SAS Annotated Output
Factor Analysis

This page shows an example of a factor analysis with footnotes explaining the output.  The data used in this example were collected by Professor James Sidanius, who has generously shared them with us.  You can download the data set here.

Overview:  The "what" and "why" of factor analysis

Factor analysis is a method of data reduction.  It does this by seeking underlying unobservable (latent) variables that are reflected in the observed variables (manifest variables).  There are many different methods that can be used to conduct a factor analysis (such as principal axis factor, maximum likelihood, generalized least squares, unweighted least squares), There are also many different types of rotations that can be done after the initial extraction of factors, including orthogonal rotations, such as varimax and equimax, which impose the restriction that the factors cannot be correlated, and oblique rotations, such as promax, which allow the factors to be correlated with one another.  You also need to determine the number of factors that you want to extract.  Given the number of factor analytic techniques and options, it is not surprising that different analysts could reach very different results analyzing the same data set.  However, all analysts are looking for simple structure.  Simple structure is pattern of results such that each variable loads highly onto one and only one factor. 

Factor analysis is a technique that requires a large sample size.  Factor analysis is based on the correlation matrix of the variables involved, and correlations usually need a large sample size before they stabilize.  Tabachnick and Fidell (2001, page 588) cite Comrey and Lee's (1992) advise regarding sample size: 50 cases is very poor, 100 is poor, 200 is fair, 300 is good, 500 is very good, and 1000 or more is excellent.  As a rule of thumb, a bare minimum of 10 observations per variable is necessary to avoid computational difficulties.

For the example below, we are going to do a rather "plain vanilla" factor analysis.  We will use iterated principal axis factor with three factors as our method of extraction, a varimax rotation, and for comparison, we will also show the promax oblique solution.  The determination of the number of factors to extract should be guided by theory, but also informed by running the analysis extracting different numbers of factors and seeing which number of factors yields the most interpretable results.  We have used the priors = smc option on the proc factor statement so that the squared multiple correlation is used on the diagonal of the correlation matrix.  (If this option is not used, 1's are on the diagonal, and you will do a principal components analysis instead of a principal axis factor analysis.)

In this example we have included many options, including the original correlation matrix, the scree plot and the eigenvectors.  While you may not wish to use all of these options, we have included them here to aid in the explanation of the analysis.  We have also created a page of annotated output for a principal components analysis that parallels this analysis.  For general information regarding the similarities and differences between principal components analysis and factor analysis, see Tabachnick and Fidell, for example.

proc factor data = "d:\m255_sas" nfactors = 3 corr scree ev rotate = varimax method = prinit priors = smc;
var item13 item14 item15 item16 item17 item18 item19 item20 item21 item22 item23 item24 ;
run;
The FACTOR Procedure

                                           Correlations

                                                                  ITEM13       ITEM14       ITEM15

ITEM13   INSTRUC WELL PREPARED                                   1.00000      0.66146      0.59999
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.66146      1.00000      0.63460
ITEM15   INSTRUCTOR CONFIDENCE                                   0.59999      0.63460      1.00000
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.56626      0.50003      0.50535
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.57687      0.55150      0.58664
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.40898      0.43311      0.45707
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.28632      0.32041      0.35869
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.30418      0.31481      0.35568
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.47553      0.44896      0.50904
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.33255      0.33313      0.36884
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.56399      0.56461      0.58233
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.45360      0.44281      0.43481

                                           Correlations

                                                                  ITEM16       ITEM17       ITEM18

ITEM13   INSTRUC WELL PREPARED                                   0.56626      0.57687      0.40898
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.50003      0.55150      0.43311
ITEM15   INSTRUCTOR CONFIDENCE                                   0.50535      0.58664      0.45707
ITEM16   INSTRUCTOR FOCUS LECTURES                               1.00000      0.58649      0.40479
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.58649      1.00000      0.55474
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.40479      0.55474      1.00000
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.33540      0.44930      0.62660
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.31676      0.41682      0.52055
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.45245      0.59526      0.55417
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.36255      0.44976      0.53609
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.45880      0.61302      0.56950
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.42967      0.52058      0.47382

                                           Correlations

                                                                  ITEM19       ITEM20       ITEM21

ITEM13   INSTRUC WELL PREPARED                                   0.28632      0.30418      0.47553
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.32041      0.31481      0.44896
ITEM15   INSTRUCTOR CONFIDENCE                                   0.35869      0.35568      0.50904
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.33540      0.31676      0.45245
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.44930      0.41682      0.59526
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.62660      0.52055      0.55417
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   1.00000      0.44647      0.49921
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.44647      1.00000      0.42479
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.49921      0.42479      1.00000
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.48404      0.38297      0.50651
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.44401      0.40962      0.59751
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.37383      0.35722      0.49977

