Factor analysis can be applied in order to explore a content area, structure a domain, map unknown concepts, classify or reduce data, illuminate causal nexuses, screen or transform data, define relationships, test hypotheses, formulate theories, control variables, or make inferences.
Interdependency and pattern delineation. If a scientist has a table of data--say, UN votes, personality characteristics, or answers to a questionnaire--and if he suspects that these data are interrelated in a complex fashion, then factor analysis may be used to untangle the linear relationships into their separate patterns. Each pattern will appear as a factor delineating a distinct cluster of interrelated data.
Parsimony or data reduction. Factor analysis can be useful for reducing a mass of information to an economical description. For example, data on fifty characteristics for 300 nations are unwieldy to handle, descriptively or analytically. The management, analysis, and understanding of such data are facilitated by reducing them to their common factor patterns. These factors concentrate and index the dispersed information in the original data and can therefore replace the fifty characteristics without much loss of information.
Structure. Factor analysis may be employed to discover the basic structure of a domain. As a case in point, a scientist may want to uncover the primary independent lines or dimensions--such as size, leadership, and age--of variation in group characteristics and behavior.
Classification or description. Factor analysis is a tool for developing an empirical typology. It can be used to group interdependent variables into descriptive categories, such as ideology, revolution, liberal voting, and authoritarianism. It can be used to classify nation profiles into types with similar characteristics or behavior. Or it can be used on data matrices of a transaction type or a social-choice type to show how individuals, social groups, or nations cluster on their transactions with or choices of each other.
Scaling. A scientist often wishes to develop a scale on which individuals, groups, or nations can be rated and compared. The scale may refer to such phenomena as political participation, voting behavior, or conflict. A problem in developing a scale is to weight the characteristics being combined. Factor analysis offers a solution by dividing the characteristics into independent sources of variation (factors). Each factor then represents a scale based on the empirical relationships among the characteristics.
Hypothesis testing. Hypotheses abound regarding dimensions of attitude, personality, group, social behavior, voting, and conflict. Since the meaning usually associated with "dimension" is that of a cluster or group of highly intercorrelated characteristics or behavior, factor analysis may be used to test for their empirical existence. Which characteristics or behavior should, by theory, be related to which dimensions can be postulated in advance and statistical tests of significance can be applied to the factor analysis results.
Besides those relating to dimensions, there are other kinds of hypotheses that may be tested. To illustrate: if the concern is with a relationship between economic development and instability, holding other things constant, a factor analysis can be done of economic and instability variables along with other variables that may affect (hide, mediate, depress) their relationship. The resulting factors can be so defined (rotated) that the first several factors involve the mediating measures (to the maximum allowed by the empirical relationships). A remaining independent factor can be calculated to best define the postulated relationships between the economic and instability measures. The magnitude of involvement of both variables in this pattern enables the scientist to see whether an economic development-instability pattern actually exists when other things are held constant.
Data transformation. Factor analysis can be used to transform data to meet the assumptions of other techniques. For instance, application of the multiple regression technique assumes (if tests of significance are to be applied to the regression coefficients) that predictors--the so-called independent variables--are statistically unrelated (Ezekiel and Fox, 1959, pp. 283-84). If the predictor variables are correlated in violation of the assumption, factor analysis can be employed to reduce them to a smaller set of uncorrelated factor scores. The scores may be used in the regression analysis in place of the original variables, with the knowledge that the meaningful variation in the original data has not been lost. Likewise, a large number of dependent variables also can be reduced through factor analysis.
Exploration. In a new domain of scientific interest like peace research, the complex interrelations of phenomena have undergone little systematic investigation. The unknown domain may be explored through factor analysis. It can reduce complex interrelationships to a relatively simple linear expression and it can uncover unsuspected, perhaps startling, relationships. Usually the social scientist is unable to manipulate variables in a laboratory but must deal with the manifold complexity of behaviors in their social setting. Factor analysis thus fulfills some functions of the laboratory and enables the scientist to untangle interrelationships, to separate different sources of variation, and to partial out or control for undesirable influences on the variables of concern.Mapping. Besides facilitating exploration, factor analysis also enables a scientist to map the social terrain. Mapping means the systematic attempt to chart major empirical concepts and sources of variation. These concepts may then be used to describe a domain or to serve as inputs to further research. Some social domains, such as international relations, family life, and public administration, have yet to be charted. In some other areas, however, such as personality, abilities, attitudes, and cognitive meaning, considerable mapping has been done.