I'll help you perform the suitability checks for exploratory factor analysis (EFA) using KMO (Kaiser-Meyer-Olkin) measure of sampling adequacy and Bartlett's test of sphericity. These tests assess whether your data is suitable for factor analysis: KMO should ideally be >0.6 (higher is better, up to 1.0), and Bartlett's test should be significant (p < 0.05) to reject the null hypothesis of an identity matrix.

Assuming you're using R (a common tool for this), I'll provide code using the psych package, which is excellent for EFA. If you're using Python (e.g., via factor_analyzer), let me know for alternative code. You'll need to load your dataset as a data frame (e.g., df) with numeric variables only—exclude categoricals, IDs, etc.

Step 1: Install and Load Required Packages

# Install if needed (run once)
install.packages(c("psych", "GPArotation"))
# Load
library(psych)

Step 2: Prepare Your Data

# Example: Assume your data is in 'df' (replace with your actual dataset)
# df <- read.csv("your_data.csv")  # Load your data here
# Select relevant numeric columns if needed
# df_numeric <- df[, c("var1", "var2", "var3")]  # Replace with your variable names
# Check for missing values and handle if necessary
sum(is.na(df_numeric))  # Should be 0 for clean analysis

Step 3: Run KMO and Bartlett's Test

# Perform the tests
suitability <- KMO(df_numeric)  # KMO for individual and overall MSA
cortest.bartlett(df_numeric)    # Bartlett's test (uses correlation matrix)

• KMO Output:


• Overall MSA (measure of sampling adequacy): Aim for >0.6 (0.8+ is great).


• Individual MSAs: Variables with <0.5 may need removal—rerun after excluding them.


• Bartlett's Test Output:


• Chi-square statistic and p-value: Significant p < 0.05 indicates the correlation matrix is not an identity matrix (suitable for EFA). If p > 0.05, your data may have few factors or issues like multicollinearity.

Example Output Interpretation

# Demo with built-in 'bfi' dataset (personality traits)
data(bfi)  # Load sample data from psych
bfi_numeric <- bfi[, 1:25]  # Select agreeableness, etc. (exclude keys/gender/education)
# Run tests
KMO(bfi_numeric)

Sample KMO output:

Kaiser-Meyer-Olkin MSA Sampling Adequacy 
Call: KMO(r = r)
MSA for individual: 
 A1  A2  A3  A4  A5  ... 
0.82 0.75 0.68 0.71 0.69 ...
Overall MSA =  0.85

Interpretation: Overall MSA=0.85 (meritorious—proceed). Remove any variable with MSA <0.5 if present.

Sample Bartlett's output:

Bartlett test of Sphericity 
Call: cortest.bartlett(r = r, n = n)
    X-squared   df      p.value     
4.23e+03    190    < 2.22e-16  # Highly significant (p << 0.05)

Interpretation: Significant—data is suitable.

Next Steps If Suitable

# Example EFA with 3 factors (determine number via scree plot or eigenvalues >1)
fa_result <- fa(df_numeric, nfactors=3, rotate="varimax", fm="ml")
print(fa_result)
fa.diagram(fa_result)  # Visualize loadings

Troubleshooting

• Low KMO (<0.6): Too few variables (<5-10), high multicollinearity, or non-normal data. Try removing problematic variables or use PCA instead.


• Non-significant Bartlett's: Data may not have underlying factors—consider descriptive stats or correlation matrix first (cor(df_numeric)).


• Small sample size: Need n > 5-10x number of variables (ideally 100+).


• In Python: Use from factoranalyzer import calculatekmo; calculatebartlettsphericity(data). Let me know if needed.