                                           Correlations

                                                                  ITEM22       ITEM23       ITEM24

ITEM13   INSTRUC WELL PREPARED                                   0.33255      0.56399      0.45360
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.33313      0.56461      0.44281
ITEM15   INSTRUCTOR CONFIDENCE                                   0.36884      0.58233      0.43481
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.36255      0.45880      0.42967
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.44976      0.61302      0.52058
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.53609      0.56950      0.47382
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.48404      0.44401      0.37383
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.38297      0.40962      0.35722
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.50651      0.59751      0.49977
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      1.00000      0.49317      0.44440
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.49317      1.00000      0.70464
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.44440      0.70464      1.00000

The table above was included in the output because we included the corr option on the proc factor statement.  This table gives the correlations between the original variables (which are specified on the var statement).  Before conducting a principal components analysis, you want to check the correlations between the variables.  If any of the correlations are too high (say above .9), you may need to remove one of the variables from the analysis, as the two variables seem to be measuring the same thing.  Another alternative would be to combine the variables in some way (perhaps by taking the average).  If the correlations are too low, say below .1, then one or more of the variables might load only onto one factor (in other words, make its own factor).  This is not helpful, as the whole point of the analysis is to reduce the number of items (variables).

Initial Factor Method: Iterated Principal Factor Analysis

                           Prior Communality Estimates: SMCa

    ITEM13          ITEM14          ITEM15          ITEM16          ITEM17          ITEM18

0.56418325      0.55109842      0.53781427      0.44669710      0.58542518      0.57168198

    ITEM19          ITEM20          ITEM21          ITEM22          ITEM23          ITEM24

0.45593942      0.32641074      0.51564224      0.39697338      0.66171378      0.52583313

Preliminary Eigenvalues: Total = 6.13941289  Average = 0.51161774
        Eigenvalueb   Differencec   Proportiond   Cumulativee

   1    5.77616022    5.05422468        0.9408        0.9408
   2    0.72193554    0.46721447        0.1176        1.0584
   3    0.25472107    0.17543468        0.0415        1.0999
   4    0.07928639    0.08287783        0.0129        1.1128
   5    -.00359143    0.02084644       -0.0006        1.1122
   6    -.02443788    0.04141429       -0.0040        1.1083
   7    -.06585217    0.00923826       -0.0107        1.0975
   8    -.07509043    0.02834695       -0.0122        1.0853
   9    -.10343738    0.01757618       -0.0168        1.0685
  10    -.12101355    0.02261532       -0.0197        1.0487
  11    -.14362888    0.01200974       -0.0234        1.0254
  12    -.15563862                     -0.0254        1.0000

a.  Prior Communality Estimates:  SMC - This gives the communality estimates prior to the rotation.  The communalities (also known as h2) are the estimates of the variance of the factors, as opposed to the variance of the variable which includes measurement error.

b.  Eigenvalue - This is the initial eigenvalue.  An eigenvalue is the variance of the factor.  Because this is an unrotated solution, the first factor will account for the most variance, the second will account for the second highest amount of variance, and so on.  Some of the eigenvalues are negative because the matrix is not of full rank.  This means that there are probably only four dimensions (corresponding to the four factors whose eigenvalues are greater than zero).  Although it is strange to have a negative variance, this happens because the factor analysis is only analyzing the common variance, which is less than the total variance.  If we were doing a principal components analysis, we would have had 1's on the diagonal, which means that all of the variance is being analyzed (which is another way of saying that we are assuming that we have no measurement error), and we would not have negative eigenvalues.  In general, it is not uncommon to have negative eigenvalues.

c.  Difference - This column gives the difference between the eigenvalues.  For example, 5.05 = 5.77 - 0.72.  This column allows you to see how quickly the eigenvalues are decreasing.

d.  Proportion - This is the proportion of the total variance that each factor accounts for.  For example, 0.9408 = 5.77/6.139.

e.  Cumulative - This is the sum of the proportion column.  For example, 1.0584 = 0.9408 + 0.1176.


3 factors will be retained by the NFACTOR criterion.

