Factor Analysis

(mathematics) Given sets of variables which are related linearly, factor analysis studies techniques of approximating each set relative to the others; usually the variables denote numbers.

A method of quantitative multivariate analysis with the goal of representing the interrelationships among a set of continuously measured variables (usually represented by their intercorrelations) by a number of underlying, linearly independent reference variables called factors. Although the term factor analysis has come to represent a family of analysis methods, the two most commonly used approaches are the full component model, in which the entire variance of the variables (represented by unities inserted in the principal diagonal of the correlation matrix) is analyzed, and the common factor model, in which the proportion of the variance that is accounted for by the common factors (represented by communality estimates inserted in the principal diagonal) is analyzed.

The method was developed in England around the turn of the century and was first applied to the study of the structure of intellectual abilities. Since then it has been used in many disciplines, from agriculture to zoology, in which the underlying structure of multiple variables and their representation in that structure are of interest. Another application of factor analysis is to represent parsimoniously the variables in the set on which the observations are made by a smaller number of underlying reference variables or factors. See also Statistics.

Mathematical procedure used to reduce a large amount of data into a structure that can be more easily studied. Factor analysis summarizes information contained in a large number of variables and condenses it into a smaller number of factors containing variables that are interrelated. For example: In a study about a group of women, their characteristics of height, weight, hobbies, activities, and interests might be summarized, using factor analysis, as size (height and weight) and lifestyles (the combination of hobbies, activities, and interests). In so doing, five variables have been condensed into two separate factors.

Mathematical procedure used to reduce a large amount of data into a structure that can be more easily studied. Factor analysis summarizes information contained in a large number of variables and condenses it into a smaller number of factors containing variables that are interrelated. For example, in a study about a group of women, their characteristics of height, weight, hobbies, activities, and interests might be summarized, using factor analysis, as size (height and weight) and lifestyles (the combination of hobbies, activities, and interests). In so doing, five variables have been condensed into two separate factors.

A multivariate statistical technique, usually used to make analysis more simple. Sets of original, unique data are replaced by a smaller number of sets. This method can be illustrated by considering a number of characteristics which often go together. For example, if we think of a typical left-wing woman we would expect her to be in favour of abortion, and gender and racial equality, and against capital punishment and stringent immigration policy. Where these views do coincide, they are said to be a factor. Factor analysis can be used to see how closely these aspects are related to the individual, or it can be used to see how far all these variables can be reduced to a smaller set; if we can be sure that all pro-abortionists are anti-capital punishment then we can save a great deal of time in an analysis.

Factor analysis attempts to determine a possible underlying pattern of relationships so that the data may be reordered and reduced to a smaller set of factors. From this it is, in theory, possible to select the dependent variables. (R. J. Johnston, 1978.)

A statistical model that attempts to explain the correlation between a number of measured interval level variables in terms of a smaller number of latent, or unobserved, factors. The measured variables are assumed to depend on the underlying factors, but they also include random error. Factor analysis is particularly useful when direct measurement is impossible, as for social attitudes such as national sentiment, or psychological concepts such as intelligence. It is also used to detect summary dimensions in the pattern of correlation in a set of variables. For example, Arend Lijphart (Patterns of Democracy, 1999) found two dimensions (called executives-parties and federal-unitary) to be sufficient to explain the variation in ten measured characteristics of political institutions in democracies. Factor analysis is similar in its aims to principal component analysis.

— Stephen Fisher

A complex statistical procedure in which the correlations between a large set of observed variables are explained in terms of a smaller number of new variables called factors. Factor analysis has been used especially in sociology and psychology. In the case of personality analysis, it has been used to discover the constituent irreducible traits from a complex mass of data.