---
title: "Higher Order Models"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Higher Order Models}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup}
library(plssem)
```

# Higher Order Constructs

It is possible to estimate models with second order construcst with the `pls()` function,
using the two-stage approach. Here we see an example using the `TPB_2SO` dataset,
from the `modsem` package.
The model below contains two second order latent variables,
`INT` (intention) which is a second order latent variable of `ATT` (attitude) and `SN` (subjective norm),
and `PBC` (perceived behavioural control) which is a second order latent variable of
`PC` (perceived control) and `PB` (perceived behaviour).

```{r}
library(modsem)

tpb_2so <- '
  # First order latent variables
  ATT =~ att1 + att2 + att3
  SN  =~ sn1 + sn2 + sn3
  PB =~ pb1 + pb2 + pb3
  PC =~ pc1 + pc2 + pc3
  BEH =~ b1 + b2

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

  # Structural model
  BEH ~ PBC + INT + INT:PBC
'

fit <- pls(tpb_2so, data = TPB_2SO, bootstrap = TRUE, boot.R = 50)
summary(fit)
```