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$^1$ (Before factor rotation) variances of factors (pr. components) are the eigenvalues of the correlation/covariance matrix of the data if the FA is PCA method; variances of factors are the eigenvalues of the reduced correlation/covariance matrix with final communalities on the diagonal, if the FA is PAF method of extraction; variances of factors do not correspond to eigenvalues of correlation/covariance matrix in other FA methods such as ML, ULS, GLS (see). In all cases, variances of orthogonal factors are the SS of the extracted/rotated - final - loadings.

$^1$ (Before factor rotation) variances of factors (pr. components) are the eigenvalues of the correlation/covariance matrix of the data if the FA is PCA method; variances of factors are the eigenvalues of the reduced correlation/covariance matrix with final communalities on the diagonal, if the FA is PAF method of extraction; variances of factors do not correspond to eigenvalues of correlation/covariance matrix in other FA methods such as ML, ULS, GLS (see). In all cases, variances of factors are the SS of the extracted/rotated - final - loadings.

$^1$ (Before factor rotation) variances of factors (pr. components) are the eigenvalues of the correlation/covariance matrix of the data if the FA is PCA method; variances of factors are the eigenvalues of the reduced correlation/covariance matrix with final communalities on the diagonal, if the FA is PAF method of extraction; variances of factors do not correspond to eigenvalues of correlation/covariance matrix in other FA methods such as ML, ULS, GLS (see). In all cases, variances of orthogonal factors are the SS of the extracted/rotated - final - loadings.

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The (default in SPSS) Kaiser rule "eigenvalues>1" was used to decide how many factors to extract, so, 4 factors will come. The "eigenvalues>1" rule is based on PCA's eigenvalues (i.e. the eigenvalues of the intact, input correlation matrix).

The (default in SPSS) Kaiser rule "eigenvalues>1" was used to decide how many factors to extract, so, 4 factors will come.

The (default in SPSS) Kaiser rule "eigenvalues>1" was used to decide how many factors to extract, so, 4 factors will come. The "eigenvalues>1" rule is based on PCA's eigenvalues (i.e. the eigenvalues of the intact, input correlation matrix).

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  1. No, you can't speak of eigenvalues after rotation. No matter be it orthogonal or oblique.
  2. You can't even say - at least should better avoid - of eigenvalues even after extraction of factors unless these factors are principal components$^1$. (An instructive example showing confusion similar to yours with ML factor extraction.) Variances of factors are SS loadings, not eigenvalues, generally.
  3. Rotated factors don't correspond one-to-one to the extracted ones.
  4. The % of total variation explained by the factors is 40.477% in your example, not 50.317%. The first number is less because FA factors explain all the assumed common variation which is less than the portion of total variation skimmed by the same number of PCs. May say in your report, "The 4-factor solution is responsible for the common variance constituting 40.5% of the total variance; while 4 principal components would account for 50.3% of the total variance".

$^1$ (Before factor rotation) variances of factors (pr. components) are the eigenvalues of the correlation/covariance matrix of the data if the FA is PCA method; variances of factors are the eigenvalues of the reduced correlation/covariance matrix with final communalities on the diagonal, if the FA is PAF method of extraction; variances of factors do not correspond to eigenvalues of correlation/covariance matrix in other FA methods such as ML, ULS, GLS (see). In all cases, variances of factors are the SS of the extracted/rotated - final - loadings.

  1. No, you can't speak of eigenvalues after rotation. No matter be it orthogonal or oblique.
  2. You can't even say - at least should better avoid - of eigenvalues even after extraction of factors unless these factors are principal components. (An instructive example showing confusion similar to yours with ML factor extraction.) Variances of factors are SS loadings, not eigenvalues, generally.
  3. Rotated factors don't correspond one-to-one to the extracted ones.
  4. The % of total variation explained by the factors is 40.477% in your example, not 50.317%. The first number is less because FA factors explain all the assumed common variation which is less than the portion of total variation skimmed by the same number of PCs. May say in your report, "The 4-factor solution is responsible for the common variance constituting 40.5% of the total variance; while 4 principal components would account for 50.3% of the total variance".
  1. No, you can't speak of eigenvalues after rotation. No matter be it orthogonal or oblique.
  2. You can't even say - at least should better avoid - of eigenvalues even after extraction of factors unless these factors are principal components$^1$. (An instructive example showing confusion similar to yours with ML factor extraction.) Variances of factors are SS loadings, not eigenvalues, generally.
  3. Rotated factors don't correspond one-to-one to the extracted ones.
  4. The % of total variation explained by the factors is 40.477% in your example, not 50.317%. The first number is less because FA factors explain all the assumed common variation which is less than the portion of total variation skimmed by the same number of PCs. May say in your report, "The 4-factor solution is responsible for the common variance constituting 40.5% of the total variance; while 4 principal components would account for 50.3% of the total variance".

$^1$ (Before factor rotation) variances of factors (pr. components) are the eigenvalues of the correlation/covariance matrix of the data if the FA is PCA method; variances of factors are the eigenvalues of the reduced correlation/covariance matrix with final communalities on the diagonal, if the FA is PAF method of extraction; variances of factors do not correspond to eigenvalues of correlation/covariance matrix in other FA methods such as ML, ULS, GLS (see). In all cases, variances of factors are the SS of the extracted/rotated - final - loadings.

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