medpolish Median Polish (Robust Twoway Decomposition) of a Matrix

Description

Fits an additive model (twoway decomposition) using Tukey's median polish procedure.

Usage

medpolish(x, eps = 0.01, maxiter = 10, trace.iter = TRUE,
          na.rm = FALSE)

Arguments

x	a numeric matrix.
eps	real number greater than 0. A tolerance for convergence: see ‘Details’.
maxiter	the maximum number of iterations
trace.iter	logical. Should progress in convergence be reported?
na.rm	logical. Should missing values be removed?

Details

The model fitted is additive (constant + rows + columns). The algorithm works by alternately removing the row and column medians, and continues until the proportional reduction in the sum of absolute residuals is less than eps or until there have been maxiter iterations. The sum of absolute residuals is printed at each iteration of the fitting process, if trace.iter is TRUE. If na.rm is FALSE the presence of any NA value in x will cause an error, otherwise NA values are ignored.

medpolish returns an object of class medpolish (see below). There are printing and plotting methods for this class, which are invoked via by the generics print and plot.

Value

An object of class medpolish with the following named components:

overall	the fitted constant term.
row	the fitted row effects.
col	the fitted column effects.
residuals	the residuals.
name	the name of the dataset.

References

Tukey, J. W. (1977). Exploratory Data Analysis, Reading Massachusetts: Addison-Wesley.

See Also

median; aov for a mean instead of median decomposition.

Examples

require(graphics)

## Deaths from sport parachuting;  from ABC of EDA, p.224:
deaths <-
    rbind(c(14,15,14),
          c( 7, 4, 7),
          c( 8, 2,10),
          c(15, 9,10),
          c( 0, 2, 0))
dimnames(deaths) <- list(c("1-24", "25-74", "75-199", "200++", "NA"),
                         paste(1973:1975))
deaths
(med.d <- medpolish(deaths))
plot(med.d)
## Check decomposition:
all(deaths ==
    med.d$overall + outer(med.d$row,med.d$col, "+") + med.d$residuals)