Initial Factor Method: Iterated Principal Factor Analysis

Scree Plot of Eigenvalues
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   0 +                               4      5      6      7      8
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     ----+------+------+------+------+------+------+------+------+------+------+------+------+----
         0      1      2      3      4      5      6      7      8      9     10     11     12

                                                 Number

The scree plot graphs the eigenvalue against the factor number.  You can see these values in the first two columns of the table immediately above.  From the third factor on, you can see that the line is almost flat, meaning the each successive factor is accounting for smaller and smaller amounts of the total variance. 


Initial Factor Method: Iterated Principal Factor Analysis

Iterationf Changeg                                  Communalitiesh

    1      0.0722  0.63235  0.60163  0.58315  0.47076  0.62245  0.64391  0.52673  0.36802  0.55072
                   0.44262  0.73027  0.58020
    2      0.0314  0.65638  0.61511  0.59176  0.47107  0.62531  0.66684  0.55310  0.37241  0.55236
                   0.44807  0.76168  0.60660
    3      0.0152  0.66649  0.61878  0.59279  0.46942  0.62437  0.67484  0.56471  0.37121  0.55092
                   0.44706  0.77683  0.61976
    4      0.0075  0.67126  0.61963  0.59244  0.46846  0.62365  0.67765  0.57040  0.36997  0.54996
                   0.44578  0.78429  0.62641
    5      0.0037  0.67367  0.61966  0.59202  0.46805  0.62329  0.67856  0.57338  0.36925  0.54949
                   0.44498  0.78797  0.62979
    6      0.0018  0.67494  0.61950  0.59174  0.46789  0.62314  0.67877  0.57500  0.36887  0.54927
                   0.44456  0.78979  0.63153
    7      0.0009  0.67562  0.61934  0.59156  0.46783  0.62308  0.67875  0.57591  0.36868  0.54917
                   0.44434  0.79068  0.63243

Convergence criterion satisfied.

f.  Iteration - This column lists the number of the iteration.  In this analysis, seven iterations were required before the criteria was met.

g.  Change - When the change becomes smaller than the criterion, the iterating process stops.  The numbers in this column are the largest absolute difference between iterations.  For example, the difference between the first and the second iteration for item23 is 0.0314 = 0.73027 - 0.76168.  The difference given for the first iteration is the difference between the values at the first iteration and the squared multiple correlations (sometimes called iteration 0).

h.  Communalities - These are the communality estimates at each iteration.  For each iteration, the communality for each variable is listed.  For example, 0.63235 is the communality for the first variable.

Eigenvalues of the Reduced Correlation Matrix: Total = 7.01500876  Average = 0.58458406

        Eigenvaluei   Differencej   Proportionk   Cumulativel

   1    5.85107872    5.04474488        0.8341        0.8341
   2    0.80633384    0.44633935        0.1149        0.9490
   3    0.35999449    0.22853697        0.0513        1.0003
   4    0.13145752    0.07654351        0.0187        1.0191
   5    0.05491400    0.02332205        0.0078        1.0269
   6    0.03159195    0.03030953        0.0045        1.0314
   7    0.00128242    0.00617263        0.0002        1.0316
   8    -.00489021    0.01439730       -0.0007        1.0309
   9    -.01928750    0.02693109       -0.0027        1.0281
  10    -.04621859    0.01408519       -0.0066        1.0216
  11    -.06030378    0.03064032       -0.0086        1.0130
  12    -.09094410                     -0.0130        1.0000

Initial Factor Method: Iterated Principal Factor Analysis

                                           Eigenvectorsm

                                                                       1            2            3

ITEM13   INSTRUC WELL PREPARED                                   0.29486     -0.44338      0.15269
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.29074     -0.37797      0.16283
ITEM15   INSTRUCTOR CONFIDENCE                                   0.29819     -0.27308      0.17609
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.26782     -0.21061      0.18546
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.32375     -0.08174      0.11086
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.30573      0.38422      0.18861
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.25481      0.46205      0.25759
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.22744      0.26655      0.15574
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.30252      0.13020      0.00062
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.25337      0.29080     -0.03839
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.33865     -0.02903     -0.57488
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.28729      0.02042     -0.64369

i.  Eigenvalue - This is the eigenvalue obtained after the principal axis factoring but before the varimax rotation.  An eigenvalue is the variance of the factor.  Because this is an unrotated solution, the first factor will account for the most variance, the second will account for the second highest amount of variance, and so on.  Some of the eigenvalues are negative because the matrix is not of full rank.  This means that there are probably only four dimensions (corresponding to the four factors whose eigenvalues are greater than zero).  Although it is strange to have a negative variance, this happens because the factor analysis is only analyzing the common variance, which is less than the total variance.  If we were doing a principal components analysis, we would have had 1's on the diagonal, which means that all of the variance is being analyzed (which is another way of saying that we are assuming that we have no measurement error), and we would not have negative eigenvalues.  In general, it is not uncommon to have negative eigenvalues.

