5.4.5 - Factor Loadings - Teradata Warehouse Miner

Teradata Warehouse Miner User Guide - Volume 3Analytic Functions

Product
Teradata Warehouse Miner
Release Number
5.4.5
Published
February 2018
Language
English (United States)
Last Update
2018-05-04
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The term factor loadings is sometimes used to refer to the coefficients of the linear combinations of factors that make up the original variables in a factor analysis model. The appropriate term for this, however, is the factor pattern. A factor loadings matrix is sometimes also assumed to indicate the correlations between the factors and the original variables, for which the appropriate term is factor structure. The good news is that whenever factors are mutually orthogonal or independent of each other, the factor pattern P and the factor structure S are the same. They are related by the equation S = PQ where Q is the matrix of correlations between factors.

In the case of principal components analysis, factor loadings are labeled as component loadings and represent both factor pattern and structure. For other types of analysis, loadings are labeled as factor pattern but indicate structure also, unless a separate structure matrix is also given (as is the case after oblique rotations, described later).

Keeping the above caveats in mind, the component loadings, pattern or structure matrix is interpreted for its structure properties in order to understand the meaning of each new factor variable. When the analysis is based on a correlation matrix, the loadings, pattern or structure can be interpreted as a correlation matrix with the columns corresponding to the factors and the rows corresponding to the original variables. Like all correlations, the values range in absolute value from 0 to 1 with the higher values representing a stronger correlation or relationship between the variables and factors. By looking at these values, the user gets an idea of the meaning represented by each factor. Teradata Warehouse Miner stores these so called factor loadings and other related values in metadata result tables to make them available for scoring.