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Factor Analysis

Factor Analysis is a field of study that seeks to understand the underlying patterns in a dataset and explain those relationships in a more condensed fashion. In other words, it attempts to condense the information content into what are called factors that reflect the uniqueness of the data - especially if there exists redundancy in the initial information being examined. Some terms used in factor analysis are:

Eigenvalue - column sum of squared loadings for a factor - also referred to as the latent root. It represents the amount of variance accounted for by a factor. Factor loadings - Correlation between the original variables and the factors, and the key to understanding the nature of a particular factor. Squared factor loadings indicate what percentage of the variance in an original variable is explained by a factor.

Factor rotation: process of manipulating or adjusting the factor axes to achieve a simpler and pragmatically more meaningful factor solution.

Factor score: Composite measure created for each observation on each factor extracted in the factor analysis. The factor weights are used in conjunction with the original variable values to calculate each observation's score.

Orthogonal factor rotation: Factor rotation computed so that the extracted factors are extracted so that the axes are at 90 degrees so that the factors have a zero correlation with one another. If this kind of rotation is elected, then the factor analysis is sometimes referred to as Principal Component Analysis where one desires a set of factors that are not correlated with one another.

An example of Factor Analysis might be to examine information about a group of companies to uncover what factors relate to their success. Let's say you have collected financial information - ratios, accounting information, annual report numbers, etc. Such information is often highly correlated with one another. Factor analysis might help you collapse this information into say 3 or 4 main factors that could be described as profitability, size, and industry. A factor analysis might show that the majority of the original variables are heavily "loaded" on three factors - and after you examine the nature of the original variables, the factors might represent some dimension of say profitability, size, and industry.

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