layout: post title: "How Many Factors to Retain in Factor Analysis" author: Dominique Makowski author_web: https://dominiquemakowski.github.io/ date: 2018-05-24 summary: The method agreement procedure to find how many factors to retain in factor analysis.
When running a factor analysis, one often needs to know how many components / latent variables to retain. Fortunately, many methods exist to statistically answer this question. Unfortunately, there is no consensus on which method to use. Therefore, the n_factors()
function, available in the psycho package, performs the method agreement procedure: it runs all the routines and returns the number of factors with the highest consensus.
# devtools::install_github("neuropsychology/psycho.R") # Install the last psycho version if needed
library(tidyverse)
library(psycho)
results <- attitude %>%
psycho::n_factors()
print(results)
## The choice of 1 factor is supported by 5 (out of 9; 55.56%) methods (Optimal Coordinates, Acceleration Factor, Parallel Analysis, Velicer MAP, VSS Complexity 1).
We can have an overview of all values by using the summary
method.
| n.Factors| n.Methods| Eigenvalues| Cum.Variance| |----------:|----------:|------------:|-------------:| | 1| 5| 3.72| 0.53| | 2| 3| 1.14| 0.69| | 3| 1| 0.85| 0.81| | 4| 0| 0.61| 0.90| | 5| 0| 0.32| 0.95| | 6| 0| 0.22| 0.98| | 7| 0| 0.14| 1.00|
And, of course, plot it :)
plot(results)
The plot shows the number of methods (in yellow), the Eigenvalues (red line) and the cumulative proportion of explained variance (blue line).
For more details, we can also extract the final result (the optimal number of factors) for each method:
summary(results)
| Method | n_optimal| |:-------------------------------|-----------:| | Optimal Coordinates | 1| | Acceleration Factor | 1| | Parallel Analysis | 1| | Eigenvalues (Kaiser Criterion) | 2| | Velicer MAP | 1| | BIC | 2| | Sample Size Adjusted BIC | 3| | VSS Complexity 1 | 1| | VSS Complexity 2 | 2|
We can also provide a correlation matrix, as well as changing the rotation and the factoring method.
df <- psycho::affective
cor_mat <- psycho::correlation(df)
cor_mat <- cor_mat$values$r
results <- cor_mat %>%
psycho::n_factors(rotate = "oblimin", fm = "mle", n=nrow(df))
print(results)
## The choice of 2 factors is supported by 5 (out of 9; 55.56%) methods (Parallel Analysis, Eigenvalues (Kaiser Criterion), BIC, Sample Size Adjusted BIC, VSS Complexity 2).
plot(results)
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