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This document demonstrates how to use stdmod_lavaan()
from the package stdmod
to compute the standardized
moderation effect in a path model fitted by
lavaan::sem()
.
More about this package can be found in
vignette("stdmod", package = "stdmod")
or at https://sfcheung.github.io/stdmod/.
library(stdmod) # For computing the standardized moderation effect conveniently
library(lavaan) # For doing path analysis in lavaan.
#> This is lavaan 0.6-17
#> lavaan is FREE software! Please report any bugs.
data(test_mod1)
round(head(test_mod1, 3), 3)
#> dv iv mod med cov1 cov2
#> 1 23.879 -0.133 -0.544 10.310 -0.511 -0.574
#> 2 23.096 1.456 1.539 11.384 0.094 -0.264
#> 3 23.201 0.319 1.774 9.615 -0.172 0.488
This test data set has 300 cases, six variables, all continuous.
lavaan::sem()
The product term can be formed manually or by the colon operator,
:
. stdmod_lavaan()
will work in both
cases.
This is the model to be tested:
<-
mod "
med ~ iv + mod + iv:mod + cov1
dv ~ med + cov2
"
<- sem(mod, test_mod1, fixed.x = FALSE)
fit summary(fit)
#> lavaan 0.6.17 ended normally after 1 iteration
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 23
#>
#> Number of observations 300
#>
#> Model Test User Model:
#>
#> Test statistic 1.058
#> Degrees of freedom 5
#> P-value (Chi-square) 0.958
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> med ~
#> iv 0.221 0.030 7.264 0.000
#> mod 0.104 0.030 3.489 0.000
#> iv:mod 0.257 0.025 10.169 0.000
#> cov1 0.104 0.025 4.099 0.000
#> dv ~
#> med 0.246 0.041 5.962 0.000
#> cov2 0.191 0.023 8.324 0.000
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> iv ~~
#> mod 0.481 0.063 7.606 0.000
#> iv:mod -0.149 0.059 -2.501 0.012
#> cov1 -0.033 0.058 -0.575 0.565
#> cov2 -0.071 0.059 -1.216 0.224
#> mod ~~
#> iv:mod -0.180 0.062 -2.923 0.003
#> cov1 -0.060 0.059 -1.010 0.313
#> cov2 -0.107 0.061 -1.763 0.078
#> iv:mod ~~
#> cov1 -0.051 0.061 -0.837 0.403
#> cov2 0.063 0.063 1.001 0.317
#> cov1 ~~
#> cov2 0.071 0.061 1.158 0.247
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .med 0.201 0.016 12.247 0.000
#> .dv 0.169 0.014 12.247 0.000
#> iv 0.954 0.078 12.247 0.000
#> mod 1.017 0.083 12.247 0.000
#> iv:mod 1.088 0.089 12.247 0.000
#> cov1 1.039 0.085 12.247 0.000
#> cov2 1.076 0.088 12.247 0.000
The results show that mod
significantly moderates the
effect of iv
on med
.
As in the case of regression, the coefficient of iv:mod
in the standardized solution is not the desired standardized coefficient
because it standardizes the product term.
standardizedSolution(fit)[3, ]
#> lhs op rhs est.std se z pvalue ci.lower ci.upper
#> 3 med ~ iv:mod 0.466 0.043 10.842 0 0.382 0.55
After fitting the path model by lavaan::lavaan()
, we can
use stdmod_lavaan()
to compute the standardized moderation
effect using the standard deviations of the focal variable, the
moderator, and the outcome variable (Cheung, Cheung, Lau, Hui,
& Vong, 2022).
The minimal arguments are:
fit
: The output from lavaan::lavaan()
and
its wrappers, such as lavaan::sem()
.x
: The focal variable, the variable with its effect on
the outcome variable being moderated.y
: The outcome variable.w
: The moderator.x_w
: The product term.<- stdmod_lavaan(fit = fit,
fit_iv_mod_std x = "iv",
y = "med",
w = "mod",
x_w = "iv:mod")
fit_iv_mod_std#>
#> Call:
#> stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod")
#>
#> Variable
#> Focal Variable iv
#> Moderator mod
#> Outcome Variable med
#> Product Term iv:mod
#>
#> lhs op rhs est se z pvalue ci.lower ci.upper
#> Original med ~ iv:mod 0.257 0.025 10.169 0 0.208 0.307
#> Standardized med ~ iv:mod 0.440 NA NA NA NA NA
The standardized moderation effect of mod
on the
iv
-med
path is 0.440.
stdmod_lavaan()
can also be used to form nonparametric
bootstrap confidence interval for the standardized moderation
effect.
There are two approaches to do this. First, if bootstrap confidence intervals was requested when fitting the model, the stored bootstrap estimates will be used. This is efficient because there is no need to do bootstrapping again.
We fit the model again, with bootstrapping:
<- sem(mod, test_mod1, fixed.x = FALSE,
fit se = "boot",
bootstrap = 2000,
iseed = 987543)
If bootstrapping has been done when fitting the model, just adding
boot_ci = TRUE
is enough to request nonparametric
percentile bootstrap confidence interval:
<- stdmod_lavaan(fit = fit,
fit_iv_mod_std_ci x = "iv",
y = "med",
w = "mod",
x_w = "iv:mod",
boot_ci = TRUE)
fit_iv_mod_std_ci#>
#> Call:
#> stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod",
#> boot_ci = TRUE)
#>
#> Variable
#> Focal Variable iv
#> Moderator mod
#> Outcome Variable med
#> Product Term iv:mod
#>
#> lhs op rhs est se z pvalue ci.lower ci.upper
#> Original med ~ iv:mod 0.257 0.035 7.298 0 0.184 0.322
#> Standardized med ~ iv:mod 0.440 NA NA NA 0.322 0.539
#>
#> Confidence interval of standardized moderation effect:
#> - Level of confidence: 95%
#> - Bootstrapping Method: Nonparametric
#> - Type: Percentile
#> - Number of bootstrap samples requests:
#> - Number of bootstrap samples with valid results: 2000
#>
#> NOTE: Bootstrapping conducted by the method in 0.2.7.5 or later. To use
#> the method in the older versions for reproducing previous results, set
#> 'use_old_version' to 'TRUE'.
The 95% confidence interval of the standardized moderation effect is 0.322 to 0.539.
The second approach, not covered here, uses do_boot()
from the manymome
package. to generate bootstrap estimates. To use the stored bootstrap
estimates, set boot_out
to the output of
do_boot()
. The stored bootstrap estimates will then be
used. This method can be used when non-bootstrapping confidence
intervals are needed when fitting the model.
The function stdmod_lavaan()
can be used for more
complicated path models. The computation of the standardized moderation
effect in a path model depends only on the standard deviations of the
three variables involved (x
, w
, and
y
).
The computation of the standardized moderation effect is based on the simple formula presented in the following manuscript, using the standard deviations of the outcome variable, focal variable, and the moderator:
Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022) Improving an old way to measure moderation effect in standardized units. Health Psychology, 41(7), 502-505. https://doi.org/10.1037/hea0001188.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.