j.  Difference - This column gives the difference between the eigenvalues.  For example, 5.0447 = 5.85107 - 0.8633.  This column allows you to see how quickly the eigenvalues are decreasing.

k.  Proportion - This is the proportion of the total variance that each factor accounts for.  For example, 0.8341 = 5.85107/7.015.

l.  Cumulative - This is the sum of the proportion column.  For example, 0.9490 = 0.8341 + 0.1149.

m.  Eigenvectors - Eigenvectors are linear combinations of the original variables.  They tell you about the strength of the relationship between the original variables and the (latent) factors.

                                          Factor Patternn

                                                                 Factor1      Factor2      Factor3

ITEM13   INSTRUC WELL PREPARED                                   0.71324     -0.39814      0.09162
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.70328     -0.33941      0.09770
ITEM15   INSTRUCTOR CONFIDENCE                                   0.72130     -0.24522      0.10565
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.64783     -0.18912      0.11128
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.78311     -0.07340      0.06652
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.73953      0.34501      0.11316
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.61635      0.41490      0.15455
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.55015      0.23935      0.09344
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.73178      0.11691      0.00037
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.61288      0.26113     -0.02304
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.81916     -0.02607     -0.34493
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.69493      0.01834     -0.38621

n.  Factor Pattern - This table contains the unrotated factor loadings, which are the correlations between the variable and the factor.  Because these are correlations, possible values range from -1 to +1.

     Variance Explained by Each Factor

   Factor1         Factor2         Factor3

 5.8510787       0.8063338       0.3599945

                       Final Communality Estimateso: Total = 7.017407p

    ITEM13          ITEM14          ITEM15          ITEM16          ITEM17          ITEM18

0.67562309      0.61934326      0.59156382      0.46783384      0.62307645      0.67874757

    ITEM19          ITEM20          ITEM21          ITEM22          ITEM23          ITEM24

0.57591368      0.36868496      0.54916770      0.44434233      0.79068338      0.63242696

o.  Final Communality Estimates - This is the proportion of each variable's variance that can be explained by the factors (e.g., the underlying latent continua).  The values here indicate the proportion of each variable's variance that can be explained by the retained factors prior to the rotation.  Variables with high values are well represented in the common factor space, while variables with low values are not well represented.  (In this example, we don't have any particularly low values.)  They are the reproduced variances from the factors that you have extracted.  You can find these values on the diagonal of the reproduced correlation matrix.

p.  Total -   7.017407 = 5.8510787 + 0.8063338 + 0.3599945

Rotation Method: Varimax

            Orthogonal Transformation Matrixq

                       1               2               3

       1         0.65843         0.61225         0.43773
       2        -0.68417         0.72927         0.00910
       3         0.31366         0.30547        -0.89906

q.  Orthogonal Transformation Matrix - This is the matrix by which you multiply the unrotated factor matrix to get the rotated factor matrix

                                      Rotated Factor Patternr

                                                                 Factor1s     Factor2s     Factor3s

ITEM13   INSTRUC WELL PREPARED                                   0.77075      0.17432      0.22622
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.72592      0.21291      0.21693
ITEM15   INSTRUCTOR CONFIDENCE                                   0.67583      0.29506      0.21852
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.59084      0.29271      0.18181
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.58671      0.44625      0.28233
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.28638      0.73896      0.22512
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.17044      0.72715      0.13462
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.22779      0.53993      0.15899
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.40195      0.53341      0.32106
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.21766      0.55864      0.29137
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.44901      0.37716      0.66845
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.32388      0.32087      0.65159

r.  Rotated Factor Pattern - This table contains the rotated factor loadings, which are the correlations between the variable and the factor.  Because these are correlations, possible values range from -1 to +1. 

s.  Factor - These columns are the rotated factors that have been extracted.  These are the factors that analysts are most interested in and try to name.  For example, the first factor might be called "instructor competence" because items like "instructor well prepare" and "instructor competence" load highly on it.  The second factor might be called "relating to students" because items like "instructor is sensitive to students" and "instructor allows me to ask questions" load highly on it.  The third factor has to do with comparisons to other instructors and courses.

