Calculates comparison contrasts within a multi-way table of means (R.W. Payne).
Options
PRINT = string token |
Controls printed output (contrasts); default cont |
|---|---|
COMBINATIONS = string token |
Factor combinations for which to form the predicted means (full, present, estimable); default esti |
ADJUSTMENT = string token |
Type of adjustment to be made when forming the predicted means (marginal, equal, observed); default marg |
WEIGHTS = table |
Weights classified by some or all of the factors in the model; default * |
OFFSET = scalar |
Value of offset on which to base predictions; default mean of offset variate |
METHOD = string token |
Method of forming margin (mean, total); default mean |
ALIASING = string token |
How to deal with aliased parameters (fault, ignore); default faul |
BACKTRANSFORM = string token |
What back-transformation to apply to the values on the linear scale, before calculating the predicted means (link, none); default link |
SCOPE = string token |
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 |
NOMESSAGE = string tokens |
Which warning messages to suppress (dispersion, nonlinear); default * |
DISPERSION = scalar |
Value of dispersion parameter in calculation of s.e.s; default is as set in the MODEL statement |
DMETHOD = string token |
Basis of estimate of dispersion, if not fixed by DISPERSION option (deviance, Pearson); default is as set in the MODEL statement |
NBINOMIAL = scalar |
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 |
SAVE = identifier |
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 |
|---|---|
ESTIMATES = scalars |
Saves the estimated contrasts |
SE = scalars |
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.
See also
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
READ 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