devami/factorana.qmd at main · KODAQS/devami · GitHub

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---
title: "Exploratory factor analysis (principal axis factoring)"
format: html
author:
    - Melanie Viola Partsch
    - Katharina Groskurth
    - Matthias Blümke
    - Isabelle Schmidt
keywords:
  - Survey Data
  - Measurement
  - Validity
license: "CC BY-NC 4.0"
citation:
    type: "document"
    title: |
        R Code for the Development and Validation of Measurement Instruments in the Social Sciences: Psychometric Analyses (Dimensionality, Reliability, Measurement Invariance)
    container-title: GESIS, Cologne. Data File Version 1.0.0,
    author:
      - Melanie Viola Partsch
      - Katharina Groskurth
      - Matthias Blümke
      - Isabelle Schmidt
    doi: 10.7802/1.1982
    issued: 2020
---

Load the required packages
```{r}
#| label: setup
library(rio)
library(psych)

packageVersion("rio")
packageVersion("psych")
```

Read the example data.

```{r}
#| label: read_data
example1 <- rio::import("example1.sav")
```


Build character vector with variable names for use below

```{r}
ext <- c(
    "bfi2_1", "bfi2_6", "bfi2_11R", "bfi2_16R", "bfi2_21", "bfi2_26R",
    "bfi2_31R", "bfi2_36R", "bfi2_41", "bfi2_46", "bfi2_51R",
    "bfi2_56"
)
```


## Conduct parallel analysis, print eigen values and display screeplot

Function with arguments specified below corresponds to default:

- Eigenvalues are found based on the communalities of a one factor minres EFA solution;

- 20 resampled or simulated random datasets are used and the empirical eigen values are compared to the mean of the resampled or simulated eigenvalues;

- suitable for the use of continuous data

Alternatives to default settings:
- Find eigenvalues based on iterating for communalities starting with squared multiple correlations: specify `fm = NULL`, `nfactors = NULL`, `SMC = TRUE` (suggested number of factors reflects both major and minor factors; thus, suggested number of factors usually higher than when using default settings)

- Increase number of resampled or simulated datasets (e.g., to `n.iter = 100`) and choose a quantile of resampled/simulated data to compare the empirical eigenvalues against (e.g., `quant = .95`; the suggested number of factors likely might decrease with a high value for `quant`)

- When using categorical data: specify `cor = "poly"`

```{r}
fa.parallel(example1[ext],
    fa = "fa",
    fm = "minres", nfactors = 1, SMC = F,
    n.iter = 20, # quant = .95,
    cor = "cor"
)$fa.values
```

## Conduct EFA (principal axis factoring (PAF))

Function below specifies the following:
- extraction of 3 factors;

- orthogonal rotation using "varimax" rotation;

- using regression to find factor scores;

- using squared multiple correlations as initial communality estimates;

- suitable for the use of continuous data

Alternatives to default settings:

- no rotation (i.e., initial orthogonal solution): specify `rotate = "none"`

- oblique rotation: specify `rotation = "oblimin"` (corresponds to default) or `rotation = "promax"` (the latter includes Kaiser normalization)

- obtain oblique factor scores: use ten Berge's correlation-preserving approach and the pattern matrix to find factor scores: specify `scores = "tenBerge"`, `oblique.scores = TRUE`

- When using categorical data: specify `cor = "poly"`

```{r}
myPAF <- fa(example1[ext],
    fm = "pa",
    nfactors = 3,
    rotate = "varimax",
    scores = "regression", oblique.scores = F,
    SMC = TRUE,
    cor = "cor"
)
myPAF
```