Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

Survey on Multivariate Methods

In order to get an overview of multivariate methods (which are quite numerous, many of them being similar to each other, and some of these being known by different names in different fields of science) one can try to classify these methods according to some basic questions:

1) Are the variables connected to each other in a way that no clear disctinction between explanatory and response variables can be made, or is it possible to specify which variables are the independent (explanatory) variables and which one are the response variables?

1a) In the case of clearly specified explanatory and response variables: how many independent and how many response variables are available?

2) What is the level of measurement of the variables?

The answers to these questions result in the following coarse classification of multivariate methods:

 Dependence of Variables Number of Variables Level of Measurements Methods (Examples) explanatory and response variables clearly distinguished one single response variable metric multiple correlation multiple regression categorical several explanatory variables metric MANOVA canonical analysis RBF networks categorical canonical analysis based on auxiliary variables mutual dependence - metric factor analysis principal component analysis multidimensional scaling cluster analysis categorical multidimensional scaling correspondence analysis

Apart from this rather formal classification of statistical procedures there are several methods which do not clearly fit into the above mentioned scheme. For example, principal component regression is a combination of principal component analysis and multiple linear regression. Further, there are methods such as neural networks which are based on greatly differing assumptions and which implement highly different scenarios. Such methods are difficult to classify at all.