Saves information from the analysis of a multitiered design by `AMTIER`

(C.J. Brien & R.W. Payne).

### Options

`RESIDUALS` = variate |
Saves the residuals |
---|---|

`FITTEDVALUES` = variate |
Saves the fitted values |

`AOVTABLE` = pointer |
Saves the analysis-of-variance table |

`SKELETON` = string token |
Whether to save only the skeleton analysis-of-variance table (`yes` , `no` ); default `no` |

`PSEUDOLINES` = string token |
Whether to include lines for pseudo-terms in the analysis-of-variance table (`yes` , `no` ); default `no` |

`OMITMISSINGLINES` = string token |
Whether to omit lines of the analysis-of-variance table that contain only missing values (`yes` , `no` ); default `no` |

`SAVE` = pointer |
Save structure for the analysis; if this is not set, information is saved from the most recent `AMTIER` analysis |

### No parameters

### Description

The `AMTIER`

procedure analyses data from designs that require up to three model formulae to specify their analysis (resulting from three or more tiers for the experiment). Information from an `AMTIER`

analysis can be saved by the `SAVE`

parameter, and input to `AMTKEEP`

using its own `SAVE`

parameter. Alternatively, if `SAVE`

is not set, `AMTKEEP`

will use the information from the most recent `AMTIER`

analysis.

The `RESIDUALS`

and `FITTEDVALUES`

options save the residuals and fitted values, respectively, in variates.

The `AOVTABLE`

option saves the analysis-of-variance table. You can set option `PSEUDOLINES=yes`

to include lines for all the component pseudo-terms of a term; by default lines are included only for the term itself. You can set option `SKELETON=yes`

to obtain a “skeleton” analysis of variance, omitting the columns for sums of squares, mean squares and variance ratios. You can set option `OMITMISSINGLINES=yes`

to omit lines of the analysis-of-variance table, such as stratum headers, that contain only missing values.

Options: `RESIDUALS`

, `FITTEDVALUES`

, `AOVTABLE`

, `SKELETON`

, `PSEUDOLINES`

, `OMITMISSINGLINES`

, `SAVE`

.

Parameters: none.

### Method

Multitiered experiments are defined by Brien (1983), their design is discussed by Brien & Bailey (2006) and Brien *et al.* (2011), and their analysis of variance is described by Brien & Payne (1999), Brien & Bailey (2009) and Bailey & Brien (2013).

### References

Bailey, R.A. & Brien C.J. (2013). Randomization-based models for multitiered experiments. I. A chain of randomizations. arXiv preprint arXiv:1310.4132: 30.

Brien, C.J. (1983). Analysis of variance tables based on experimental structure. *Biometrics*, 39, 53-59.

Brien, C.J. & Bailey, R.A. (2006). Multiple randomizations. *Journal of the Royal Statistical Society, Series B*, 68, 571-609.

Brien, C.J. & Bailey, R.A. (2009). Decomposition tables for multitiered experiments. I. A chain of randomizations. *The Annals of Statistics*, 36, 4184-4213.

Brien, C.J., Harch, B.D., Correll, R.L. & Bailey, R.A. (2011). Multiphase experiments with at least one later laboratory phase. I. Orthogonal designs. *Journal of Agricultural, Biological and Environmental Statistics*, 16, 422-450.

Brien, C.J. & Payne, R.W. (1999). Tiers, structure formulae and the analysis of complicated experiments. *The Statistician*, 48, 41-52.

### See also

Procedures: `AMTIER`

, `AMTDISPLAY`

.

Commands for: Analysis of variance.

### Example

CAPTION 'AMTKEEP example','Example from Brien & Payne (1999).';\ STYLE=meta,plain SPLOAD [PRINT=*] '%gendir%/examples/Amtier.gsh' AMTIER [PRINT=aovtable; FACTORIAL=5;\ F1=((Occasions/Intervals/Sittings)*Judges)/Positions;\ F2=(Rows*(Squares/Columns))/Halfplots; F3=Trellis*Method] Score AMTKEEP [AOVTABLE=aovtable] PRINT aovtable[]