Calculates comparison contrasts within a multi-way table of predicted means from a `REML`

analysis (R.W. Payne).

### Options

`PRINT` = string tokens |
Controls printed output (`contrasts` , `Waldtests` ); default `cont` |
---|---|

`MODEL` = formula |
Indicates which model terms (fixed and/or random) are to be used in forming the predictions; default `*` includes all the fixed terms and relevant random terms |

`OMITTERMS` = formula |
Specifies terms to be excluded from the `MODEL` ; default `*` i.e. none |

`FACTORIAL` = scalar |
Limit on the number of factors or variates in each term in the models specified by `MODEL` or `OMITTERMS` ; default 3 |

`PRESENTCOMBINATIONS` = identifiers |
Lists factors for which averages should be taken across combinations that are present |

`WEIGHTS` = tables |
One-way tables of weights classified by factors in the model; default `*` |

`GROUPS` = factors |
Groups for which to estimate each contrast |

`DFMETHOD` = string token |
Specifies which degrees of freedom to use for the comparisons (`fddf` , `given` , `tryfddf` , `none` ); default `fddf` |

`DFGIVEN` = scalar |
Specifies the number of degrees of freedom to use for the comparisons when `DFMETHOD=given` , or if d.d.f. are unavailable when `DFMETHOD=tryfddf` |

`FMETHOD` = string token |
Controls how to calculate denominator degrees of freedom for the F-statistics, if these are not already available in the `REML` save structure (`automatic` , `algebraic` , `numerical` ); default `auto` |

`SAVE` = identifier |
`REML` save structure for the analysis from which the comparisons are to be calculated |

### Parameters

`CONTRAST` = tables |
Defines the comparisons to be estimated |
---|---|

`ESTIMATE` = scalars or variates |
Saves the estimated contrasts |

`SE` = scalars or variates |
Saves standard errors of the contrasts |

`VCOVARIANCE` = symmetric matrices |
Save the variance-covariance matrices of contrasts estimated for `GROUPS` |

`STATISTIC` = scalars or variates |
Saves saves the test statistic (t or Wald) |

`DF` = scalars or variates |
Saves estimated numbers of residual degrees of freedom of the contrasts |

`PROBABILITY` = scalars or variates |
Saves the probabilities of the contrasts |

`WALD` = scalars |
Wald statistic for each comparison, combining the tests within groups |

`FSTATISTIC` = scalars |
F statistics for each comparison, if available, combining the tests within groups |

`NDF` = scalars |
Numerator d.f. for `FSTATISTIC` |

`DDF` = scalars |
Denominator d.f. for `FSTATISTIC` |

### Description

`VTCOMPARISON`

makes comparisons within multi-way tables of predicted means from a `REML`

analysis. The data should previously have been analysed by the `REML`

directive in the usual way. The `SAVE`

option can be used to specify the save structure from the analysis for which the comparisons are to be calculated (see the `SAVE`

option of `REML`

). If `SAVE`

is not specified, the comparisons are calculated from the most recent `REML`

analysis.

Each comparison is specified in a table supplied by the `CONTRAST`

parameter. `VTCOMPARISON`

calculates the means using the `VPREDICT`

directive. The calculations consist of two steps. The first step is to calculate a table of fitted values. The `MODEL`

, `OMITTERMS`

and `FACTORIAL`

options specify the model to use for this. The formula specified by `MODEL`

is expanded into a list of model terms, deleting any that contain more variates or factors than the limit specified by the `FACTORIAL`

option. Then, any terms in the formula specified by `OMITTERMS`

are removed. The second step averages the fitted values over the classifications that are not in the list that was supplied by the `CLASSIFY`

parameter. The `WEIGHTS`

option can supply one-way tables classified by any of the factors in the model. These are used to calculate the weight to be used for each fitted value when calculating the averages. Equal weights are assumed for any factor for which no table of weights has been supplied. In the averaging all the fitted values are generally used. However, if you define a list of factors using the `PRESENTCOMBINATIONS`

option, any combination of levels of these factors that does not occur in the data will be omitted from the averaging. Where a prediction is found to be inestimable, i.e. not invariant to the model parameterization, a missing value is given.

The `GROUPS`

option is useful if you want to calculate the same comparisons for several groups, defined by the combinations of levels of one or more factors in the `REML`

analysis. You can then use the `CONTRAST`

parameter to define the comparison-definition tables ignoring the groups, and the `GROUPS`

option to specify the factors defining the groups.

The `DFMETHOD`

option specifies how to obtain the numbers of residual degrees of freedom for the comparisons. The default is to use the numbers of denominator degrees of freedom printed by `REML`

in the `d.d.f.`

column in the table of tests for fixed tests (produced by setting option `PRINT=wald`

). These degrees of freedom are relevant for assessing the fixed term as a whole, and may differ over the various comparisons amongst its means, or for predictions produced with different models or weightings from those used in `REML`

and `VDISPLAY`

. So the t-probabilities should be used with caution. If you want a more exact probability for a comparison, you should set up a covariate to fit this explicitly in the analysis. The `FMETHOD`

option controls how the denominator degrees of freedom should be calculated, if they are not already available in the `REML`

save structure (e.g. because they were printed in the original analysis). The settings are the same as in the `REML`

and `VKEEP`

directives, except that there is no `none`

setting. (You would set this option only if you really do want to calculate them.)

