EFA 3

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 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.

• Estimation of the factor loading matrix

  1. Initial unrotated factor loading matrix is estimated

  2. Rotational method is employed to achieve simpler factor loadings structure

  3. Facilitates interpretation of the loading pattern and item-factor assignment

• Two types of rotation

  1. Orthogonal rotation

  2. Oblique 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.

• 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)