Oblique Promax Rotation Applied to the Solutions in Multiple Correspondence Analysis

There are many approaches to formulate multiple correspondence analysis of multi-item categorical data. A lower-rank approximation approach gives the freedom for the oblique rotation of axes. In the current paper, we apply the oblique rotation of axes to a variable-by-dimension matrix to arrive at simple structure. This matrix is defined in either of two different manners, that is, by treating categories as variables or, alternatively, by treating items as variables. For each of these two options, the standardized inner products between dimensions and variables are used as the elements of the component structure matrix. We adopt a promax method for the oblique rotation. In this method, scores are rotated in such a way that the above matrix is matched with the target matrix obtained from the result of the varimax rotation.