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Enjoy this brief demonstration of the fit latent data module (i.e., a simple mediation model).
Also, please see Fit Observed Data.
# Number of observations
n <- 1000
# Coefficient for a path (x -> m)
a <- .75
# Coefficient for b path (m -> y)
b <- .80
# Coefficient for total effect (x -> y)
c <- .60
# Coefficient for indirect effect (x -> m -> y)
ab <- a * b
# Coefficient for direct effect (x -> y)
cd <- c - ab
# Compute x, m, y values
set.seed(100)
x <- rnorm(n)
m <- a * x + sqrt(1 - a^2) * rnorm(n)
eps <- 1 - (cd^2 + b^2 + 2*a * cd * b)
y <- cd * x + b * m + eps * rnorm(n)
data <- data.frame(y = y,
x = x,
m = m)model <- "
# direct effect
y ~ c*x
# mediator
m ~ a*x
y ~ b*m
# indirect effect (a*b)
ab := a*b
# total effect
cd := c + (a*b)"
fit <- lavaan::sem(model, data = data)
lavaan::summary(fit)
#> lavaan 0.6-10 ended normally after 1 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 5
#>
#> Number of observations 1000
#>
#> Model Test User Model:
#>
#> Test statistic 0.000
#> Degrees of freedom 0
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> y ~
#> x (c) 0.022 0.018 1.242 0.214
#> m ~
#> x (a) 0.759 0.020 38.118 0.000
#> y ~
#> m (b) 0.752 0.018 40.944 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .y 0.142 0.006 22.361 0.000
#> .m 0.421 0.019 22.361 0.000
#>
#> Defined Parameters:
#> Estimate Std.Err z-value P(>|z|)
#> ab 0.570 0.020 27.899 0.000
#> cd 0.593 0.019 31.357 0.000bayesian.fit <- bfw::bfw(project.data = data,
latent = "x,m,y",
saved.steps = 50000,
latent.names = "Independent,Mediator,Dependent",
additional = "indirect <- xm * my , total <- xy + (xm * my)",
additional.names = "AB,C",
jags.model = "fit",
silent = TRUE)
round(bayesian.fit$summary.MCMC[,3:7],3)
#> Mode ESS HDIlo HDIhi n
#> beta[2,1]: Mediator vs. Independent 0.760 48988 0.720 0.799 1000
#> beta[3,1]: Dependent vs. Independent 0.024 13042 -0.012 0.058 1000
#> beta[3,2]: Dependent vs. Mediator 0.751 13230 0.715 0.786 1000
#> indirect[1]: AB 0.571 21431 0.531 0.611 1000
#> total[1]: C 0.591 49074 0.555 0.630 1000biased.sigma <-matrix(c(1,1,0,1,1,0,0,0,1),3,3)
set.seed(101)
noise <- MASS::mvrnorm(n=2,
mu=c(200, 300, 0),
Sigma=biased.sigma,
empirical=FALSE)
colnames(noise) <- c("y","x","m")
biased.data <- rbind(data,noise)biased.fit <- lavaan::sem(model, data = biased.data)
lavaan::summary(biased.fit)
#> lavaan 0.6-10 ended normally after 31 iterations
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 5
#>
#> Number of observations 1002
#>
#> Model Test User Model:
#>
#> Test statistic 0.000
#> Degrees of freedom 0
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> y ~
#> x (c) 0.665 0.001 499.371 0.000
#> m ~
#> x (a) 0.004 0.002 1.528 0.127
#> y ~
#> m (b) 0.250 0.018 14.152 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .y 0.320 0.014 22.383 0.000
#> .m 1.028 0.046 22.383 0.000
#>
#> Defined Parameters:
#> Estimate Std.Err z-value P(>|z|)
#> ab 0.001 0.001 1.519 0.129
#> cd 0.666 0.001 457.040 0.000biased.bfit <- bfw::bfw(project.data = data,
latent = "x,m,y",
saved.steps = 50000,
latent.names = "Independent,Mediator,Dependent",
additional = "indirect <- xm * my , total <- xy + (xm * my)",
additional.names = "AB,C",
jags.model = "fit",
run.robust = TRUE,
jags.seed = 101,
silent = TRUE)
round(biased.bfit$summary.MCMC[,3:7],3)
#> Mode ESS HDIlo HDIhi n
#> beta[2,1]: Mediator vs. Independent 0.763 31178 0.721 0.799 1000
#> beta[3,1]: Dependent vs. Independent 0.022 7724 -0.014 0.057 1000
#> beta[3,2]: Dependent vs. Mediator 0.751 7772 0.714 0.786 1000
#> indirect[1]: AB 0.572 12913 0.531 0.610 1000
#> total[1]: C 0.590 31362 0.557 0.631 1000These 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.