# higher order interactions

    library(modsem)

As of yet, the `modsem` package does not support using the interaction operator `:` between two higher order constructs. However, you can still attempt to estimate the interaction effect between two higher order constructs by specifying the interaction term in models using the product indicator approaches (higher order constructs are not supported at all in the `lms` and `qml` approaches yet). The `modsem` package will then attempt to estimate the interaction effect between the two higher order constructs.

# Interaction between two higher order constructs

WARNING: Please note that the literature on higher order interactions in product indicator approaches is virtually non-existant, and you will likely need to experiment with different approaches to find one that works. As well as experiment with adding constraints to the model.

In `modsem` there are two datasets which are variants of the Theory of Planned Behaviour (`TPB`) dataset. The `TPB_2SO` contains two second order constructs, `INT` (intention) which is a second order construct of `ATT` (attitude) and `SN` (subjective norm), and `PBC` (perceived behavioural control) which is a second order construct of `PC` (perceived control) and `PB` (perceived behaviour).

    tpb <- '
      # First order constructs
      ATT =~ att1 + att2 + att3
      SN  =~ sn1 + sn2 + sn3
      PB =~ pb1 + pb2 + pb3
      PC =~ pc1 + pc2 + pc3
      BEH =~ b1 + b2

      # Higher order constructs
      INT =~ ATT + SN
      PBC =~ PC + PB

      # Higher order interaction
      INTxPBC =~ ATT:PC + ATT:PB + SN:PC + SN:PB

      # Structural model
      BEH ~ PBC + INT + INTxPBC
    '

    est_ca <- modsem(tpb, data = TPB_2SO, method = "ca")
    summary(est_ca)

    est_dblcent <- modsem(tpb, data = TPB_2SO, method = "dblcent")
    summary(est_dblcent)

# Interaction between a first order and a higher order construct

In the `TPB_1SO` dataset, the `INT` construct is a second order construct of `ATT`, `SN` and `PBC`. In this example, we will estimate the interaction between the `INT` (higher order construct) and `PBC` (first order construct).

    tpb <- '
      # First order constructs
      ATT =~ att1 + att2 + att3
      SN  =~ sn1 + sn2 + sn3
      PBC =~ pbc1 + pbc2 + pbc3
      BEH =~ b1 + b2

      # Higher order constructs
      INT =~ ATT + PBC + SN

      # Higher order interaction
      INTxPBC =~ ATT:PBC + SN:PBC + PBC:PBC

      # Structural model
      BEH ~ PBC + INT + INTxPBC
    '

    est_ca <- modsem(tpb, data = TPB_1SO, method = "ca")
    summary(est_ca)

    est_dblcent  <- modsem(tpb, data = TPB_1SO, method = "dblcent")
    summary(est_dblcent)