Exploratory factor analysis is a statistical approach that can be used to analyze interrelationships among a large number of variables and to explain these variables in terms of a smaller number of common underlying dimensions. This involves finding a way of condensing the information contained in some of the original variables into a smaller set of implicit variables (called factors) with a minimum loss of information.
For example, suppose you would like to test the observation that customer satisfaction is based on product knowledge, communications skills and people skills. You develop a new questionnaire about customer satisfaction with 30 questions: 10 concerning product knowledge, 10 concerning communication skills and 10 concerning people skills. Before using the questionnaire on your sample, you pretest it on a group of people similar to those who will be completing your survey.
You perform a factor analysis to see if there are really these three factors. If they do, you will be able to create three separate scales, by summing the items on each dimension.
Factor analysis is based on a correlation table. If there are k items in the study (e.g. k questions in the above example) then the correlation table has k × k entries of form rij where each rij is the correlation coefficient between item i and item j. The main diagonal consists of entries with value 1.
Closely related to factor analysis is principal component analysis, which creates a picture of the relationships between the variables useful in identifying common factors.
Factor analysis is based on various concepts from Linear Algebra, in particular eigenvalues, eigenvectors, orthogonal matrices and the spectral theorem. We review these concepts first before explaining how principal component analysis and factor analysis work.
- Linear Algebra Background
- Principal Component Analysis (PCA)
- Basic Concepts of Factor Analysis
- Factor Extraction
- Determining the Number of Factors to Retain
- Factor Scores
- Validity of Correlation Matrix and Sample Size
- Principal Axis Method of Factor Extraction
- Real Statistics Functions and Data Analysis Tools
To illustrate Factor Analysis we will use an example. Click here for a complete description of this example.