Interpreting a Factor Analysis
The purpose of conducting our factor analysis is to define dimensions for an existing measure. The fundamental research question for a factor analysis is: Is there a single factor or are multiple factors underlying the test/scale? The analysis conducted for this assignment will answer this question based on the course dataset (MoneyData.sav—See Week 2 Resources). Understanding the factor structure of a test is important because this will provide information about whether subscores can be reported for the test. For example, if someone were developing a coping questionnaire, they may have written items that they believe to tap into two different factors related to coping. The results of the factor analysis would provide empirical evidence that may either support the two factors or just support one overall coping factor.
Factor analysis is a powerful statistical technique that is frequently used in test construction. When performing factor analysis, researchers look at correlations between test items or variables and, in doing so, seek to discover underlying dimensions. It may be discovered that groups of items measure the same dimension, which may in turn lead to the discovery of subscales. Exploratory factor analysis is used to discover how items group together; confirmatory factor analysis is used to see if the items group together in a way that is consistent with theory or expectation.
For this Assignment, you interpret an exploratory factor analysis on the provided dataset (MoneyData.sav—See Week 2 Resources). Because factor analysis is so important in test construction, the steps on how to perform a factor analysis are presented below. You may wish to work through these steps on your own in SPSS because familiarity with this process may benefit you in the future; however, you are not required to do so.
To perform a factor analysis on the provided MoneyData dataset, click ANALYZE>DIMENSION REDUCTION>FACTOR. Move the 18 test items into the VARIABLES box, L1 to L5, L6R (remember L6R represents the L6 recoded variable—Refer to Week 6 Quiz for more details), D1 to D6, R1 to R6. Click the EXTRACTION button. For METHOD select “Principle Axis Factoring.” For DISPLAY, uncheck “Unrotated factor solution” and check “Scree Plot.” Under “Extract,” select “Fixed number of factors” and enter “3″ in the “Factors to extract” box. Click “Continue.” Click the ROTATION button and select “Direct Oblimin” as the rotation method, click “Continue,” and then click “OK.”
Principle axis factoring extraction with direct oblimin rotation was used to estimate the likely number of factors; this is a common method when one wishes to examine a solution that assumes that the factors are correlated with one another. The importance of each factor can be assessed by their factor loadings and the percent variance overlap between the variable and the factor. The table below, “Total Variance Explained,” provides information about the eigenvalues (factors with eigenvalues greater than one are usually examined further) and the percent of variance explained by each of the factors. The first three factors account for the highest percentage of variance.
The figure below is a Scree Plot. The scree plot shows how many distinct factors are present in your data. The number of factors above the “elbow” is the number of factors that you should retain. In this case, three factors should be retained (these three factors have been circled in the figure below).
Based on the Pattern Matrix below, it shows, for the most part, that each item loads on only one factor. Each item has a high loading in only one column and negligible loadings on the other two factors. The factor analysis shows that there are three distinct scales, with 6 items each.
In exploratory factor analysis, a researcher usually tries to characterize a factor by assigning it a name or a label. Generally, a researcher must consider whether or not the factors can be replicated, whether or not the factors are useful, as well as the complexity of the factors. For this example, the three factors that have been identified correspond to Financial risk taking tendencies (Factor 1), Desire for a luxurious lifestyle (Factor 3), and Tendency to depend on others for financial support (Factor 2).
The factor analysis for the Final Project will use this same dataset (MoneyData.sav—found in Week 2 Resources). Given the information that has been provided; consider how you would interpret the results of this factor analysis. You will need to incorporate your interpretation into your Final Project paper.
Interpret the results of the factor analysis. You do not need to submit this analysis this week, but you should incorporate it into your Final Project report. The factor analysis results for your Final Project report should include a discussion of the type of extraction method used, the type of rotation, the total number of items under analysis, number of factors that were extracted, interpretive labels for each of the factors, include tables and scree plot including loadings of variables on factors, percent of variance explained by each of the extracted factors. The factor analysis results, as well as the entire Final Project report should be written in APA format.