---
title: "Example 2: Assessing Factor Simplicity from psych::fa() Output"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Example 2: Assessing Factor Simplicity from psych::fa() Output}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(facomplex)
library(lavaan)
library(psych)
if (!requireNamespace("psych", quietly = TRUE)) {
  knitr::opts_chunk$set(eval = FALSE)
}
if (!requireNamespace("lavaan", quietly = TRUE)) {
  knitr::opts_chunk$set(eval = FALSE)
}
```

# Example 2: Assessing Factor Simplicity from `psych::fa()` Output

This example demonstrates how to compute factor simplicity and complexity indices using loadings obtained from an exploratory factor analysis conducted via `psych::fa()`.

## Step 1: Load data from `psych`

We use the `bfi` dataset available in the `psych` package.

```{r}
data(bfi, package = "psych")
```

## Step 2: Fit a 2-factor exploratory model

We fit an EFA model with 2 factors using oblimin rotation and unweighted least squares (ULS) estimation.

```{r}
fa.output <- psych::fa(bfi[, 1:10], 
                       nfactors = 2, 
                       rotate = "oblimin",
                       fm = "uls")
```

## Step 3: View and save the loading matrix

We inspect the factor loadings and convert them to a standard data frame for analysis.

```{r}
unclass(fa.output$loadings)
fa.load <- as.data.frame(unclass(fa.output$loadings))
```

## Step 4: Compute complexity and simplicity indices

We now use the `facomplex` package to compute various measures of factor simplicity and complexity.

### Hofmann Index

```{r}
Hofmann(fa.load)
```

### Bentler’s Simplicity Index

```{r}
BSI(fa.load)
```

### Kaiser-Cerny (KC) Criterion

```{r}
KC(data = fa.load, b = 4)
```

### Factor Simplicity Index (FSI)

We define the target items for each factor to compute the total, factor-level, and item-level simplicity.

```{r}
simload(data = fa.load, 
    items_target = list(
      ULS1 = c(6,7,8,9,10), 
      ULS2 = c(1,2,3,4,5)
    ))
```

------------------------------------------------------------------------

This example shows how to apply `facomplex` to factor solutions derived from classical exploratory methods, making it an accessible tool for researchers working with `psych::fa()` and other traditional EFA approaches.