R中斜交旋转探索性因子分析后，如何提供各因子解释方差比例？

Hey there! I totally get the confusion—oblique rotation muddles the variance explained metrics a bit because factors are no longer independent, unlike orthogonal rotations like Varimax. Let's break down exactly what you need to report for your reviewer, using the psych package's output.

Key Background: Oblique vs. Orthogonal Rotation #

• In orthogonal rotation, factors are uncorrelated, so the variance each factor explains is entirely unique—summing their variance proportions gives the total variance explained by all factors.
• In oblique rotation (like Oblimin or Promax), factors share variance (they’re correlated), so we have two distinct ways to measure "variance explained per factor":
  1. Variance relative to the total variance of all variables (each variable is standardized to variance = 1, so total variance equals the number of variables)
  2. Variance relative to the total common variance (the sum of variance all variables share with the factors, i.e., sum of variable communalities h2)

What to Pull from psych's fa() Output #

When you run your EFA with oblique rotation, for example:

library(psych)
# Example EFA code (adjust to your data/method)
efa_results <- fa(your_dataset, nfactors = 3, rotate = "oblimin", fm = "ml")

Look at the $Vaccounted component of the output—it’s a matrix with critical rows:

1. SS loadings #

This is the sum of squared loadings for each factor. It represents the total variance (including overlap with other factors) that the factor captures from the variables.

2. Proportion Var #

This is SS loadings divided by the total number of variables (since each variable’s variance is 1, total variance = number of variables). This is the percentage of the overall dataset variance explained by each factor.

3. Proportion Explained #

This is SS loadings divided by the sum of all SS loadings (total common variance across factors). This tells you what percentage of the shared variance among variables is accounted for by each factor.

Which One to Report to Your Reviewer? #

• Most reviewers ask for the Proportion Var values—this is the standard "percent of variance explained per factor" relative to the entire dataset.
• Critical note: Since oblique factors overlap, the sum of Proportion Var will not equal the total variance explained by all factors (unlike orthogonal rotation). You must mention this in your manuscript to avoid confusion!
• For thoroughness, you can also report Proportion Explained (label it clearly as "proportion of common variance explained")—this helps contextualize how much each factor contributes to the shared variance structure.

Example Output Interpretation #

Suppose your efa_results$Vaccounted looks like this:

PA1   PA2   PA3
SS loadings    2.45 1.82 1.11
Proportion Var 0.20 0.15 0.09
Cumulative Var 0.20 0.35 0.44
Proportion Explained 0.41 0.30 0.19
Cumulative Proportion 0.41 0.71 0.90

You’d report: "The three oblique factors explained 20%, 15%, and 9% of the total variance in the dataset, respectively. Relative to the total common variance captured by all factors, the factors accounted for 41%, 30%, and 19% of shared variance."

Quick Tip for SPSS Alignment #

If you need to match SPSS output:

• SPSS’s "Extraction Sums of Squared Loadings" = SS loadings
• SPSS’s "% of Variance" = Proportion Var (multiplied by 100)
• SPSS doesn’t directly report Proportion Explained, but you can calculate it manually if needed.

内容的提问来源于stack exchange，提问作者sophar