Multidimensional Statistical Analysis – Introduction

  • if statistical analysis holds more statistical properties – result: multidimensional data
  • data analyzed simultaneously

Example:

i
\(X_1\)
\(X_2\)
\(X_3\)
Nonameheightweighteye.color
17 Doe Jane 165 69 blue
18 Roe Richard 185 70 brown
  • observations for Jane Doe compose a vector of values, say \(x\Tr_{17} = (165, 69, \text{blue})\).
  • mathematically, the above table of values is the matrix \[\mathbf X = \begin{bmatrix} x\Tr_1 \\ x\Tr_2 \\ \vdots \\ x\Tr_n \end{bmatrix} = \begin{bmatrix} x_{11} & x_{12} & \dots & x_{1p} \\ x_{21} & x_{22} & \dots & x_{2p} \\ \vdots & \vdots & & \vdots \\ x_{n1} & x_{n2} & & x_{np} \end{bmatrix}\] where \(p\) is the number of statistical properties and \(n\) is the number of statistical units.

Methods

  • principal component analysis (PCA),
  • cluster analysis (CA),
  • factor analysis (FA),
  • regression and classification trees,
  • discriminant analysis.

All these methods evaluate the multidimensional data simultaneously, usually using matrix algebra.