Sunday, 4 September 2011

Rotation methods in Factor Analysis

The purpose of rotation is to have a better view of the data. By rotation you are just viewing data from different view points. If you are not satisfied by the output you may rotate and see, if the data fits into your research. Rotation serves to make the output more understandable and is usually necessary to facilitate the interpretation of factors.

Varimax rotation is an orthogonal rotation of the factor axes to maximize the variance of the squared loadings of a factor (column) on all the variables (rows) in a factor matrix, which has the effect of differentiating the original variables by extracted factor. Each factor will tend to have either large or small loadings of any particular variable. A varimax solution yields results which make it as easy as possible to identify each variable with a single factor. This is the most common rotation option. Varimax is the oldest and was designed when there are no computers. However, one of the disadvantages of varimax is it provides more factors.

Quartimax rotation is an orthogonal alternative which minimizes the number of factors needed to explain each variable. This type of rotation often generates a general factor on which most variables are loaded to a high or medium degree. Such a factor structure is usually not helpful to the research purpose.

Equimax rotation is a compromise between Varimax and Quartimax criteria.

Direct oblimin rotation is the standard method when one wishes a non-orthogonal (oblique) solution – that is, one in which the factors are allowed to be correlated. This will result in higher Eigen values but diminished interpretability of the factors. See below.

Promax rotation is an alternative non-orthogonal (oblique) rotation method which is computationally faster than the direct oblimin method and therefore is sometimes used for very large datasets.

Something on the selection of the methods

The choice of rotation method used is dictated by the theory and purpose behind doing the factor analysis. Orthogonal rotations like Varimax, Quartimax and Equimax are based on the assumption that the underlying factors you are trying to extract are completely uncorrelated to each other. If you believe that the factors you are trying to extract are correlated to each other, then it is better to use Oblique rotations like Oblimin, promax, etc.

Most factor analyses methods are trying to find groupings between data elements and reduce them into cluster-like groups. To do this it has to look for commonality and 'distance' which it does by looking for orthogonality, or how far apart these groups are in n-dimensions.

So a non-rotated solution works if the data are cleanly orthogonal at 90-degrees along x and y axes. But this often fails with real world data, so over time different ways of rotating the x and y axes were done to experiment with other kinds of orthogonal relationships. Therefore, Quartimax rotates the axes by 45-degrees and sees if that is a better fit (orthogonally).

Varimax tends to be the strongest in this because it lets all the n-axes float until it finds the best fits to the data being analysed and doesn't force-feed the models a pre-defined axis rotation scheme.

Author : Priyanka Bagla (13029)

Group: Finance 6

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