# Many-to-many-to-many analysis (ABC type analysis)

ABO analysis analyzes the relationship between the element of view A and the element of view B.

An application of this is also a way to analyze the relationships between the elements of each of the three perspectives A, B and C. In addition, this idea can be used even if it is increased to four or more.

## Many-to-many analysis data

I think the basis of many-to-many analysis is matrix-shaped data. It is easy to think that AA type analysis and AB type analysis will start with this data.

If you know tensors, you may be asked "Does many-to-many-to-many use tensors?", But tensors are mathematically complicated and it takes time to work with data. Above all, it is difficult to imagine the data.

If you want to generalize a many-to-many analysis, it's a tensor, but here's a more limited case. The data handled here is data with three qualitative variables.

If there are three quantitative variables and you want to analyze them many-to-many-to-many, I think it's a tensor, but there are quantitative variables, and there are qualitative variables and quantitative variables. In mixed situations, one-dimensional clustering can be used to convert data to qualitative variables only, so you can use the method on this page.

## Analysis of data with three qualitative variables

Using log-linear analysis for data with three qualitative variables , this is an analysis of the relationship between the three variables, but not a many-to-many-to-many analysis.

As a method of many-to-many-to-many analysis of data with three qualitative variables, the analysis of grouping of individual categories is applicable.

### Multiple correspondence analysis

Procedure of multiple correspondence analysis, and the data with two qualitative variables to start, correspondence analysis is the same as when the (correspondence analysis).

Multiple correspondence analysis not only creates closeness of individual categories, but also creates variables for analysis that are not in the original data and can be seen in relation to them. Many of the grouping analyzes for individual categories do not create these variables.

## Software

Example of R is in the page, Correspondence analysis by R .