---
title: "Alignment Invariance Workflow"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Alignment Invariance Workflow}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

# Alignment Invariance Workflow

Alignment optimization can be run from item-level data or from loading and
intercept matrices. Matrix input is useful for compact reproducible examples.

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

```{r alignment-matrices}
lambda <- matrix(
  c(0.70, 0.80, 0.75,
    0.72, 0.78, 0.74),
  nrow = 2,
  byrow = TRUE
)
nu <- matrix(
  c(0.00, 0.00, 0.00,
    0.10, 0.05, 0.08),
  nrow = 2,
  byrow = TRUE
)
```

```{r alignment-run, eval = FALSE}
alignment <- inv_align_auto(lambda = lambda, nu = nu, language = "eng")
summary(alignment)
```

When item-level data are available, use `data` and `group` instead of `lambda`
and `nu`.