---
title: "higher order interactions"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{higher order interactions}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
EVAL_DEFAULT <- FALSE
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  eval = EVAL_DEFAULT
)
```

```{r setup}
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).

```{r}
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).

```{r}
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)
```