5.9 Assessing the need for EFA

As explained in the previous module, we need to determine if the data is suitable for factor analysis by examining the KMO and Bartlet’s test of sphericity. Remember that KMO measures the sampling adequacy of each observed variables in the model as well as the complete model, whereas the Bartlet’s test of sphericity is used to test the hypothesis that the correlation matrix is an identity matrix. Note that KMO and the Bartlet’s test of sphericity are calculated from the correlation matrix.

# Find the correlation between the factors
correlation <- cor(data.us.only)

# Used the correlation matrix to find the KMO. Note that KMO function is from the psych package.
KMO(correlation)

## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = correlation)
## Overall MSA =  0.92
## MSA for each item = 
##  INTICT1  INTICT2  INTICT3  INTICT4  INTICT5  INTICT6 COMPICT1 COMPICT2 COMPICT3 
##     0.93     0.88     0.90     0.95     0.89     0.94     0.95     0.94     0.93 
## COMPICT4 COMPICT5   AUICT1   AUICT2   AUICT3   AUICT4   AUICT5 SOIAICT1 SOIAICT2 
##     0.92     0.91     0.91     0.91     0.92     0.92     0.92     0.93     0.92 
## SOIAICT3 SOIAICT4 SOIAICT5 
##     0.94     0.90     0.91

# Bartlet's test of Sphericity
bart.test <- cortest.bartlett(correlation, n = nrow(data.us.only))
bart.test$p.value # extract p-value

## [1] 0

From the result, the overall measure of sampling adequacy is 0.92 which can be interpreted as Marvelous and the KMO for each observed variable are above 0.90 except INTICT2 which has a KMO of 0.88. Test from the Bartlet’s test shows that the correlation matrix is not an identity matrix since we have a p-value < 0.05. These results suggest that our data is well-suited for factor analysis.