---
title: "interactions with ordered data"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{interactions with ordered data}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

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

```{r setup}
library(modsem)
set.seed(2938472)
```

`modsem` implements a Monte-Carlo correction for LMS and QML
models with ordinal data. Here we refer to these informally as
`MC-LMS-ORD` and `MC-QML-ORD`.

The `MC-LMS-ORD` and `MC-QML-ORD` algorithms are based on 
[Slupphaug, Mehmetoglu, and Mittner (2026)](https://osf.io/preprints/psyarxiv/fwzj6_v1)
For a more direct implementation of the original algorithm, we
recommend checking out the [`plssem` package](https://CRAN.R-project.org/package=plssem).

# Example

Here we ordinalize the data in the `oneInt` dataset.

```{r}
ordinalize <- function(x, probs = c(0, 0.35, 0.7, 1)) {
  x <- (x - mean(x)) / sd(x)
  cut(
    x,
    breaks = stats::quantile(x, probs = probs),
    include.lowest = TRUE,
    ordered_result = TRUE
  )
}

oneIntOrd <- as.data.frame(lapply(oneInt, ordinalize))
```

Now we can estimate our model, indicating which variables are ordinal, using
the `ordered=` argument.

```{r}
model <- "
  X =~ x1 + x2 + x3
  Z =~ z1 + z2 + z3
  Y =~ y1 + y2 + y3

  Y ~ X + Z + X:Z
"

fit_lms_ord <- modsem(
  model,
  data = oneIntOrd,
  method = "lms",
  ordered = colnames(oneIntOrd)
)

summary(fit_lms_ord)
```