Saves output from analysis of an unbalanced design (by `AUNBALANCED`

) (R.W. Payne).

### Options

`FACTORIAL` = scalar |
Limit on number of factors in the model terms generated from the `TERMS` parameter; default 3 |
---|---|

`RESIDUALS` = variate |
To save residuals from the analysis |

`FITTEDVALUES` = variate |
To save fitted values |

`COMBINATIONS` = string token |
Factor combinations for which to form predicted means (`present` , `estimable` ); default `esti` |

`ADJUSTMENT` = string token |
Type of adjustment to be made when predicting means (`marginal` , `equal` , `observed` ); default `marg` |

`LSDLEVEL` = scalar |
Significance level (as a percentage) for the least significant differences |

`RMETHOD` = string token |
Type of residuals to form if the `RESIDUALS` option is set (`simple` , `standardized` ); default `simp` |

`SAVE` = identifier |
Save structure (from `AUNBALANCED` ) containing details of the analysis for which further output is required; if omitted, output is from the most recent use of `AUNBALANCED` |

### Parameters

`TERMS` = formula |
Model terms for which information is required |
---|---|

`MEANS` = table or pointer to tables |
Predicted means for each term |

`SEMEANS` = table or pointer to tables |
Standard errors of the means for each term |

`SEDMEANS` = symmetric matrix or pointer to symmetric matrices |
Standard errors of differences between means |

`ESEMEANS` = table or pointer to tables |
Approximate effective standard errors of the means: these are formed by procedure `SED2ESE` with the aim of allowing good approximations to the standard errors for differences to be calculated by the usual formula sed_{i}_{,j} = √( ese_{i}^{2} + ese_{j}^{2} ) |

`LSD` = symmetric matrix or pointer to symmetric matrices |
Least significant differences |

### Description

This procedure can be used, following the use of procedure `AUNBALANCED`

, to save output for the analysis of variance of an unbalanced design.

Options are provided to save information about the analysis as a whole. The `RESIDUALS`

and `FITTEDVALUES`

options allow variates to be specified to store the residuals and fitted values, respectively. The `RMETHOD`

option controls whether simple or standardized residuals are saved; by default `RMETHOD=simple`

.

The `SAVE`

option can be set to the save structure from the analysis from which output is to be saved. If `SAVE`

is not set, output will be produced for the most recent analysis from `AUNBALANCED`

; however, none of the Genstat regression directives (`MODEL`

, `TERMS`

, `FIT`

, `ADD`

, `DROP`

and so on) must then have been used in the interim.

The parameters of `AUKEEP`

save information about particular model terms in the analysis. With the `TERMS`

parameter you specify a model formula, which Genstat expands to form the series of model terms about which you wish to save information. As in `AUNBALANCED`

, the `FACTORIAL`

option sets a limit on the number of factors in each term. Any term containing more than that limit is deleted. The subsequent parameters allow you to specify identifiers of data structures to store various components of information for each of the terms that you have specified. The `MEANS`

parameter saves tables of predicted means, the `SEMEANS`

parameter saves tables of standard errors for the means, the `SEDMEANS`

parameter saves symmetric matrices of standard errors of differences, the `ESEMEANS`

parameter saves tables of approximate effective standard errors, and the `LSD`

parameter saves symmetric matrices of least significant differences. If you have a single term, you can supply a table or symmetric matrix for each of these parameters, as appropriate. However, if you have several terms, you must supply a pointer which will then be set up to contain as many tables or symmetric matrices as there are terms. The `LSDLEVEL`

option sets the significance level (as a percentage) for the least significant differences.

Tables of means are calculated using the `PREDICT`

directive. The first step (A) of the calculation forms the full table of predictions, classified by every factor in the model. The second step (B) averages the full table over the factors that do not occur in the table of means. The `COMBINATIONS`

option specifies which cells of the full table are to be formed in Step A. The default setting, `estimable`

, fills in all the cells other than those that involve parameters that cannot be estimated, for example because of aliasing. Alternatively, setting `COMBINATIONS=present`

excludes the cells for factor combinations that do not occur in the data. The `ADJUSTMENT`

option then defines how the averaging is done in Step B. The default setting, `marginal`

, forms a table of marginal weights for each factor, containing the proportion of observations with each of its levels; the full table of weights is then formed from the product of the marginal tables. The setting `equal`

weights all the combinations equally. Finally, the setting `observed`

uses the `WEIGHTS`

option of `PREDICT`

to weight each factor combination according to its own individual replication in the data.

Options: `FACTORIAL`

, `RESIDUALS`

, `FITTEDVALUES`

, `COMBINATIONS`

, `ADJUSTMENT`

, `LSDLEVEL`

, `RMETHOD`

, `SAVE`

.

Parameters: `TERMS`

, `MEANS`

, `SEMEANS`

, `SEDMEANS`

, `ESEMEANS`

, `LSD`

.

### Method

The output is obtained mainly using the directives `RKEEP`

and `PREDICT`

.

### Action with `RESTRICT`

If the y-variate originally analysed by `AUNBALANCED`

was restricted, only the units not excluded by the restriction will have been analysed.

### See also

Procedures: `AUNBALANCED`

, `AUDISPLAY`

, `AUGRAPH`

, `AUPREDICT`

, `AUMCOMPARISON`

.

Commands for: Analysis of variance.

### Example

CAPTION 'AUKEEP example',\ 'Data from Genstat 5 Release 1 Reference Manual, page 340.';\ STYLE=meta,plain FACTOR [NVALUES=36; LEVELS=3; VALUES=12(1...3)] Block FACTOR [NVALUES=36; LABELS=!t(baresoil,emerald,emergo)] Leachate & [LABELS=!t('1','1/4','1/16','1/64')] Dilution VARIATE [NVALUES=36] Nhatch,Nnohatch READ Leachate,Dilution,Nhatch,Nnohatch 1 2 109 318 3 4 54 350 3 1 * 415 2 2 783 212 3 3 652 1375 2 4 490 816 1 3 95 1219 2 1 1012 66 1 4 166 943 3 2 1059 313 1 1 257 1006 2 3 1058 234 2 4 507 1119 1 2 194 840 1 3 175 1707 1 1 326 609 3 4 142 980 2 3 286 230 3 2 546 313 2 2 * 301 2 1 2471 112 3 3 76 489 1 4 208 503 3 1 * 325 1 1 322 913 1 2 255 2246 3 2 1774 1446 2 2 999 193 2 4 388 1836 3 4 221 1800 1 3 220 1902 2 1 2821 187 3 1 1486 463 3 3 717 1473 1 4 143 941 2 3 968 550 : CALCULATE Logit%h = LOG(Nhatch/Nnohatch) BLOCKSTRUCTURE Block TREATMENTSTRUCTURE Leachate*Dilution AUNBALANCED [PRINT=*] Logit%h AUKEEP Leachate + Dilution;\ MEANS=!p(LeachateMeans,DilutionMeans);\ SEDMEANS=!p(LeachateSED,DilutionSED) PRINT [RLPRINT=integers,labels,identifiers;\ CLPRINT=integers,identifiers]\ LeachateMeans,LeachateSED,DilutionMeans,DilutionSED