Standardized Moderation Effect and Its Bootstrap CI in 'lavaan'

Compute the standardized moderation effect in a structural equation model fitted by lavaan::lavaan() or its wrappers and form the nonparametric bootstrap confidence interval.

Usage

stdmod_lavaan(
  fit,
  x,
  y,
  w,
  x_w,
  standardized_x = TRUE,
  standardized_y = TRUE,
  standardized_w = TRUE,
  boot_ci = FALSE,
  boot_out = NULL,
  R = 100,
  conf = 0.95,
  use_old_version = FALSE,
  ...
)

Arguments

fit: The SEM output by lavaan::lavaan() or its wrappers.
x: The name of the focal variable in the model, the variable with its effect on the outcome variable being moderated.
y: The name of the outcome variable (dependent variable) in the model.
w: The name of the moderator in the model.
x_w: The name of the product term (x * w) in the model. It can be the variable generated by the colon operator, e.g., "x:w", which is only in the model and not in the original data set.
standardized_x: If TRUE, the default, x is standardized when computing the standardized moderation effect.
standardized_y: If TRUE, the default, y is standardized when computing the standardized moderation effect.
standardized_w: If TRUE, the default, w is standardized when computing the standardized moderation effect.
boot_ci: Boolean. Whether nonparametric bootstrapping will be conducted. Default is FALSE.
boot_out: If set to the output of manymome::do_boot(), the stored bootstrap estimates will be retrieved to form the bootstrap confidence interval. If set, bootstrap estimates stored in fit, if any, will not be used. Default is NULL.
R: (Not used in the current version. Used when use_old_version is set to TRUE.) The number of nonparametric bootstrapping samples. Default is 100. Set this to at least 2000 in actual use.
conf: The level of confidence. Default is .95, i.e., 95%.
use_old_version: If set to TRUE, it will use the bootstrapping method used in 0.2.7.4 or before. Included only for reproducing previous results if necessary. Default is FALSE.
...: (Not used in the current version. Used when use_old_version is set to TRUE.) Optional arguments to be passed to boot::boot(). Parallel processing can be used by adding the appropriate arguments in boot::boot().

Value

A list of class stdmod_lavaan with these elements:

stdmod: The standardized moderation effect.
ci: The nonparametric bootstrap confidence interval. NA if confidence interval not requested.
boot_out: The raw output from boot::boot(). NA if confidence interval not requested.
fit: The original fit object.

Details

Important Notes

Starting from Version 0.2.7.5, of stdmod_lavaan() adopts an approach to bootstrapping different from that in the previous versions (0.2.7.4 and before), yielding bootstrapping results different from those in previous versions (for reasons explained later).

To reproduce results from the older version of this function, set use_old_version to TRUE.

How it works

stdmod_lavaan() accepts a lavaan::lavaan object, the structural equation model output returned by lavaan::lavaan() and its wrappers (e.g, lavaan::sem()) and computes the standardized moderation effect using the formula in the appendix of Cheung, Cheung, Lau, Hui, and Vong (2022).

The standard deviations of the focal variable (the variable with its effect on the outcome variable being moderated), moderator, and outcome variable (dependent variable) are computed from the implied covariance matrix returned by lavaan::lavInspect(). Therefore, models fitted to data sets with missing data (e.g., with missing = "fiml") are also supported.

Partial standardization can also be requested. For example, standardization can be requested for only the focal variable and the outcome variable.

There are two ways to request nonparametric bootstrap confidence interval. First, the model is fitted with se = "boot" or se = "bootstrap" in lavaan. The stored bootstrap estimates will then be retrieved automatically to compute the standardized moderation effect. This is the most efficient approach if the bootstrap confidence intervals are also needed for other parameters in the model. Bootstrapping needs to be done only once.

Second, bootstrap estimates can be generated by manymome::do_boot(). The output is then supplied through the argument boot_out. Bootstrapping also only needs to be done once. This approach is appropriate when bootstrapping confidence intervals are not needed for other model parameters, or another type of confidence interval is needed when fitting the model. Please refer to the help page of manymome::do_boot() on how to use this function.

In both approaches, the standard deviations are also computed in each bootstrap samples. This ensures that the sampling variability of the standard deviations is also taken into account in computing the bootstrap confidence interval of the standardized moderation effect.

Note on the differences between the current version (Version 0.2.7.5 or later) and previous versions (0.2.7.4 and before)

In older versions, stdmod_lavaan() does not allow for partial standardization. Moreover, it uses boot::boot() to do the bootstrapping. Even with the same seed, the results from boot::boot() are not identical to those of lavaan with se = "boot" because they differ in the way the indices of resampling are generated. Both approaches are correct, They just use the generated random numbers differently. To have results consistent with those from lavaan, the current version of stdmod_lavaan() adopts a resampling algorithm identical to that of lavaan. Last, in older versions, stdmod_lavaan() does bootstrapping every time it is called. This is inefficient.

The bootstrapping results in the current version are not identical to those in older versions due to the use of different resampling algorithms, To reproduce previous results, set use_old_version to TRUE

References

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. doi:10.1037/hea0001188

Author

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

Examples


#Load a test data of 500 cases

dat <- test_mod1
library(lavaan)
mod <-
"
med ~ iv + mod + iv:mod + cov1
dv ~ med + cov2
"

fit <- sem(mod, dat)

# Compute the standardized moderation effect
out_noboot <- stdmod_lavaan(fit = fit,
                            x = "iv",
                            y = "med",
                            w = "mod",
                            x_w = "iv:mod")
out_noboot
#> 
#> 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

# Compute the standardized moderation effect and
# its percentile confidence interval using
# nonparametric bootstrapping
# Fit the model with bootstrap confidence intervals
# At least 2000 bootstrap samples should be used
# in real research. 50 is used here only for
# illustration.
fit <- sem(mod, dat, se = "boot", bootstrap = 50,
           iseed = 89574)
out_boot <- stdmod_lavaan(fit = fit,
                          x = "iv",
                          y = "med",
                          w = "mod",
                          x_w = "iv:mod",
                          boot_ci = TRUE)
out_boot
#> 
#> 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 0.033 7.725      0    0.173    0.297
#> Standardized med  ~ iv:mod 0.440    NA    NA     NA    0.316    0.520
#> 
#> 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: 50
#> 
#> 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'.