 17.92150 22.91594 2.940388 3.832698 #> 3 10.327471 17.83178 22.14201 3.012678 5.770532 #> 4 11.196969 20.01750 25.05038 3.120056 4.654931 #> 5 11.887811 22.08645 28.47312 4.440018 3.959033 #> 6 8.198297 16.95198 20.73549 2.495083 3.763712
It has one predictor (x), one mediator (m),
one outcome variable (y), and two control
variables (c1 and c2).
This simple mediation model with two
control variables (c1 and c2)
will be fitted:
We first fit the model by lavaan::sem():
mod <- " m ~ x + c1 + c2 y ~ m + x + c1 + c2 " fit_lavaan <- sem(model = mod, data = dat, fixed.x = FALSE, estimator = "MLR") summary(fit_lavaan) #> lavaan 0.6-19 ended normally after 1 iteration #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 15 #> #> Number of observations 100 #> #> Model Test User Model: #> Standard Scaled #> Test Statistic 0.000 0.000 #> Degrees of freedom 0 0 #> #> Parameter Estimates: #> #> Standard errors Sandwich #> Information bread Observed #> Observed information based on Hessian #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> m ~ #> x 0.935 0.075 12.437 0.000 #> c1 0.198 0.079 2.507 0.012 #> c2 -0.168 0.099 -1.703 0.089 #> y ~ #> m 0.785 0.233 3.363 0.001 #> x 0.508 0.323 1.573 0.116 #> c1 0.140 0.188 0.747 0.455 #> c2 -0.154 0.214 -0.720 0.471 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> x ~~ #> c1 0.026 0.121 0.211 0.833 #> c2 0.100 0.084 1.186 0.235 #> c1 ~~ #> c2 -0.092 0.109 -0.841 0.400 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .m 0.681 0.085 7.976 0.000 #> .y 4.030 0.580 6.944 0.000 #> x 1.102 0.150 7.338 0.000 #> c1 1.218 0.161 7.540 0.000 #> c2 0.685 0.073 9.340 0.000
Suppose we would like to use robust "sandwich"
standard errors and confidence intervals
provided by MLR for the free parameters,
but want to use percentile nonparametric
bootstrap
confidence interval for the indirect effect.
In the call above, we used estimator = "MLR"
and did not set se = "boot".
Generate Bootstrap Estimates
We can then call do_boot() on the output of
lavaan::sem() to generate the bootstrap
estimates of all free parameters and
the implied statistics, such as the variances
of m and y, which are not free parameters
but are needed to form the confidence
interval of the standardized indirect effect.
boot_out_lavaan <- do_boot(fit = fit_lavaan, R = 500, ncores = 1, seed = 58491)
Usually, just three arguments are needed:
-
fit: The output oflavaan::sem(). -
R: The number of bootstrap samples. Should be at least 2000 or even 5000 in real research. 500 is used here just for illustration. -
ncores: The number of CPU cores to be used in generating bootstrap estimates in parallel processing. -
seed: The seed for the random number generator. To be used byset.seed(). It is recommended to set this argument such that the results are reproducible.
Parallel processing is enabled by default,
and a text progress bar (generated by the package pbapply)
will be displayed. If ncores is omitted,
the number of cores (ncores)
to be used will be decided automatically.
Therefore, users usually do not need to
use ncores. It is set to 1 here just for
illustration.
In real research with a complicated model and
moderate to large sample size, even with
parallel processing, it may take several minutes,
or even over twenty minutes in some cases.
Nevertheless, this only need to be conducted
once in the workflow of manymome.
If bootstrapping takes an appreciable time to
run, it is recommended to save
the output using saveRDS() or save():
### Use saveRDS() ### # Save the output saveRDS(boot_out_lavaan, file = "boot_out_lavaan.rds") # Load the output boot_out_lavaan <- readRDS("boot_out_lavaan.rds") ### Use save() ### # Save the output save(boot_out_lavaan, file = "boot_out_lavaan.RData") # Load the output load("boot_out_lavaan.RData")
We recommend readRDS() although save()
is probably a more popular function.
Using the Output of do_boot() in Other Functions of manymome
When calling indirect_effect() or
cond_indirect_effects(), the
argument boot_out can be assigned the
output of do_bout(). They will then
retrieve he stored bootstrap estimates
to form the percentile bootstrap confidence
intervals, if requested.
out_lavaan <- indirect_effect(x = "x", y = "y", m = "m", fit = fit_lavaan, boot_ci = TRUE, boot_out = boot_out_lavaan) out_lavaan #> #> == Indirect Effect == #> #> Path: x -> m -> y #> Indirect Effect: 0.733 #> 95.0% Bootstrap CI: [0.270 to 1.228] #> #> Computation Formula: #> (b.m~x)*(b.y~m) #> #> Computation: #> (0.93469)*(0.78469) #> #> #> Percentile confidence interval formed by nonparametric bootstrapping #> with 500 bootstrap samples. #> #> Coefficients of Component Paths: #> Path Coefficient #> m~x 0.935 #> y~m 0.785
Reusing the bootstrap estimates can ensure that all analysis with bootstrap confidence intervals are based on the same set of bootstrap samples.
