The best fitted regression line procedure for analytic rotation in factor analysis

الملخص EN

Factor analysis (FA) sometimes show complicated patterns, and they are not easy to interpret.

When the coefficients of a given (FA) are all with similar sizes, or when a few are large and the remainders are small, the factor looks easy to interpret.

When there are intermediate loadings, as well as large and small ones, the factor is more difficult to interpret.

To overcome this problem one can perform a rotation on the factors to produce some new factors.

In this paper a new method of rotation is proposed, depends on the best fitted regression line.

Key words: Factor analysis, Interpretability of factors, Rotation of axes, Regression.

1- Introduction Thurstone (1947) presents most of the rationales for rotating factors, while Cattell (1978) defended its use.

They confirm that this procedure simplifies the factor structure.

Therefore, makes its interpretation easier.

Carroll (1953) presented the first analytic criterion for determining psychologically interpretable factors.

The most popular rotation method is the varimax rotation developed by Kaiser (1958).

Clarkson and Jennrich (1988) have unified this approach in rotation programs.

The rotation methods are usually employed to rotate the factors to factors whose coefficients are as close to 0 or 1 as possible.

These methods are designed to attain the properties of what Thurstone (1947) and Cattell (1978) called simple structure.

The objective of simple structure is to produce a new set of vectors, each one involving primarily a subset of the original variables with as little overlap as possible so that the original variables are divided into groups somewhat independent of each other.

Note that, ideal simple structure is difficult to obtain and the rotated variables are no longer uncorrelated.