stats (version 3.3)

medpolish: Median Polish of a Matrix

Description

Fits an additive model 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?

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.

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.

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)