In some of the more complicated analyses, `REML`

may be unable to calculate the denominator degrees of freedom. You might then want to supply the number of degrees of freedom yourself, using the `DFGIVEN`

option, rather than having no probabilities at all. For example, you could use the number of denominator degrees of freedom from the analysis of an earlier similar design. However, the results will only be as good as the degrees of freedom that you have supplied, and thus should be used with caution! You can set option `DFMETHOD=tryfddf`

to use the denominator degrees of freedom, if these can be calculated, or those specified by `DFGIVEN`

otherwise. The setting `DFMETHOD=given`

always uses the degrees of freedom specified by `DFGIVEN`

.

If no d.d.f. are available, `VTCOMPARISONS`

forms Wald statistics instead of t-statistics, and calculates their probabilities using the fact that, asymptotically, they have chi-square distributions with one degree of freedom. The Wald probabilities tend to be biased (giving too many significant results), and should thus be used with caution. You can set `DFMETHOD=none`

to enforce the use of Wald statistics.

The `PRINT`

option controls printed output, with settings:

`contrasts` |
prints the contrasts (default); and |
---|---|

`Waldtests` |
when `GROUPS` is set this prints Wald tests combining the tests of each contrast in the various groups, F tests are also given provided `REML` has been able to estimate the d.d.f. |

The `ESTIMATE`

parameter allows you to save the estimates for the comparisons. If the `GROUPS`

option is not set, each comparison will have a single estimate which will be saved in a scalar. Alternatively, if there are groups, there will be an estimate for each group, and these will be saved in a variate defined with unit labels that identify the groups. Similarly, the `SE`

parameter can save the standard errors of the comparisons, the `DF`

parameter can save their estimated number of residual degrees for freedom, the `STATISTIC`

parameter can save their test statistics (t or Wald), and the `PROBABILITY`

parameter can save their probabilities.

When there are groups, the variances and covariances of the estimates for each contrast can be saved in a symmetric matrix, using the `VCOVARIANCE`

parameter. The `WALD`

, `FSTATISTIC`

, `NDF`

and `DDF`

parameters can save the results of the tests combining the tests for each contrast in the various groups.

Options: `PRINT`

, `MODEL`

, `OMITTERMS`

, `FACTORIAL`

, `PRESENTCOMBINATIONS`

, `WEIGHTS`

, `GROUPS`

, `DFMETHOD`

, `DFGIVEN`

, `FMETHOD`

, `SAVE`

.

Parameters: `CONTRAST`

, `ESTIMATE`

, `SE`

, `VCOVARIANCE`

, `STATISTIC`

, `DF`

, `PROBABILITY`

, `WALD`

, `FSTATISTIC`

, `NDF`

, `DDF`

.

### See also

Directive: `VPREDICT`

.

Procedures: `FCONTRASTS`

, `RTCOMPARISONS`

.

Commands for: REML analysis of linear mixed models.

### Example

CAPTION 'VTCOMPARISON example',!t('Split plot design, see the',\ 'Guide to Genstat, Part 2, Section 4.2.1.'); STYLE=meta,plain FACTOR [NVALUES=72; LEVELS=6] Blocks & [LEVELS=3] Wplots & [LEVELS=4] Subplots GENERATE Blocks,Wplots,Subplots FACTOR [LABELS=!T('0 cwt','0.2 cwt','0.4 cwt','0.6 cwt')] Nitrogen & [LABELS=!T(Victory,'Golden rain',Marvellous)] Variety VARIATE Yield; DECIMALS=2; EXTRA=' of oats in cwt. per acre' READ [SERIAL=yes] Nitrogen,Variety,Yield 4 3 2 1 1 2 4 3 1 2 3 4 3 1 2 4 4 1 2 3 2 1 3 4 2 3 4 1 4 2 3 1 1 4 2 3 3 4 1 2 1 3 4 2 2 3 4 1 4 1 3 2 3 4 1 2 3 4 2 1 3 1 4 2 4 3 1 2 1 2 3 4 : 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 1 1 1 1 3 3 3 3 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 3 3 3 3 1 1 1 1 2 2 2 2 3 3 3 3 : 156 118 140 105 111 130 174 157 117 114 161 141 104 70 89 117 122 74 89 81 103 64 132 133 108 126 149 70 144 124 121 96 61 100 91 97 109 99 63 70 80 94 126 82 90 100 116 62 96 60 89 102 112 86 68 64 132 124 129 89 118 53 113 74 104 86 89 82 97 99 119 121 : VCOMPONENTS [FIXED=Variety*Nitrogen] Blocks/Wplots/Subplots REML [PRINT=means] Yield TABLE [CLASSIFICATION=Variety] Comp1; VALUES=!(1,0,-1) TABLE [CLASSIFICATION=Nitrogen] Comp2; VALUES=!(-1,0.25,0.25,0.5) TABLE [CLASSIFICATION=Variety,Nitrogen] Comp3,Comp4;\ VALUES=!(1,0,0,0, -1,0,0,0, 0,0,0,0),\ !(1,0,0,0, 0,0,0,0, 0,0,0,-1) PRINT Comp1 & Comp2 & Comp3 & Comp4 VTCOMPARISONS Comp1,Comp2,Comp3,Comp4