We now discuss this general process in more detail. Factor Analysis Factor analysis is a statistical tool used to represent information contained in a large set of variables with a smaller set of variables. That is, an underlying assumption of factor analysis is that there are a few latent factors that are manifest in the values of many observable variables. For example, the desire for wealth might be a latent factor in our lottery example. This latent factor might be responsible for values we observe on such variables as the amount of money wagered in a given time period or the frequency with which a person purchases a lottery ticket.
Factor analysis is conducted in an effort to determine possible latent factors.
This process involves the formulation of a mathematical model that describes the relationship between the latent and manifest variables, as well as subjective evaluations to recognize and describe the latent factors. Once latent factors have been determined, cluster analysis is used to separate or segment a population of items into groups with similar values for the latent factors. The underlying belief is that individuals with similar latent traits will react in a similar manner to a marketing campaign. In our Arizona Lottery example, we first conducted a factor analysis of the responses of all 3,084 respondents to a list of 45 statements about their attitudes toward the lottery and general gaming. As noted previously, identification of latent factors requires both mathematical models and subjective decision making.