The function also supports bias-corrected (BC)
confidence interval, which can be requested
by adding boot_type = "bc" to the call
of indirect_effect(). However, authors
in some recent work do not advocate this
method (e.g., Falk & Biesanz, 2015;
Hayes, 2022; Tofighi & Kelley, 2020).
Therefore, this option is provided merely
for research purpose.
Demonstration: lm()
Fit the Model by Several Calls to lm()
Suppose we estimate the parameters using
multiple regression. We need to fit two
regression models, one predicts m and
the other predicts y:
# Fit Models lm_m <- lm(m ~ x + c1 + c2, dat) lm_y <- lm(y ~ m + x + c1 + c2, dat) # # ###### Regression: Predict m ###### summary(lm_m) #> #> Call: #> lm(formula = m ~ x + c1 + c2, data = dat) #> #> Residuals: #> Min 1Q Median 3Q Max #> -1.82810 -0.56016 -0.08481 0.52524 2.09155 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 9.68941 0.91979 10.534 <2e-16 *** #> x 0.93469 0.08083 11.563 <2e-16 *** #> c1 0.19778 0.07678 2.576 0.0115 * #> c2 -0.16841 0.10305 -1.634 0.1055 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 0.8425 on 96 degrees of freedom #> Multiple R-squared: 0.5981, Adjusted R-squared: 0.5855 #> F-statistic: 47.62 on 3 and 96 DF, p-value: < 2.2e-16 # # ###### Regression: Predict y ###### # summary(lm_y) #> #> Call: #> lm(formula = y ~ m + x + c1 + c2, data = dat) #> #> Residuals: #> Min 1Q Median 3Q Max #> -4.1336 -1.3365 -0.1014 1.4597 6.5470 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 4.4152 3.3016 1.337 0.18432 #> m 0.7847 0.2495 3.145 0.00222 ** #> x 0.5077 0.3057 1.661 0.10004 #> c1 0.1405 0.1941 0.724 0.47093 #> c2 -0.1544 0.2554 -0.604 0.54695 #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 2.06 on 95 degrees of freedom #> Multiple R-squared: 0.3576, Adjusted R-squared: 0.3305 #> F-statistic: 13.22 on 4 and 95 DF, p-value: 1.336e-08
To use do_boot(), we first combine the
regression outputs to one object using
lm2list(). The output is an
lm_list-class object.
fit_lm <- lm2list(lm_m, lm_y) fit_lm #> #> The model(s): #> m ~ x + c1 + c2 #> y ~ m + x + c1 + c2
Generate Bootstrap Estimates
We can now use do_boot() as described
above, using the output of lm2list()
instead of the output of lavaan::sem():
boot_out_lm <- do_boot(fit = fit_lm, R = 500, seed = 98715, ncores = 1)
Like working on the outputs of lavaan::lavaan(),
parallel processing is also used by default.
ncores is the number of CPU cores to
be used. Because
the output may not be saved, it is
recommended to set the seed of the random
number generation using seed, set
to 98715 in the above example. The seed can
be any integer within the range allowed
in R, see set.seed(). Setting the seed
ensures that the same R set of bootstrap
samples will be generated every time.
Using the Output of do_boot() in Other Functions of manymome
When calling indirect_effect() or
cond_indirect_effects(), we cab set the
argument boot_out to the output of
do_bout():
out_lm <- indirect_effect(x = "x", y = "y", m = "m", fit = fit_lm, boot_ci = TRUE, boot_out = boot_out_lm) out_lm #> #> == Indirect Effect == #> #> Path: x -> m -> y #> Indirect Effect: 0.733 #> 95.0% Bootstrap CI: [0.292 to 1.201] #> #> Computation Formula: #> (b.m~x)*(b.y~m) #> #> Computation: #> (0.93469)*(0.78469) #> #> #> Percentile confidence interval formed by nonparametric bootstrapping #> with 500 bootstrap samples. #> #> Coefficients of Component Paths: #> Path Coefficient #> m~x 0.935 #> y~m 0.785
As long as users are aware of the potential
problem with bias-corrected (BC) bootstrap
confidence interval (see the references
cited above), boot_type = "bc" can be
used to request BC bootstrap confidence
interval instead of the default percentile
bootstrap confidence interval.
