The FACTOR Procedure

Time Requirements

\begin{eqnarray*} n & = & \mbox{number of observations} \\ v & = & \mbox{number of variables} \\ f & = & \mbox{number of factors} \\ i & = & \mbox{number of iterations during factor extraction} \\ r & = & \mbox{length of iterations during factor rotation} \\ \end{eqnarray*}

The time required to compute…

  

is roughly proportional to

an overall factor analysis

 

$iv^3$

the correlation matrix

 

$nv^2$

PRIORS=SMC or ASMC

 

$v^3$

PRIORS=MAX

 

$v^2$

eigenvalues

 

$v^3$

final eigenvectors

 

$fv^2$

generalized Crawford-Ferguson

 

$rvf^2$

family of rotations,

   

PROMAX, or HK

   

ROTATE=PROCRUSTES

 

$vf^2$

Each iteration in the PRINIT or ALPHA method requires computation of eigenvalues and f eigenvectors.

Each iteration in the ML or ULS method requires computation of eigenvalues and $v - f$ eigenvectors.

The amount of time that PROC FACTOR takes is roughly proportional to the cube of the number of variables. Factoring 100 variables, therefore, takes about 1000 times as long as factoring 10 variables. Iterative methods (PRINIT, ALPHA, ULS, ML) can also take 100 times as long as noniterative methods (PRINCIPAL, IMAGE, HARRIS).