Factor loadings

orthogonal

Communality

Communality (h2). Proportion of variance explained by the common factors.

Orthogonal factor analysis: Sum of the squared loadings of an observed variable j

Explained variance by a factor. Represents the total variance explained by each factor. Orthogonal FA: Sum of the squared loadings per column

Factor scores

Factor scores are z-standardized composite scores estimated for each respondent on the derived factors

Interpretation (example): Participant #1 scores 0.74 standard deviations above the mean on factor F1 in this sample. #5 scores 1.81 SDs below the sample mean on F1.

Three processes of factor interpretation

Estimation of the factor loading matrix

Initial unrotated factor loading matrix is estimated

Rotational method is employed to achieve simpler factor loadings structure

Facilitates interpretation of the loading pattern and item-factor assignment

Two types of rotation

Orthogonal rotation

Oblique rotation

Rotation

Through rotation the factor loading matrix is transformed into a simpler one that is easier to interpret

After rotation, each factor should have nonzero loadings for only some of the variables. Each variable should have nonzero loadings with only a few factors, if possible, with only one àIndependent cluster solution

The rotation is called orthogonal rotation if the axes are maintained at right angles.

The rotation is called oblique rotation if the axes are not maintained at right angles: factors can correlate

Varimax procedure

• Varimax procedure.

Axes maintained at right angles

Most common method for orthogonal rotation

An orthogonal method of rotation that minimizes the number of variables with high loadings on a factor

Oblique rotation.

Axes not maintained at right angles

Factors can be correlated: Unrestricted factor correlations; i.e., factor correlations are freely estimated

Oblique rotation should be used when factors in the population are likely to be moderately or strongly correlated (i.e., approximately r ≥ .30)

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