I developed a scale with 21 items to measure study skills of students. I wish to check the unidimensionality of the scale.  I judged from the following facts:

1. After deleting two items, all items had infit and outfit statistics within the reasonable range for
observations (ie, between 0.6 ¡V1.4).
2. The PCA analysis listed below.  (Unexplned variance in 1st contrast =          2.7 )

Does it means that the unexplained variance in 1st contrast is too large and implied that there is another dimension in the scale (ie. not unidimensional)?

could anyone please advise the steps of checking unidimensionality? Thanks.
Best,
Thomas


TABLE 23.0 2012 Study skills                     ZOU675WS.TXT  Apr 19 22:03 2012
INPUT: 65 Person  21 Item  REPORTED: 64 Person  19 Item  76 CATS WINSTEPS 3.74.0
--------------------------------------------------------------------------------

     Table of STANDARDIZED RESIDUAL variance (in Eigenvalue units)
                                                 -- Empirical --    Modeled
Total raw variance in observations     =         30.2 100.0%         100.0%
  Raw variance explained by measures   =         11.2  37.1%          37.2%
    Raw variance explained by persons  =          4.5  14.7%          14.8%
    Raw Variance explained by items    =          6.8  22.4%          22.5%
  Raw unexplained variance (total)     =         19.0  62.9% 100.0%   62.8%
    Unexplned variance in 1st contrast =          2.7   8.9%  14.1%
    Unexplned variance in 2nd contrast =          2.2   7.2%  11.5%
    Unexplned variance in 3rd contrast =          1.9   6.4%  10.2%
    Unexplned variance in 4th contrast =          1.6   5.3%   8.4%
    Unexplned variance in 5th contrast =          1.5   5.0%   8.0%


2012 Study skills
------------------------------------------------------------------------------
| Person      65 INPUT      64 MEASURED               INFIT         OUTFIT   |
|          TOTAL     COUNT     MEASURE  REALSE     IMNSQ   ZSTD  OMNSQ   ZSTD|
| MEAN      52.3      18.9         .58     .42      1.01    -.2   1.01    -.2|
| S.D.       9.1        .5        1.42     .28       .69    1.9    .68    1.8|
| REAL RMSE    .50 TRUE SD    1.33  SEPARATION  2.63  Person RELIABILITY  .87|
|----------------------------------------------------------------------------|
| Item      21 INPUT      19 MEASURED                 INFIT         OUTFIT   |
|          TOTAL     COUNT     MEASURE  REALSE     IMNSQ   ZSTD  OMNSQ   ZSTD|
| MEAN     176.2      63.6         .00     .19      1.00     .0   1.01     .1|
| S.D.      18.7        .6         .54     .02       .15     .8    .16     .8|
| REAL RMSE    .19 TRUE SD     .51  SEPARATION  2.64  Item   RELIABILITY  .87|
------------------------------------------------------------------------------

Thomas, let's see what your Table tells us.

Your scale has 19 active items. 63% of the variance is unexplained. This suggests that the item difficulties and person abilities are central. In fact, the items (22%) are more dispersed than the person (15%). This may be good or it may be bad.

For instance, for nurses at the end of their training, we expect them to have very similar competencies. We want to see very littlle dispersion in the nurse ability estimates. So, if the study skills of your sample are good, we are happy to see that there is little dispersion of the skill "abilities".

The eigenvalue of the 1st contrast is 2.7. This suggests that there is a secondary artifact with the strength of about 3 items (out of 19) in your scale. Is this a dimension or an accident or what? To investigate, we need to look at the content of the items.

Your Table 23.2 has an interesting vertical distribution in its Figure. We can see that items A,B,C are off on their own. Which items are they? Table 23.3 tells us ss9, ss10, ss5. Now we need the text of those items. (It is easier when the text is summarized in the item labels). What do those items have in common that the other items don't have? If there is something. Then it is a secondary dimension or merely a content strand (like addition vs. subtraction in arithmetic). If there is nothing, then the eignevalue of 2.7 may be an accident.

OK?