Publication date: 04/12/2021

The exact model type that you choose depends on how the data was collected. For example, are the operators measuring the same parts (in which case you have a crossed design) or are they measuring different parts (in which case you have a nested design)? To illustrate, in a model where B is nested within A, multiple measurements are nested within both B and A, and there are na•nb•nw measurements, the following statements hold:

• na random effects are due to A

• na•nb random effects due to each nb B levels within A

• na•nb•nw random effects due to each nw levels within B within A:

.

The Zs are the random effects for each level of the classification. Each Z is assumed to have a mean of zero and to be independent from all other random terms. The variance of the response y is the sum of the variances due to each z component:

.

Table 5.3 shows the supported models and what the effects in the model would be.

Model |
Factors |
Effects in the Model |
---|---|---|

Main Effects |
1 2 unlimited |
A A, B and so on, for more factors |

Crossed |
1 2 3 4 unlimited |
A A, B, A*B A, B, A*B, C, A*C, B*C, A*B*C A, B, A*B, C, A*C, B*C, A*B*C, D, A*D, B*D, A*B*D, C*D, A*C*D, B*C*D, A*B*C*D, and so on, for more factors |

Nested |
1 2 3 4 unlimited |
A A, B(A) A, B(A), C(A,B) A, B(A), C(A,B), D(A,B,C) and so on, for more factors |

Crossed then Nested |
3 |
A, B, A*B, C(A,B) |

Nested then Crossed |
3 |
A, B(A), C, A*C, C*B(A) |

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