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# RTCOMPARISONS procedure

Calculates comparison contrasts within a multi-way table of means (R.W. Payne).

### Options

`PRINT` = string token Controls printed output (`contrasts`); default `cont` Factor combinations for which to form the predicted means (`full`, `present`, `estimable`); default `esti` Type of adjustment to be made when forming the predicted means (`marginal`, `equal`, `observed`); default `marg` Weights classified by some or all of the factors in the model; default `*` Value of offset on which to base predictions; default mean of offset variate Method of forming margin (`mean, total`); default `mean` How to deal with aliased parameters (`fault`, `ignore`); default `faul` What back-transformation to apply to the values on the linear scale, before calculating the predicted means (`link, none`); default `link` Controls whether the variance of predictions is calculated on the basis of forecasting new observations rather than summarizing the data to which the model has been fitted (`data`, `new`); default `data` Which warning messages to suppress (`dispersion`, `nonlinear`); default `*` Value of dispersion parameter in calculation of s.e.s; default is as set in the `MODEL` statement Basis of estimate of dispersion, if not fixed by `DISPERSION` option (`deviance, Pearson`); default is as set in the `MODEL` statement Supplies the total number of trials to be used for prediction with a binomial distribution (providing a value n greater than one allows predictions to be made of the number of “successes” out of n, whereas the value one predicts the proportion of successes); default 1 Regression or `ANOVA` save structure for the analysis from which the comparisons are to be calculated

### Parameters

`CONTRAST` = tables Defines the comparisons to be estimated Saves the estimated contrasts Saves standard errors of the contrasts

### Description

`RTCOMPARISONS` makes comparisons within multi-way tables of predicted means from a linear or generalized linear regression or an analysis of variance. The model should previously have been fitted by the `FIT` or `ANOVA` directives 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 the `MODEL` or `ANOVA` directives). If `SAVE` is not specified, the comparisons are calculated from the most recent regression analysis.

Each comparison is specified in a table supplied by the `CONTRAST` parameter. For a regression or generalized linear models analysis, `RTCOMPARISONS` calculates the means 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, or `COMBINATIONS=full` uses all the cells. 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. Alternatively, you can supply your own table of weights, using the `WEIGHTS` option. The `COMBINATIONS` and `ADJUSTMENT` options are irrelevant if a `SAVE` structure is from an `ANOVA` analysis – the means are then obtained using `AKEEP` (and correspond to those that would be printed by `ANOVA`). The options `OFFSET`, `METHOD`, `ALIASING`, `BACKTRANSFORM`, `SCOPE`, `NOMESSAGE`, `DISPERSION`, `DMETHOD` and `NBINOMIAL` are also relevant only to regression, and operate exactly as in the `PREDICT` directive.

The `PRINT` option controls printed output, with setting:

    `contrasts` to print the contrasts (default).

The `ESTIMATE` parameter allows you to save the estimated contrast, and the `SE` parameter can save its standard error.

Options: `PRINT`, `COMBINATIONS`, `ADJUSTMENT`, `WEIGHTS`, `OFFSET`, `METHOD`, `ALIASING`, `BACKTRANSFORM`, `SCOPE`, `NOMESSAGE`, `DISPERSION`, `DMETHOD`, `NBINOMIAL`, `SAVE`.

Parameters: `CONTRAST`, `ESTIMATE`, `SE`.

### Method

The predicted means and their variances and covariances are obtained using the `PREDICT` directive for a regression analysis, or using `AKEEP` for an analysis of variance. The comparisons and their standard errors are then calculated using Genstat’s table and matrix calculation facilities.

Directive: `PREDICT`.

Procedures: `FCONTRASTS`, `RCOMPARISONS`, `VTCOMPARISONS`.

Commands for: Regression analysis.

### Example

```CAPTION       'RTCOMPARISONS example',\
!t('3x2 factorial experiment (Snedecor & Cochran, 1980,',\
'Statistical Methods, seventh edition, p. 305).');\
STYLE=meta,plain
FACTOR        [NVALUES=60; LABELS=!T(high,low); VALUES=3(1,2)10] Amount
&             [LABELS=!T(beef,cereal,pork); VALUES=(1...3)20] Source
VARIATE       [NVALUE=60] Gain
73  98  94  90 107  49
102  74  79  76  95  82
118  56  96  90  97  73
104 111  98  64  80  86
81  95 102  86  98  81
107  88 102  51  74  97
100  82 108  72  74 106
87  77  91  90  67  70
117  86 120  95  89  61
111  92 105  78  58  82 :
MODEL         Gain
FIT           Source*Amount
CAPTION       !t('Comp1 compares high beef with low cereal, and Comp2',\
'compares the mean of high beef & high pork with low cereal.')
TABLE         [CLASSIFICATION=Amount,Source] Comp1,Comp2;\
VALUES=!(1,0,0,0,-1,0),!(0.5,0,0.5,0,-1,0)
PRINT         Comp1
&             Comp2
RTCOMPARISONS Comp1,Comp2
```
Updated on June 18, 2019