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 1000