4 Demonstration
4.1 Multiple Imputation
This data set, with missing data introduced, will be used for illustration.
library(manymome)
dat <- data_med
dat[1, 1] <- dat[2, 3] <- dat[3, 5] <- dat[4, 3] <- dat[5, 2] <- NA
head(dat)
#> x m y c1 c2
#> 1 NA 17.89644 20.73893 1.426513 6.103290
#> 2 8.331493 17.92150 NA 2.940388 3.832698
#> 3 10.327471 17.83178 22.14201 3.012678 NA
#> 4 11.196969 20.01750 NA 3.120056 4.654931
#> 5 11.887811 NA 28.47312 4.440018 3.959033
#> 6 8.198297 16.95198 20.73549 2.495083 3.763712It has one predictor (x), one mediator (m), one outcome variable (y), and two control variables (c1 and c2).
The following simple mediation model with two control variables (c1 and c2) will be fitted:
plot of chunk do_mc_lavaan_mi_draw_model
In practice, the imputation model needs to be decided and checked (van Buuren, 2018). For the sake of illustration, we just use the default of mice::mice() to do the imputation:
library(mice)
#>
#> Attaching package: 'mice'
#> The following object is masked from 'package:stats':
#>
#> filter
#> The following objects are masked from 'package:base':
#>
#> cbind, rbind
set.seed(26245)
out_mice <- mice(dat, m = 5, printFlag = FALSE)
dat_mi <- complete(out_mice, action = "all")
# The first imputed dataset
head(dat_mi[[1]])
#> x m y c1 c2
#> 1 9.762412 17.89644 20.73893 1.426513 6.103290
#> 2 8.331493 17.92150 25.68452 2.940388 3.832698
#> 3 10.327471 17.83178 22.14201 3.012678 3.969419
#> 4 11.196969 20.01750 24.87107 3.120056 4.654931
#> 5 11.887811 20.82502 28.47312 4.440018 3.959033
#> 6 8.198297 16.95198 20.73549 2.495083 3.763712
# The last imputed dataset
head(dat_mi[[5]])
#> x m y c1 c2
#> 1 8.301276 17.89644 20.73893 1.426513 6.103290
#> 2 8.331493 17.92150 22.93143 2.940388 3.832698
#> 3 10.327471 17.83178 22.14201 3.012678 6.238426
#> 4 11.196969 20.01750 26.90840 3.120056 4.654931
#> 5 11.887811 20.82502 28.47312 4.440018 3.959033
#> 6 8.198297 16.95198 20.73549 2.495083 3.7637124.2 Fit a Model by semTools::sem.mi()
We then fit the model by semTools::sem.mi():
library(semTools)
#>
#> ###############################################################################
#> This is semTools 0.5-6
#> All users of R (or SEM) are invited to submit functions or ideas for functions.
#> ###############################################################################
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit_lavaan <- sem.mi(model = mod,
data = dat_mi)
summary(fit_lavaan)
#> lavaan.mi object based on 5 imputed data sets.
#> See class?lavaan.mi help page for available methods.
#>
#> Convergence information:
#> The model converged on 5 imputed data sets
#>
#> Rubin's (1987) rules were used to pool point and SE estimates across 5 imputed data sets, and to calculate degrees of freedom for each parameter's t test and CI.
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Regressions:
#> Estimate Std.Err t-value df P(>|t|)
#> m ~
#> x 0.891 0.080 11.117 Inf 0.000
#> c1 0.162 0.077 2.118 5182.950 0.034
#> c2 -0.114 0.102 -1.117 6281.324 0.264
#> y ~
#> m 0.736 0.251 2.935 3642.608 0.003
#> x 0.616 0.298 2.065 383.680 0.040
#> c1 0.181 0.193 0.939 Inf 0.348
#> c2 -0.156 0.254 -0.616 3050.071 0.538
#>
#> Variances:
#> Estimate Std.Err t-value df P(>|t|)
#> .m 0.682 0.098 6.959 Inf 0.000
#> .y 4.151 0.597 6.958 8812.141 0.0004.3 Generate Monte Carlo Estimates
The other steps are identical to those illustrated in vignette("do_mc"). It and related functions will use the pooled point estimates and variance-covariance matrix when they detect that the model is fitted by semTools::sem.mi() or semTools::runMI() (i.e., the fit object is of the class lavaan.mi).
We call do_mc() on the output of semTools::sem.mi() to generate the Monte Carlo 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.
mc_out_lavaan <- do_mc(fit = fit_lavaan,
R = 10000,
seed = 4234)
#> Stage 1: Simulate estimates
#> Stage 2: Compute implied statisticsUsually, just three arguments are needed:
fit: The output oflavaan::sem().R: The number of Monte Carlo replications. Should be at least 10000 in real research.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 not used. However, the time taken is rarely long because there is no need to refit the model many times.
For the structure of the output, please refer to vignette("do_mc").
4.4 Using the Output of do_mc() in Other Functions of manymome
When calling indirect_effect() or cond_indirect_effects(), the argument mc_out can be assigned the output of do_mc(). They will then retrieve the stored simulated estimates to form the Monte Carlo confidence intervals, if requested.
out_lavaan <- indirect_effect(x = "x",
y = "y",
m = "m",
fit = fit_lavaan,
mc_ci = TRUE,
mc_out = mc_out_lavaan)
out_lavaan
#>
#> == Indirect Effect ==
#>
#> Path: x -> m -> y
#> Indirect Effect 0.656
#> 95.0% Monte Carlo CI: [0.219 to 1.130]
#>
#> Computation Formula:
#> (b.m~x)*(b.y~m)
#> Computation:
#> (0.89141)*(0.73569)
#>
#> Monte Carlo confidence interval with 10000 replications.
#>
#> Coefficients of Component Paths:
#> Path Coefficient
#> m~x 0.891
#> y~m 0.736Reusing the simulated estimates can ensure that all analysis with Monte Carlo confidence intervals are based on the same set of simulated estimates.