---
title: "Multilevel Models with plssem"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Multilevel Models with plssem}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  eval = identical(Sys.getenv("IN_PKGDOWN"), "true")
)

library(plssem)
```

This vignette shows examples of two-level (multilevel) models, with and without
random slopes, with both continuous and ordinal data. Two-level models are
specified with separate models for the within (`level: 1`) and between
(`level: 2`) levels, and the cluster variable is given by the `cluster` argument.

## Two-Level Model

```{r two-level-syntax}
two_level_model <- "
  level: 1
    fw =~ y1 + y2 + y3
    fw ~ x1 + x2 + x3
  level: 2
    fb =~ y1 + y2 + y3
    fb ~ w1 + w2
"
```

### Continuous Indicators

```{r two-level-continuous, message=FALSE, warning=FALSE}
fit_two_level_cont <- pls(
  two_level_model,
  data      = randomSlopes,
  cluster   = "cluster",
  bootstrap = TRUE,
  boot.R    = 50
)
summary(fit_two_level_cont)
```

### Ordered Indicators

```{r two-level-ordered, message=FALSE, warning=FALSE}
fit_two_level_ord <- pls(
  two_level_model,
  data      = randomSlopesOrdered,
  cluster   = "cluster",
  bootstrap = TRUE,
  boot.R    = 50,
  ordered   = colnames(randomSlopesOrdered) # explicitly specify variables as ordered
)
summary(fit_two_level_ord)
```

## Random Slopes Model

Random slopes are specified with `rv()` modifiers at level 1, where the random
slopes (here `s1` and `s2`) are variables at level 2.

```{r slopes-syntax}
slopes_model <- '
  level: 1
    fw =~ y1 + y2 + y3
    fw ~ rv("s1")*x1 + rv("s2")*x2 + x3
  level: 2
    fb =~ y1 + y2 + y3
    fb ~ w1 + w2
    # the random slopes are latent variables at the between level
    s1 + s2 ~ w1 + w2
'
```

### Continuous Indicators

```{r slopes-continuous, message=FALSE, warning=FALSE}
fit_slopes_cont <- pls(
  slopes_model,
  data      = randomSlopes,
  cluster   = "cluster",
  bootstrap = TRUE,
  boot.R    = 50
)
summary(fit_slopes_cont)
```

### Ordered Indicators

```{r slopes-ordered, message=FALSE, warning=FALSE}
fit_slopes_ord <- pls(
  slopes_model,
  data      = randomSlopesOrdered,
  cluster   = "cluster",
  bootstrap = TRUE,
  boot.R    = 50,
  ordered   = colnames(randomSlopesOrdered) # explicitly specify variables as ordered
)
summary(fit_slopes_ord)
```