Читать книгу Exploratory Factor Analysis - W. Holmes Finch - Страница 11

Much research in fields such as psychology is focused on variables that cannot be directly measured. These variables are often referred to as being latent, and include such constructs as intelligence, personality, mood, affect, and aptitude. These latent variables are frequently featured in social science research and are also the focus for clinicians who want to gain insights into the psychological functioning of their clients. For example, a researcher might be interested in determining whether there is a relationship between extraversion and job satisfaction, whereas a clinician may want to know whether her client is suffering from depression. In both cases, the variables of interest (extraversion, job satisfaction, and depression) are conceived of as tangible, real constructs, though they cannot be directly measured or observed. We talk about an individual as being an extravert or we conclude that a person is suffering from depression, yet we have no direct way of observing either of those traits. However, as we will see in this book, these latent variables can be represented in the statistical model that underlies factor analysis.

If latent variables are, by their very nature, not observable, then how can we hope to measure them? We make inferences about these latent variables by using variables that we can measure, and which we believe are directly impacted by the latent variables themselves. These observed variables can take the form of items on a questionnaire, a test, or some other score that we can obtain directly, such as behavior ratings made by a researcher of a child’s behavior on the playground. We generally conceptualize the relationship between the latent and observed variables as being causal, such that one’s level on the latent variable will have a direct impact on scores that we obtain on the observed variable. This relationship can take the form of a path diagram, as in Figure 1.1.

Figure 1.1 Example Latent Model Structure

We can see that each observed variable, represented by the squares, is linked to the latent variable, denoted as F1, with unidirectional arrows. These arrows come from the latent to the observed variables, indicating that the former has a causal impact on the latter. Note also that each observed variable has an additional unique source of variation, known as error and represented by the circles at the far right of the diagram. Error represents everything that might influence scores on the observed variable, other than the latent variable that is our focus. Thus, if the latent variable is mathematics aptitude, and the observed variables are responses to five items on a math test, then the errors are all of the other things that might influence those math test responses, such as an insect buzzing past, distracting noises occurring during the test administration, and so on. Finally, latent variables (i.e., the factor and error terms) in this model are represented by circles, whereas observed variables are represented by squares. This is a standard way in which such models are diagrammed, and we will use it throughout the book.

In summary, we conceptualize many constructs of interest in the social sciences to be latent, or unobserved. These latent variables, such as intelligence or aptitude, are very important, both to the goal of understanding individual human beings as well as to understanding the broader world around us. However, these constructs are frequently not directly measurable, meaning that we must use some proxy, or set of proxies, in order to gain insights about them. These proxy measures, such as items on psychological scales, are linked to the latent variable in the form of a causal model, whereby the latent variable directly causes manifest outcomes on the observed variables. All other forces that might influence scores on these observed variables are lumped together in a latent variable that we call error, and which is unique to each individual indicator variable. Next, we will describe the importance of theory in both constructing and attempting to measure these latent variables.