Multivariate Analyses |

Observations with missing values for any of the **Partial** variables are not used. Observations with **Weight** or **Freq** values that are missing or that are less than or equal to 0 are not used. Only the integer part of **Freq** values is used.

Observations with missing values for **Y** or **X** variables are not used in the analysis except for the computation of pairwise correlations. Pairwise correlations are computed from all observations that have nonmissing values for any pair of variables.

The following notation is used in this chapter:

*n*is the number of nonmissing observations.*n*_{p},*n*_{y}, and*n*_{x}are the numbers of**Partial**,**Y**, and**X**variables.*d*is the variance divisor.*w*_{i}is the*i*th observation weight (values of the**Weight**variable).**y**_{i}and**x**_{i}are the*i*th observed nonmissing Y and X vectors.- and are the sample mean vectors, ,.

The sums of squares and crossproducts of the variables are

The corrected sums of squares and crossproducts of the variables are

If you select a **Weight** variable, the sample mean vectors are

The sums of squares and crossproducts with a **Weight** variable are

The corrected sums of squares and crossproducts with a **Weight** variable are

The covariance matrices are computed as

**S**_{yy} = **C**_{yy} / *d* **S**_{yx} = **C**_{yx} / *d* **S**_{xx} = **C**_{xx} / *d*

To view or change the variance divisor *d* used in the calculation of variances and covariances, or to view or change other method options in the multivariate analysis, click on the **Method** button from the variables dialog to display the method options dialog.

**Figure 40.3:** Multivariate Method Options Dialog

The variance divisor *d* is defined as

for vardef=DF, degrees of freedom |
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for vardef=N, number of observations |
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for vardef=WDF, sum of weights minus number of partial variables minus 1 |
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for vardef=WGT, sum of weights |

By default, SAS/INSIGHT software uses **DF, degrees of freedom**.

The correlation matrices **R**_{yy}, **R**_{yx}, and **R**_{xx}, containing the Pearson product-moment correlations of the variables, are derived by scaling their corresponding covariance matrices:

**R**_{yy}=**D**_{yy}^{-1}**S**_{yy}**D**_{yy}^{-1}**R**_{yx}=**D**_{yy}^{-1}**S**_{yx}**D**_{xx}^{-1}**R**_{xx}=**D**_{xx}^{-1}**S**_{xx}**D**_{xx}^{-1}

where **D**_{yy} and **D**_{xx} are diagonal matrices whose diagonal elements are the square roots of the diagonal elements of **S**_{yy} and **S**_{xx}:

**D**_{yy}= (diag(**S**_{yy}))^{1/2}**D**_{xx}= (diag(**S**_{xx}))^{1/2}

Copyright © 2007 by SAS Institute Inc., Cary, NC, USA. All rights reserved.