Choosing the number of factors (nfactors = 2 in your code) is one of the most critical decisions in factor analysis. This choice is based on the structure of the data and certain criteria aimed at identifying how many factors best represent the underlying relationships in the dataset. Here's how to approach it:
Common Methods for Choosing the Number of Factors:
1. Kaiser Criterion (Eigenvalues > 1):
- The Kaiser criterion suggests retaining factors with eigenvalues greater than 1. This is because an eigenvalue represents the amount of variance explained by a factor. If the eigenvalue is greater than 1, that factor explains more variance than a single observed variable.
- You can check the eigenvalues by running a Principal Component Analysis (PCA), which helps reveal how much variance is explained by each component.
pca <- principal(data, nfactors = ncol(data), rotate = "none")
print(pca$values) # Check eigenvalues
If only two eigenvalues are greater than 1, then 2 factors might be a reasonable choice.
2. Scree Plot:
- A scree plot is a graphical representation of the eigenvalues against the number of factors. The idea is to look for the "elbow" in the plot, where the drop in eigenvalues starts to level off. The point just before the leveling off indicates the number of factors to retain.
If you see a sharp drop after the second factor and the remaining factors contribute much less, that suggests retaining 2 factors.
3. Parallel Analysis:
- Parallel analysis compares the eigenvalues from your dataset with those from randomly generated data. The idea is to retain only the factors that have higher eigenvalues than the corresponding random factors.
install.packages("psych")
library(psych)
fa.parallel(data)
This analysis suggests the number of factors by showing the comparison graphically.
4. Cumulative Variance Explained:
- Another rule of thumb is to retain enough factors to explain a large portion of the total variance in the data (usually 70-80%).
- You can look at the cumulative variance explained by the factors and decide how many factors to keep based on this threshold.
5. Interpretability:
- Even if statistical criteria suggest multiple factors, sometimes fewer factors might be preferred if they result in more interpretable factors. The factors retained should make logical sense within the context of your biological dataset.
Why nfactors = 2 in your case?
- If after applying these criteria (e.g., eigenvalues > 1, scree plot, and interpretability), you observe that 2 factors explain a significant portion of the variance and make sense with respect to the underlying data, you would choose nfactors = 2.
- For instance, if you have ecological data with variables like pH, nitrate, and phosphate, you might find that these two factors reflect broader environmental conditions such as "Soil Composition" and "Nutrient Content."
Example of How to Choose the Number of Factors
1. Run PCA to check eigenvalues:
pca <- principal(data, nfactors = ncol(data), rotate = "none")
print(pca$values)
2. Plot the Scree Plot to find the elbow:
plot(pca$values, type = "b", main = "Scree Plot", ylab = "Eigenvalues", xlab = "Number of Factors")
3. Use Parallel Analysis to compare eigenvalues to random data:
fa.parallel(data)
Once you've reviewed the results, you'll have a strong basis for choosing the number of factors.
Conclusion:
Choosing the number of factors in factor analysis is a critical step that directly impacts the interpretation of underlying data structures. Methods such as the Kaiser criterion, scree plots, parallel analysis, and cumulative variance provide robust statistical guidance. Ultimately, the choice should also consider the interpretability of the factors in the context of your biological dataset. By using a combination of these approaches, you can confidently select the optimal number of factors to represent your data effectively and draw meaningful insights.
Tags:
Bio Statistics