Forms summation, or relationship, matrices for model terms (C.J. Brien).

### No options

### Parameters

`TERM` = formula structures |
Model terms corresponding to design matrices whose summation matrices are required |
---|---|

`MATRIX` = symmetric matrices |
Saves the summation or relationship matrix for each term |

### Description

This procedure forms the *summation*, or *relationship*, matrix for the design matrix of a model term. This is similar to the *projection* matrix, constructed by the `FPROJECTIONMATRIX`

procedure. `FPROJECTIONMATRIX`

calculates the mean of the units of a data variate with each effect of the term, and then forms a new data variate where each unit contains the mean calculated for the relevant effect. `FRTPRODUCTDESIGNMATRIX`

calculates the sums of the data values instead of the means. The result is also a relationship matrix that indicates, using one and zero whether two units have the same levels of the factors in a term. One use for these matrices in synthesizing a variance matrix that involves a linear combination of variance components.

The term is specified (as a model formula) using the `TERM`

parameter, and the matrix is saved (as a symmetric matrix) by the `MATRIX`

parameter.

Options: none.

Parameters: `TERM`

, `MATRIX`

.

### Method

The *summation* or *relationship* matrix is

`D *+ TRANSPOSE(D)`

The design matrix `D`

is formed using the `TERMS`

directive.

### Action with `RESTRICT`

The factors must not be restricted, nor may they contain missing values.

### See also

Procedure: `FPROJECTIONMATRIX`

.

Commands for: Analysis of variance, Calculations and manipulation.

### Example

CAPTION 'FRTPRODUCTDESIGNMATRIX example'; STYLE=meta FACTOR [NVALUES=15; LEVELS=5] Blocks & [LEVELS=3] Plots GENERATE Blocks,Plots FRTPRODUCTDESIGNMATRIX TERM=!f(Blocks),!f(Blocks.Plots); MATRIX=S_B,S_BP PRINT [SERIAL=yes] S_B,S_BP; FIELDWIDTH=4; DECIMALS=1 CALCULATE Variance = 20 * S_B + 5 * S_BP PRINT Variance; FIELDWIDTH=4; DECIMALS=0