Performs a median polish of two-way data (D.B. Baird).
Options
MAXCYCLE = scalar |
Maximum number of iterations; default 50 |
---|---|
TOLERANCE = scalar |
Tolerance for convergence; default 0.0001 |
Parameters
DATA = variates or pointers or matrices or tables |
Two-way data to be polished |
---|---|
ROWS = factors |
Row definitions for a DATA variate |
COLUMNS = factors |
Column definitions for a DATA variate |
ROWEFFECTS = variate |
Row effects removed from polished results |
COLEFFECTS = variate |
Column effects removed from polished results |
POLISH = variates or pointers or matrices or tables |
Polished result in same format as DATA |
CENTRE = scalars |
Estimate of overall centre point |
Description
MPOLISH
performs a median polish of two-way data, supplied by the DATA
parameter. This can be a two-dimensional table, a matrix or a pointer of variates. Alternatively, it can be a single variate. The rows and columns are then defined by factors supplied by the ROWS
and COLUMNS
parameters, or by just the COLUMNS
parameter with the data valueS assumed to be sorted into row order within each column.
The MAXCYCLE
option sets a limit on the number of iterations. The TOLERANCE
option specifies the convergence criterion: convergence occurs when
ABS(1-SUM(ABS(OldPolish)) / SUM(ABS(NewPolish))) < TOLERANCE
The polished data can be saved by the POLISH
parameter, row effects by the ROWEFFECTS
parameter, column effects by the COLEFFECTS
parameter, and the overall centre point by the CENTRE
parameter.
Options: MAXCYCLE
, TOLERANCE
.
Parameters: DATA
, ROWS
, COLUMNS
, ROWEFFECTS
, COLEFFECTS
, POLISH
, CENTRE
.
See also
Procedures: MPOLISH
, ROBSSPM
, TUKEYBIWEIGHT
.
Commands for: Calculations and manipulation.
Example
CAPTION 'MPOLISH example'; STYLE=meta FACTOR [LEVELS=10; VALUES=8(1...10)] Block FACTOR [LABELS=!t(A,B,C,D,E,F,G,H); VALUES=(1...8)10] Treat "Log-Normally distributed effects & residuals" CALCULATE [SEED=130403] TMeans = EXP(GRNORMAL(8; 1; 2)) & [SEED=0] BMeans = EXP(GRNORMAL(10; 0.5; 1)) "Centre Effects around zero" CALCULATE TMeans,BMeans = TMeans,BMeans - MEDIAN(TMeans,BMeans) & Y = NEWLEVELS(Block;BMeans) + NEWLEVELS(Treat;TMeans) +\ EXP(GRNORMAL(80;1;0.5)) MPOLISH [TOLERANCE=0.0001] Y; ROWS=Block; COLUMNS=Treat;\ ROWEFFECTS=Blk_Effects; COLEFFECTS=Trt_Effects;\ POLISH=Residuals; CENTRE=Centre CAPTION 'True and estimated treatment effects'; STYLE=minor PRINT TMeans,Trt_Effects; FIELD=14; DECIMALS=1 CAPTION 'True and estimated block effects'; STYLE=minor PRINT BMeans,Blk_Effects; FIELD=14; DECIMALS=1 "Shade plot of residuals" TABULATE [CLASS=Block,Treat;PRINT=*] Residuals; MEANS=Res_Table DSHADE [TITLE='Residuals from MPOLISH'] Res_Table; PEN=!(4,2); NGROUPS=256