Describe principal components analysis and common factor analysis and the differences between the two methods of factor analysis

What will be an ideal response?

In principal components analysis, the total variance in the data is considered. The diagonal of the correlation matrix consists of unities, and full variance is brought into the factor matrix. Principal components analysis is recommended when the primary concern is to determine the minimum number of factors that will account for maximum variance in the data for use in subsequent multivariate analysis. The factors are called principal components.

In common factor analysis, the factors are estimated based only on the common variance. Communalities are inserted in the diagonal of the correlation matrix. This method is appropriate when the primary concern is to identify the underlying dimensions and the common variance is of interest. This method is also known as principal axis factoring.

A major difference between the two methods of factor analysis is that principal components analysis considers the total variance in the data whereas common factor analysis considers only the common variance. In common factor analysis, the factors are estimated based only on the common variance.