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