Forms information about aliased model terms in analysis of variance (R.W. Payne).
Options
PRINT = string tokens |
Controls printed output (aovtable, aliasedterms); default alia |
|---|---|
TREATMENTSTRUCTURE = formula |
Treatment model for the design; if this is not set, the default is taken from any existing setting defined by the TREATMENTSTRUCTURE directive |
BLOCKSTRUCTURE = formula |
Block model for the design; if this is not set, the default is taken from any existing setting defined by the BLOCKSTRUCTURE directive |
FACTORIAL = scalar |
Limit on number of factors in a treatment term; default 3 |
RESTRICTION = variate |
Defines a restriction on the units for the analysis; default * i.e. none |
Parameters
TERMS = formula |
Model terms whose aliased terms are to be identified; the default is to take all the terms in the treatment model |
|---|---|
ALIASTERMS = formula or pointer |
New factors, with levels (and labels) that exclude those that Saves the aliased terms |
Description
When a term is aliased in an analysis of variance, it is listed in the Information summary produced by
ANOVA [PRINT=information]
under the heading “Aliased model terms”. However, ANOVA does not indicate the terms with which it is aliased. This information can be obtained using procedure FALIASTERMS.
The block structure of the design can be specified by the BLOCKSTRUCTURE option. If this is not set, the default is taken from any existing setting defined by the BLOCKSTRUCTURE directive. Similarly, the treatments are specified by the TREATMENTSTRUCTURE option, with a default taken from any existing setting defined by the TREATMENTSTRUCTURE directive. As in ANOVA, the FACTORIAL option sets a limit on the number of factors in a treatment term; default 3. The RESTRICTION option can supply a variate to define a restriction on the units of the design. (Units where the variate contains a zero value are excluded from the analysis.)
The terms whose aliasing is to be investigated are specified by the TERMS parameter. If this is not specified, all the terms in the treatment model are investigated.
The terms to which they are aliased can be saved using the ALIASEDTERMS parameter. They are saved in a formula structure if a single term has been specified by TERMS, or in a pointer containing a formula structure for each term if it has specified several.
Printed output is controlled by the PRINT option with settings:
aovtable |
to print the analysis-of-variance table; and |
aliasterms |
to print the terms to which each term is aliased (default). |
Options: PRINT, TREATMENTSTRUCTURE, BLOCKSTRUCTURE, FACTORIAL, RESTRICTION.
Parameters: TERM, ALIASTERMS.
Method
The procedure calculates a set of dummy effects for the aliased model term, and then forms and analyses a variate in which only these effects are present. The analysis detects the model terms to which the term is aliased as those that have non-zero sums of squares.
Action with RESTRICT
A restriction can be specified using the RESTRICTION option.
See also
Directives: ANOVA, FPSEUDOFACTORS.
Procedures: AEFFICIENCY, ALIAS.
Commands for: Analysis of variance, Design of experiments.
Example
CAPTION 'FALIASTERMS example'; STYLE=meta
FACTOR [NVALUES=32; LEVEL=2] A,B,C
& [LEVEL=4] D,Blocks
& [ LEVEL=8] Plots
GENERATE A,B,C & D & Blocks,Plots
VARIATE [VALUES=13,17,25,33,18,19,22,14,26,23,31,29,25,21,18,34, \
23,19,33,36,25,23,29,18,31,30,37,33,29,27,20,36] Y
BLOCKSTRUCTURE Blocks/Plots
TREATMENTS A*B*C+D
ANOVA [PRINT=aovtable,information] Y
CAPTION !T('The aov table and information summary show that D is aliased;',\
'FALIASTERMS indicates that the aliasing is with B, C and B.C ')
FALIASTERMS D
PRINT !T('The printout below confirms this:', \
'D level 1 corresponds to B level 1 and C level 1,', \
'D level 2 corresponds to B level 1 and C level 2,', \
'D level 3 corresponds to B level 2 and C level 1,', \
'D level 4 corresponds to B level 2 and C level 2.'); \
JUSTIFICATION=left
& [RLWIDTH=3; ORIENTATION=across] D,B,C; FIELDWIDTH=2; JUST=left
PRINT !T('Use RESTRICT to analyse only the first 3 blocks;', \
'the main effect D is still aliased, exactly as before...'); \
JUSTIFICATION=left
RESTRICT Y; Blocks < 4
ANOVA [PRINT=aovtable,information] Y
FALIASTERMS [RESTRICTION=Blocks<4] D