Factor Analysis for Items or Testlets Scored in More Than Two Categories
Kimberly A. Swygert, Lori McLeod, David Thissen · 2001
Chapter 5 introduced the factor analytic model, and its development as an IRT model for items with dichotomous responses. We also laid the groundwork for the claim that it is dangerous to assume that all factor ana lytic techniques are appropriate for any data; there are necessary distinc tions among continuous, dichotomous, and polytomous (categorical) data. Researchers sometimes assume that items with many categories are equiv alent to items with continuous responses, but this is not always the case. It bears repeating here that the fewer categories the data have, the more likely it is that the distribution of the variables will be sufficiently nonnormal to disturb procedures designed for normally distributed con tinuous data. Two possible negative consequences are attenuation of the Pearson correlation coefficient, and the appearance of spurious factors composed of variables that have the same category splits and so correlate more highly with each other than with other variables, even if all variables measure the same construct.