# Quantification theory

Quantification theory is a theory for handling qualitative information in quantity.

The calculation method of quantification theory is based on the method called multivariate analysis .

However, while the method of multivariate analysis is basically the method used to see the relationships of variables, the use of quantification theory is similar to the analysis of decision trees and grouping of individual categories . .. Therefore, on this site, we have put the quantification theory within the framework of data mining .

Historically, it has been used as a text mining method from a method devised as a method for analyzing questionnaire / sensitivity evaluation data .

## Quantified data

The types of data handled in quantification theory seem to be divided into the following four types.

• Data1 :a qualitative variable dummy conversion data
• Data2 :Two-choice data, "applicable" and "not applicable"
• Data3 :AA type data
• Data4 :AB type data

Data1 and Data2 are similar, except that they always contain logic such as "if not L, either M or N".

In the case of Data1, it can be converted back to the form before dummy conversion to make it a qualitative variable, but in the case of Data2, it cannot be done.

## Classification of quantification theory

### The manual of "quantification theory" is as follows.

• Quantification type 1 :Multiple regression analysis with explanatory variables in the form of Data1
• Quantification type 2 :Discriminant analysis with explanatory variables in the form of Data1
• Quantification type 3 :An approach similar to principal component analysis for Data2
• Quantification type 4 :Similarity data in the form of Data3. Analysis with a type of multidimensional scaling
• Quantification type 5 :Dissimilarity data in the form of Data3. Analysis with a type of multidimensional scaling
• Quantification type 6 :Directed data for paired comparisons in the form of Data3. Even if A> B and B> C, when C> A instead of A> C, it is considered that the dimension of evaluation is different.

Classes 1 to 3 are methods for dealing with qualitative variables and variables in which "yes" and "no" are expressed by 0 and 1 in the theory of quantitative variables.

Classes 4 to 6 are methods for viewing the whole picture from the data obtained by paired evaluation .

Classes 3 to 6 have different mathematical procedures because the type of data to be started is different, but the point that the output is the coordinate data of each category is the same.

### Quantification theory in a broad sense

In the original quantification theory, the method to be handled is decided to a certain extent. On this site, I will expand it to the following meanings and write from that perspective. By doing this, I think it will be easier to think of an approach that uses the latest theory for what I originally wanted to do with quantification theory.

• Broadly defined quantification type 1 :The objective variable is a quantitative variable and the explanatory variable is in the form of Data1 or Data2.
• Broadly defined quantification type 2 :The objective variable is a qualitative variable and the explanatory variable is in the form of Data1 or Data2.
• Broadly defined quantification type 3 :No objective variable. A method of obtaining coordinate data of two types of categories. Data1, Data2, Data4

## There is a story unique to quantification theory

When I first learned about quantification theory, I understood that "the rest is the same as normal multivariate analysis, except that it handles 0 and 1 data."

However, within this understanding, what can be done with quantification theory is limited. In the quantification theory, when we think about what kind of model it is by handling the data that is 0 and 1, the range of analysis unique to the quantification theory has expanded.

## Quantification when there are both quantitative and qualitative variables

As mentioned above, the quantification theory when only qualitative variables are used is a method that is different from the original method that targeted quantitative variables.

That alone expands the world of data analysis, but there are times when actual data in the world has both quantitative and qualitative variables. There are two ways to proceed when there are both. If you use these properly, the world of data analysis will expand further.

### Dummy transform qualitative variables and mix with quantitative variables

This is the procedure used in quantification type I and linear mixed models .

The quantitative variables in the qualitative variables stratified you will feel to be analyzed.

### Convert quantitative variables to qualitative variables, then dummy transform all variables

This is the procedure used in the correlation analysis of individual categories .

Quantitative variables return to quantitative variables after becoming qualitative variables, but they are treated as partitioned data. It also makes it easier to see non-linear features.