Is categorization of random data necessary for parallel analysis on Likert-type data?

ABSTRACT

Random eigenvalues are the key elements in parallel analysis. When analyzing Likert-type data, is it necessary to convert the continuous random data to discrete type before estimating eigenvalues? The study compared the random eigenvalues obtained from continuous and categorized random data from two popular computer programs to be used as the basis for comparison in conducting parallel analysis on Likert-type data. Results indicated that categorized random data gave eigenvalues and number of factors similar to those obtained from continuous random data. It is suggested that when conducting parallel analysis on Likert-type data by the two programs, the conversion is unnecessary.

KEYWORDS:

• Eigenvalues
• Factor analysis
• Likert-type data
• Number of factors
• Parallel analysis

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62H25

Notes

1 Following Muthén and Kaplan (1985, 1992), another method of categorization of continuous variables proposed by Wang (2001) has also been used in previous research (e.g., Wang, 2001; Weng & Cheng, 2005; Wu, 2003). Additional simulations were therefore conducted to examine the eigenvalues obtained from this method of categorization. This method of categorization was similar to that in Thompson and Daniel (1996) with slight differences on the thresholds chosen. For example, Wang used −1.64, −0.64, 0.64, and 1.64 to discretize continuous variables to a 5-point scale, while Thompson and Daniel used −1.8, −0.6, 0.6, and 1.8. The results indicated that these two methods yielded eigenvalues extremely close.