Consider a classical mediation setup with three variables: Y is the dependent variable, X is the predictor, and M is a mediator. For illustration, we create a toy dataset containing these three variables, and fit a path analysis model that includes the direct effect of X on Y and the indirect effect of X on Y via M.

X <- rnorm(100)
M <- 0.5*X + rnorm(100)
Y <- 0.7*M + rnorm(100)
Data <- data.frame(X = X, Y = Y, M = M)
model <- ' # direct effect
             Y ~ c*X
           # mediator
             M ~ a*X
             Y ~ b*M
           # indirect effect (a*b)
             ab := a*b
           # total effect
             total := c + (a*b)
fit <- sem(model, data = Data)
lavaan 0.6-11 ended normally after 1 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                         5
  Number of observations                           100
Model Test User Model:
  Test statistic                                 0.000
  Degrees of freedom                                 0

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

                   Estimate  Std.Err  z-value  P(>|z|)
  Y ~                                                 
    X          (c)    0.036    0.104    0.348    0.728
  M ~                                                 
    X          (a)    0.474    0.103    4.613    0.000
  Y ~                                                 
    M          (b)    0.788    0.092    8.539    0.000

                   Estimate  Std.Err  z-value  P(>|z|)
   .Y                 0.898    0.127    7.071    0.000
   .M                 1.054    0.149    7.071    0.000

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)
    ab                0.374    0.092    4.059    0.000
    total             0.410    0.125    3.287    0.001

The example illustrates the use of the ":=" operator in the lavaan model syntax. This operator ‘defines’ new parameters which take on values that are an arbitrary function of the original model parameters. The function, however, must be specified in terms of the parameter labels that are explicitly mentioned in the model syntax. By default, the standard errors for these defined parameters are computed by using the so-called Delta method. As with other models, bootstrap standard errors can be requested simply by specifying se = "bootstrap" in the fitting function.