Imagine you asked a group of elite athletes to complete a questionnaire containing a set of questions about lifestyle behaviours including hours of sleep, level of protein intake, daily engagement in moderate-to-vigorous physical activity etc.
It would be reasonable to assume that an elite athlete would respond similarly to each of these questions. You’d expect them to have (for example) higher levels of each variable, compared to non-athletes.
It’s also reasonable to suspect that there is an underlying ‘dimension’ to their responses - which we might call ‘athleticism’ or ‘dedication’. This underlying dimension explains how they answer the different questions.
We can measure the factor directly, but we can speculate that it exists and causes similar responses on the questions.
Factor analysis is an important statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called ‘factors’.
So in the example above, our observed variables are correlated because of an unobserved variable or factor that we could call ‘athleticism’ (or ‘professionalism’, or ‘commitment’…).
Factor analysis aims to find the underlying structure in a set of variables.
It reduces the observed variables into a few unobserved factors for data simplification and to identify groups of related variables.
For example, think about the following variables:
These are different measures, but could reasonably be assumed to represent aspects of one factor, ‘aerobic fitness’.
Factor analysis allows us to reduce several variables into a smaller number of such factors.
Where a factor is unobserved directly, we call it a latent factor, or a latent variable.
For example, we might have a set of questions, each of which is designed to capture some aspect of an underlying factor.