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MPOLISH procedure

Performs a median polish of two-way data (D.B. Baird).

Options

`MAXCYCLE` = scalar Maximum number of iterations; default 50 Tolerance for convergence; default 0.0001

Parameters

`DATA` = variates or pointers or matrices or tables Two-way data to be polished Row definitions for a `DATA` variate Column definitions for a `DATA` variate Row effects removed from polished results Column effects removed from polished results Polished result in same format as `DATA` 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`.

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