Introduction

• Many traits are directly measurable, but many are not. For example, height and many physical traits are directly measurable, but we cannot directly measure intelligence or depression. Such hidden traits are called latent, and latent factor analysis is one method of finding them. We start with a large number of observed variables, and then factor analysis reduces them to one or a small number of latent factors.
  
  

Types

• Two types of latent factor analysis are exploratory and confirmatory. In exploratory factor analysis, we do not start with a strong sense of which observed variables relate to which latent factor, or even what precise latent factors exist in the data. In confirmatory factor analysis, we do have such a sense, usually from prior research with a different group of subjects.
  
  

Extraction of Factors

• The first step in a latent factor analysis is extraction of factors. Although different methods of doing this exist, all try to extract factors that capture as much as possible of the variance of the observed variables. We can then examine the amount of variance extracted by each factor to help us decide how many factors to retain.
  
  

Rotation of Factors

• The second step in a factor analysis is factor rotation. This involves making the extracted factors more interpretable. There are two broad types of rotation. In orthogonal rotation, each factor is uncorrelated with all the other factors; in oblique rotation, this restriction is dropped. Orthogonal rotation is simpler to interpret, but the restriction may be unrealistic.
  
  

Considerations

• Proper use of factor analysis requires considerable knowledge and experience. You will need to consider the method of factor extraction, the number of factors to retain and the method of rotation. None of these decisions can be made in an automatic way.