The Structure of the Output
Models Fitted by lavaan::sem()
The output of do_boot() in this case
is an object of the class boot_out,
which is a list of R lists, each with
three elements: est, implied_stats,
and ok.
This is the content of est of the first list:
boot_out_lavaan[[1]]$est #> lhs op rhs est #> 1 m ~ x 0.828 #> 2 m ~ c1 0.224 #> 3 m ~ c2 -0.231 #> 4 y ~ m 1.257 #> 5 y ~ x 0.089 #> 6 y ~ c1 -0.118 #> 7 y ~ c2 -0.632 #> 8 m ~~ m 0.571 #> 9 y ~~ y 4.317 #> 10 x ~~ x 1.207 #> 11 x ~~ c1 0.146 #> 12 x ~~ c2 0.115 #> 13 c1 ~~ c1 1.331 #> 14 c1 ~~ c2 0.153 #> 15 c2 ~~ c2 0.688 #> 16 m r2 m 0.618 #> 17 y r2 y 0.396
The content is just the first four columns of
the output of lavaan::parameterEstimates().
Note that only fixed and free parameters are used
so other rows, if any, are not used even if present.
This is the content of implied_stats of the
first list:
boot_out_lavaan[[1]]$implied_stats #> $cov #> m y x c1 c2 #> m 1.497 #> y 1.944 7.150 #> x 1.006 1.281 1.207 #> c1 0.383 0.241 0.146 1.331 #> c2 -0.030 -0.480 0.115 0.153 0.688 #> #> $mean #> numeric(0) #> #> $mean_lv #> numeric(0)
It has three elements. cov is the implied
variances and covariances of all variables.
If a model has latent variables, they will
be included too. The other elements,
mean and mean_lv, are the implied
means of the observed variables and
the latent variables (if any), respectively.
They are of zero length if mean structure is
not in the fitted model.
The last element, ok, denotes whether
the solution in a bootstrap sample is
admissible or not (determined by
lavaan::lavInspect() with
what = "post.check"). If not admissible,
it will not be used in forming confidence
intervals.
Models Fitted by lm()
The output of do_boot() using the
outputs of lm() is identical to
that using the output of lavaan::sem(). It is an object of the
class boot_out,
which is a list of R lists, each with
two elements: est and implied_stats.
This is the content of est of the first list:
boot_out_lm[[1]]$est #> lhs op rhs est #> 1 m ~ x 0.9583396 #> 2 m ~ c1 0.2808811 #> 3 m ~ c2 -0.3040130 #> 4 m ~1 9.9351030 #> 5 y ~ m 0.3986059 #> 6 y ~ x 0.5626298 #> 7 y ~ c1 0.5010449 #> 8 y ~ c2 -0.3614863 #> 9 y ~1 11.7212742
The content is similar in structure
to the output of lavaan::parameterEstimates().
However, the estimates are the estimates
based on lm().
This is the content of implied_stats of the
first list:
boot_out_lm[[1]]$implied_stats #> $cov #> m x c1 c2 y #> m 1.7489520 0.99463099 0.32168750 -0.15480736 1.4738922 #> x 0.9946310 1.03034065 0.04418569 0.01709202 0.9921266 #> c1 0.3216875 0.04418569 1.13244802 0.12743087 0.6744295 #> c2 -0.1548074 0.01709202 0.12743087 0.68082701 -0.2343517 #> y 1.4738922 0.99212663 0.67442949 -0.23435172 5.4383227 #> #> $mean #> m x c1 c2 y #> 18.487194 9.848009 2.329366 5.065314 23.967238
It has two elements. cov is the
variances and covariances of all variables.
Unlike the output based on lavaan::sem(),
the content is just the sample variances
and covariances of the variables in each
bootstrap sample, generated using cov().
The other element,
mean, stores sample means of all variables
in each bootstrap sample.
Further Information
For further information on do_boot(),
please refer to its help page.
References
Cheung, S. F., & Cheung, S.-H. (2023). manymome: An R package for computing the indirect effects, conditional effects, and conditional indirect effects, standardized or unstandardized, and their bootstrap confidence intervals, in many (though not all) models. Behavior Research Methods. https://doi.org/10.3758/s13428-023-02224-z
Falk, C. F., & Biesanz, J. C. (2015). Inference and interval estimation methods for indirect effects with latent variable models. Structural Equation Modeling: A Multidisciplinary Journal, 22(1), 24--38. https://doi.org/10.1080/10705511.2014.935266
Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (Third Edition). The Guilford Press.
Tofighi, D., & Kelley, K. (2020). Indirect effects in sequential mediation models: Evaluating methods for hypothesis testing and confidence interval formation. Multivariate Behavioral Research, 55(2), 188--210. https://doi.org/10.1080/00273171.2019.1618545
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