The STEPDISC Procedure

Computational Resources

In the following discussion, let

$\displaystyle  n  $
$\displaystyle  =  $
$\displaystyle  \mbox{number of observations}  $
$\displaystyle c  $
$\displaystyle  =  $
$\displaystyle  \mbox{number of class levels}  $
$\displaystyle v  $
$\displaystyle  =  $
$\displaystyle  \mbox{number of variables in the VAR list}  $
$\displaystyle l  $
$\displaystyle  =  $
$\displaystyle  \mbox{length of the CLASS variable}  $
$\displaystyle t  $
$\displaystyle  =  $
$\displaystyle  v+c-1  $

Memory Requirements

The amount of memory in bytes for temporary storage needed to process the data is

\[  c(4v^2 + 28v + 3l + 4c + 72) + 16v^2 + 92v + 4t^2 + 20t + 4l  \]

Additional temporary storage of 72 bytes at each step is also required to store the results.

Time Requirements

The following factors determine the time requirements of a stepwise discriminant analysis:

  • The time needed for reading the data and computing covariance matrices is proportional to $nv^2$. The STEPDISC procedure must also look up each class level in the list. This is faster if the data are sorted by the CLASS variable. The time for looking up class levels is proportional to a value ranging from n to $n \ln (c)$.

  • The time needed for stepwise discriminant analysis is proportional to the number of steps required to select the set of variables in the discrimination model. The number of steps required depends on the data set itself and the selection method and criterion used in the procedure. Each forward or backward step takes time proportional to $(v+c)^2$.