The basic logic of factor analysis
Factor analysis is a multivariate statistical technique that examines the pattern of correlations among a large number of observed variables in order to identify a smaller number of latent constructs, called factors, lying behind them. Charles Spearman first applied the method to research on intelligence in 1904, and it has since played a decisive part in the development of personality psychology. The underlying idea is straightforward: if several questionnaire items correlate highly with one another, they are presumably all reflecting some common latent factor. Suppose, for example, that the three items "I like parties," "I enjoy talking with people," and "I get bored when I am alone" all correlate strongly. One can then infer that a shared factor, extraversion, lies behind them. Factor analysis performs that inference with mathematical rigor, computing for each item how strongly it is associated with each factor, a quantity known as the factor loading.
Exploratory and confirmatory factor analysis
The method divides broadly into two approaches. Exploratory factor analysis (EFA) begins without a prior hypothesis about the structure of the data and is used to discover a factor structure from the data themselves. The discovery of the Big Five model came about in precisely this way: thousands of adjectives describing personality were submitted to factor analysis, and five factors emerged again and again. Confirmatory factor analysis (CFA), by contrast, is used to test whether a theoretically specified factor structure fits a given set of data. Once the Big Five model had been established, a large body of research applied CFA to new samples and to samples from other cultures in order to check whether the five-factor structure would replicate. One caution about EFA deserves emphasis: the choice of rotation method, such as varimax or promax rotation, affects the results, which leaves room for the researcher's own judgment to shape the outcome that gets reported.
What factor analysis achieves in personality research, and where it stops
Factor analysis gave personality psychology a scientific foundation, making possible an empirical approach clearly separate from subjective typologies of personality such as blood-type personality readings. The main reason the Big Five model has been so widely accepted is the strength of its replication: different researchers working with different samples keep extracting the same five factors. The method nonetheless has real limits. First, deciding how many factors to retain requires researcher judgment, and there is no guarantee that five is the correct answer; Ashton and Lee have in fact proposed a six-factor model, HEXACO. Second, factor analysis captures only linear relationships, so it can miss nonlinear interactions between personality traits. Third, it describes patterns of covariation among variables and says nothing about causation. The dimensions factor analysis extracts are labels that summarise how sets of questions tend to be answered, not the parts personality is built out of. Numbers on such a dimension therefore never reach as far as one particular exchange with one particular person. Read the five axes as a map for surveying tendencies, and a result no longer has to be either right or wrong.