Annotated Output from IML Program for Evaluating Coarse Factor Score Estimates
(annotation appears in red)

The novel output generated by the IML program is printed after the results for the factor analysis (e.g., the scree plot, eigenvalues, pattern coefficients, etc.).


Simplified Weights for Items / Factors

MEQ1           0    1
MEQ2           0    1
MEQ3           1    0
MEQ4           1    0
MEQ5           1    0
MEQ6           0    0
MEQ7           1    0
MEQ8           0    0
MEQ9           1    0
MEQ10          0    0
MEQ11          0    0
MEQ12          0    0
MEQ13          0    0
MEQ14          0    0
MEQ15          0    0
MEQ16          0    0
MEQ17          0    0
MEQ18          0    0
MEQ19          1    1

The weights chosen by the researcher are printed first. I used the IML program for computing coarse factor scores (see main page) based on the regression approach to determine the weights. As can be seen above, the coarse factor score estimates for the first factor are computed by summing items 3, 4, 5, 7, 9, and 19. The coarse factor score estimates for the second factor are computed by summing items 1, 2, and 19.

Indeterminacy / Determinacy Indices
(Multiple R, R-Squared, and Minimum Correlation)

       1     0.914     0.835     0.669
       2     0.902     0.814     0.628

The indeterminacy/determinacy indices for the factors are reported above. As shown by the high MULTR and RSQR values, the factors are fairly determinate. The MINCOR values are also fairly high. The MULTR values will be specifically used below.

Validity Coefficients

  FACTOR     VALID                               MULTR
       1     0.890     compare to MULTR -->      0.914
       2     0.821                               0.902

The validity (VALID) coefficients for the coarse factor score estimates compare fairly well to the MULTR values. The second factor showed a greater loss of information than the first. If the researcher decides that the loss of information is too great, the coarse factor score estimates will have to be improved by either adding or deleting items. Again, the IML programs for computing coarse factor score estimates will have to be used in this process. If the scores cannot be sufficiently improved, a refined set of factor score estimates may be preferred or a new factor analysis may be attempted (e.g., using a different extraction method, trying a different rotation, or selecting fewer factors).

Univocality Matrix
(Rows = Factor Scores / Columns = Factors)

  UNIV                                       FACTCOR
  .     0.552     compare to FACTCOR -->       .     0.563
 0.588   .                                    0.563   .

The Univocality information indicates the extent to which the factor score estimates are insufficiently or too highly correlated with other factors in the analysis. The rows of the above matrices represent the factor score estimates and the columns represent the factors. A desirable outcome is obtained when the two matrices above match perfectly. In this analysis the values in the two matrices are fairly similar. For example, the correlation between the first and second factor (see the FACTCOR matrix) is .563, which compares favorably to the correlation between the factor score estimates for the first factor and the second factor (r = .552 in the UNIV matrix).

Correlational Accuracy

SCORECOR                                     FACTCOR
 1.000   .        compare to FACTCOR -->      1.000   .
 0.600  1.000                                 0.563  1.000

The Correlational Accuracy information is easier to comprehend than the Univocality criteria above. The FACTCOR matrix again represents the correlations among the factors, and the SCORECOR matrix represents the correlations among the factor score estimates. Clearly, if the factor score estimates are adequate representations of the factors, the values in the two matrices should match. As shown above, the values do match fairly well, although the coarse factor score estimates for the two factors are slightly more correlated than the factors themselves.