symmetric analysis of multiple variables classified ranked orthogonal polynomials

Abstract

MCA has gained a reputation for being a very useful statistical method for determining the association between two or more categorical variables and their graphical description. For performance this method, we must calculate the singular vectors through (SVD). Which is an important primary tool that allows user to construct a low-dimensional space to describe the association between the variables categories. As an alternative procedure to use (SVD), we can use the (BMD) method, which involves using orthogonal polynomials to reflect the structure of ordered categorical responses. When the features of BMD are combined with SVD, the (HD) is formed. The aim of study is to use alternative method of (MCA) that is appropriate with ordered categorical data, this method is known as (HD). When compared the results of (HD) with (MCA), the (HD), will give the same representation, and we get a clear association interpretation among the categories in terms of linear, quadratic and higher order components for variables, also graphical display of the individual units will show an automatic clustering.