**(This is a draft and truncated version - for final and full version, see**

Concise Encyclopedia of Biostatistics for Medical Professionals)

Concise Encyclopedia of Biostatistics for Medical Professionals)

**varimax rotation**

Varimax rotation is a special kind of rotation of axes in graphical form, generally used for multidimensional phenomenon, which helps to present a clearer picture of what is happening. This strategy is commonly used for some statistical procedures such as

**factor analysis**and

**principal components**analysis.

See Figure V.3a where many features of the bar diagram are obscure but they become clear when the figure is rotated (Figure V.3b). In this case, we have rotated x- and y-axes by 20o each. This figure is in three dimensions but the same can be conceived for multidimensions. In Figures V.3, the axes continue to be perpendicular with each other (called

*orthogonal*) although they may not look so in the figure. However, methods are available that would do oblique rotation so that the axes are no longer orthogonal.

Rotation is just change of coordinates that define the location. In usual two dimensions, if a regression line has a slope of 30o and you rotate the (x, y) axes by 30o, the line will look parallel to x-axis. This may be a big convenience in interpreting the implication of the line just as rotation in Figure V.3b is for clearly seeing various bars. Algorithms are available to devise rotations for increasing or decreasing the scatter.

Varimax stands for maximizing the variance, where the variance is chosen depending on the application. For example, in case of factor analysis where this rotation is most commonly used, variance to be maximized is the sum of the

*K*-factor sample variances of the standardized

**loadings**. The factors are supposed to be on different axes in this setup and axes are orthogonal so that the factors are independent of each other. The rotation minimizes the complexity of the factors by making the large loadings larger and the small loadings smaller within each factor – thus maximizing the variance. This tends to minimize the number of variables with large loadings in each factor and helps in achieving clarity regarding the variables appearing in each factor. After this rotation, the variables with small loadings can be ignored and only the factors with high loadings are considered for interpreting the factors. See

**factor analysis**for more details.

There are other rotational methods.

*... ...*

**For final and full version, see**

Concise Encyclopedia of Biostatistics for Medical Professionals

Concise Encyclopedia of Biostatistics for Medical Professionals