Exploratory factor analysis (EFA) identifies the underlying relationships between a large number of interrelated variables when there are no prior hypotheses about factors or patterns amongst the variables.

EFA is a technique based on the common factor model which describes the measured variables by a function of the common factors, unique factors, and error of measurements. Common factors are those that influence two or more measured variables, while unique factors influence only one measured variable.

Pattern matrix

The factor pattern matrix loadings are the linear combinations of the factors that make up the original standardized variables.

Structure matrix

The factor structure matrix loadings are the correlation coefficients between the factors and the variables.

Correlation matrix

The factor correlation matrix coefficients are the correlation coefficients between the factors.

Note: When the factors are not rotated, or the rotation is orthogonal, there is no correlation between the factors and the correlation matrix is equal to the identity matrix. Also, the loadings in the pattern matrix and structure matrix are identical, although it can be useful to remember the different interpretations - as linear coefficients or correlation coefficients.
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