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Investigating Unidimensionality for Polytomous data
Once again, for the models we are presenting on this website, unidimensionality is necessary. This page will walk you through an example of a PAF analysis with data from the Agreeableness scale (polytomously scored). We will be using the SYSTAT 8.0 software package (similar procedures can be executed through SAS or SPSS). The procedure is as follows:
Opening the data in SYSTAT
Open the polytomous data file in SYSTAT
- From the menu....
- Go to 'File'
- 'Open' the appropriate file under the appropriate file type
View the data
- Go to 'View'
- Go to 'Data'
Save the syntax if desired (for future reference)
- The "syntax" is in the 'log' tab at the bottom of the SYSTAT window
- Copy the syntax from the log area
- Paste the syntax in the the sheet with the tab that is titled with the filename
- Go to 'File' and 'Save'
View of the lower portion of the SYSTAT window
Initiating a factor analysis
Run a factor analysis to determine number of factors underlying the data
- From the menu....
- Go to 'Statistics'
- Go to 'Data Reduction'
- Go to 'Factor Analysis'
Factor analysis in the SYSTAT menu
- Select all the items that are within the subtest or scale (i.e., the 10 items from the Agreeableness scale) and add them to the list of 'Model variables'
- Set 'Method' to 'Iterative principle axis'
- Keep 'Matrix for extraction' set to the default which is 'correlation'
- Keep 'Rotation' set to the default which is 'no rotation' (other rotations can be explored later)
- If desired, go to 'Save' and select any additional information in the output file to be saved
- Click 'OK'
Specifying the settings for a factor analysis in SYSTAT
Sample view of the syntax (partial)
Interpreting the SYSTAT output file
View the Factor Pattern
View of the factor patterns for the Agreeableness scale (SYSTAT output)
Examine the Eigenvalues
Note how large each factor is and the differences between them
In our example, the first factor is large and subsequent factors small, which supports our assumption of unidimensionality
View of the Eigenvalues: Agreeableness scale
Examine how much of variance is explained by each factor
Variance explained by factor
Examine the percentage of variance explained by each factor
Percent of variance explained
Examine the scree plot
Each factor from the second factor onward should be a minor contributor to the data
In this example, one primary factor acts as the underlying trait
This is adequate for our assumption of unidimensionality
Scree plot
About the scree plot: Note how the first factor dominates the other factors, that is, there is a large difference between the first and second factors. A significant drop in the contribution of the factors between the first and second factors can be seen as evidence for unidimensionality. Thus, the absence of scree, or "debris" at the bottom of the slope in the plot is desirable because it indicates that the second factor is small. Because our sample data is simulated, the actual scree may vary according to the data.
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