This document demonstrates how to use stdmod_lavaan() to compute the standardized moderation effect in a path model fitted by lavaan::sem().
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 0.488This 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
"
fit <- sem(mod, test_mod1, fixed.x = FALSE)
summary(fit)
#> lavaan 0.6-12 ended normally after 1 iterations
#>
#> 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 0.000The 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 0.55After 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.fit_iv_mod_std <- stdmod_lavaan(fit = fit,
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 NAThe 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.
Only two additional arguments are required:
boot_ci: Set it to TRUE to request nonparametric bootstrap confidence interval.R: Set the number of bootstrap samples. Should be at least 2000.However, the function can be slow if the model takes some time to fit because the model will be fitted R times. If the model cannot be fitted quickly, we highly suggest using parallel processing. This can be requested using arguments in boot::boot() because stdmod_lavaan() internally calls boot::boot() to do the bootstrapping. These are the two possible arguments to use for parallel processing:
parallel: Can be "no", "multicore", or "snow". See boot::boot() on which one to use. The following example uses "snow".ncpus: The number of processors to use. Let boot::boot() decides or set it based on the configuration of the computer.set.seed(860947)
fit_iv_mod_std_ci <- stdmod_lavaan(fit = fit,
x = "iv",
y = "med",
w = "mod",
x_w = "iv:mod",
boot_ci = TRUE,
R = 2000,
parallel = "snow",
ncpus = 6)
fit_iv_mod_std_ci#>
#> Call:
#> stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod",
#> boot_ci = TRUE, R = 100)
#>
#> 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 0.296 0.515
#>
#> Confidence interval of standardized moderation effect:
#> - Level of confidence: 95%
#> - Bootstrapping Method: Nonparametric
#> - Type: Percentile
#> - Number of bootstrap samples requests: 100
#> - Number of bootstrap samples with valid results: 100The 95% confidence interval of the standardized moderation effect is 0.296 to 0.515.
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. Advance online publication. Health Psychology. https://doi.org/10.1037/hea0001188.