Methods of Determining Factor Structure of the Test Data Based on Traditional and Modern Measurement Approaches

Usually, the dimensions or factors of a test are examined by analyzing the data obtained from its implementation using the statistical methods of exploratory and confirmatory factor analysis. Over time, depending on different theoretical models, different methods have been proposed to determine the number of dimensions or factors. The purpose of this article is to review the major commonly used methods for this purpose and to examine their strengths and weaknesses.

To achieve this goal, methods for determining the numbers of dimensions of test data are described and their performance in real data are discussed, and finally the conditions of use of each of them are described.

The application of different methods of determining the dimensions or factors requires the researcher's insight and understanding of the basics and principles of these methods, the nature of the data and the conditions contained in them.

Different dimensional approaches provide reliable results only under conditions commensurate with their nature. Otherwise, the analysis performed with different approaches is not reliable.