     Variance Explained by Each Factor

   Factor1         Factor2         Factor3

 2.9494952       2.6557251       1.4121868

                       Final Communality Estimatest: Total = 7.017407u

    ITEM13          ITEM14          ITEM15          ITEM16          ITEM17          ITEM18

0.67562309      0.61934326      0.59156382      0.46783384      0.62307645      0.67874757

    ITEM19          ITEM20          ITEM21          ITEM22          ITEM23          ITEM24

0.57591368      0.36868496      0.54916770      0.44434233      0.79068338      0.63242696

t.  Final Communality Estimates - This is the proportion of each variable's variance that can be explained by the factors (e.g., the underlying latent continua).  The values here indicate the proportion of each variable's variance that can be explained by the retained factors after the rotation.  Variables with high values are well represented in the common factor space, while variables with low values are not well represented.  (In this example, we don't have any particularly low values.)  They are the reproduced variances from the factors that you have extracted.  You can find these values on the diagonal of the reproduced correlation matrix.

u.  Total -     7.017407 = 2.9494952 + 2.6557251 + 1.4121868


The partial output below shows the solution using a promax rotation.  As you can see with an oblique rotation, such as a promax rotation, the factors are permitted to be correlated with one another.  With an orthogonal rotation, such as the varimax shown above, the factors are not permitted to be correlated (they are orthogonal to one another). Oblique rotations, such as promax, produce both factor pattern and factor structure matrices. The factor pattern matrix gives the linear combination of the variables that make up the factors. The factor structure matrix presents the correlations between the variables and the factors. To completely interpret an oblique rotation one needs to take into account both the factor pattern and the factor structure matrices and the correlations among the factors.

Please note that with orthogonal rotations the factor pattern and the factor structure matrices are the equal.

               Inter-Factor Correlations

                Factor1         Factor2         Factor3

Factor1         1.00000         0.59249         0.68096
Factor2         0.59249         1.00000         0.64863
Factor3         0.68096         0.64863         1.00000

Rotation Method: Promax (power = 3)

                  Rotated Factor Pattern (Standardized Regression Coefficients)

                                                                 Factor1      Factor2      Factor3

ITEM13   INSTRUC WELL PREPARED                                   0.85071     -0.09207      0.03379
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.78599     -0.02646      0.02406
ITEM15   INSTRUCTOR CONFIDENCE                                   0.69724      0.09144      0.01977
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.60443      0.12786     -0.00552
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.50870      0.28245      0.09868
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.06335      0.76328      0.03145
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                  -0.04152      0.81872     -0.05898
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.07314      0.55467      0.00917
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.22482      0.42982      0.18931
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION     -0.00866      0.52669      0.19811
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.16276      0.07474      0.71794
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.02282      0.04596      0.7487


                  Rotated Factor Structure (Correlations)

                                                                 Factor1      Factor2      Factor3

ITEM13   INSTRUC WELL PREPARED                                   0.81917      0.43388      0.55337
ITEM14   INSTRUC SCHOLARLY GRASP                                 0.78670      0.45484      0.54213
ITEM15   INSTRUCTOR CONFIDENCE                                   0.76488      0.51738      0.55388
ITEM16   INSTRUCTOR FOCUS LECTURES                               0.67643      0.48240      0.48901
ITEM17   INSTRUCTOR USES CLEAR RELEVANT EXAMPLES                 0.74325      0.64786      0.62829
ITEM18   INSTRUCTOR SENSITIVE TO STUDENTS                        0.53700      0.82121      0.56968
ITEM19   INSTRUCTOR ALLOWS ME TO ASK QUESTIONS                   0.40340      0.75586      0.44379
ITEM20   INSTRUCTOR IS ACCESSIBLE TO STUDENTS OUTSIDE CLASS      0.40803      0.60396      0.41876
ITEM21   INSTRUCTOR AWARE OF STUDENTS UNDERSTANDING              0.60841      0.68582      0.62121
ITEM22   I AM SATISFIED WITH STUDENT PERFORMANCE EVALUATION      0.43831      0.65006      0.53384
ITEM23   COMPARED TO OTHER INSTRUCTORS, THIS INSTRUCTOR IS       0.69593      0.63685      0.87725
ITEM24   COMPARED TO OTHER COURSES THIS COURSE WAS               0.55993      0.54515      0.79411

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