General Linear Model uses a regression approach to fit the model that you specify. First Minitab creates a design matrix, from the factors and covariates, and the model that you specify. The columns of this matrix are the predictors for the regression.

The design matrix has n rows, where n = number of observations, and one block of columns, often called indicator variables, for each term in the model. There are as many columns in a block as there are degrees of freedom for the term. The first block is for the constant and contains one column, a column of all ones. The block for a covariate also contains one column, the covariate column itself.

Suppose A is a factor with 4 levels and the model uses -1, 0, +1 coding. Then it has 3 degrees of freedom and its block contains 3 columns, call them A1, A2, A3. Each row is coded as one of the following:

Level of A | A1 | A2 | A3 |
---|---|---|---|

1 | 1 | 0 | 0 |

2 | 0 | 1 | 0 |

3 | 0 | 0 | 1 |

4 | -1 | -1 | -1 |

Suppose factor B has 3 levels nested within each level of A. Then its block contains (3 - 1) x 4 = 8 columns, call them B11, B12, B21, B22, B31, B32, B41, B42, coded as follows:

Level of A | Level of B | B11 | B12 | B21 | B22 | B31 | B32 | B41 | B42 |
---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 2 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | 3 | -1 | -1 | 0 | 0 | 0 | 0 | 0 | 0 |

2 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |

2 | 2 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |

2 | 3 | 0 | 0 | -1 | -1 | 0 | 0 | 0 | 0 |

3 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |

3 | 2 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |

3 | 3 | 0 | 0 | 0 | 0 | -1 | -1 | 0 | 0 |

4 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |

4 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

4 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | -1 |

To calculate the indicator variables for an interaction term, multiply all the corresponding dummy variables for the factors and/or covariates in the interaction. For example, suppose factor A has 6 levels, C has 3 levels, D has 4 levels, and Z and W are covariates. Then the term A * C * D * Z * W * W has 5 x 2 x 3 x 1 x 1 x 1 = 30 indicator variables. To obtain them, multiply each indicator variable for A by each for C, by each for D, by the covariates Z one time and W twice.