LAD in Multi-Way Tables
An important special case of the general linear model discussed in Chapters 1 and 2 is when the data fall into a multi-way table. The simplest case is the one-way layout, where the data are organized into c cells, with observations yjk, 1 ≤ k ≤ nj, in the jth cell, 1 ≤ j ≤ c.
KeywordsMedian Polish Rational Entry Important Special Case Column Median Half Step
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- 1.Emerson and Hoaglin (1983) discuss the relationship between LAD fitting and median polish. They also discuss “polishing” tables using other measures of location.Google Scholar
- 2.Kemperman (1983) discusses fitting to tables by other discrete Lp criteria, p > 1, but focuses mainly on the case p = 1. He also discusses general ideas in the construction of an algorithm like median polish that would be guaranteed to converge to a LAD fit.Google Scholar
- 3.Siegel (1983) has a graph-theoretic construction for moving from a polished table to a LAD fit by forcing certain extra residuals to zero.Google Scholar
- 4.Theorem 4.2 is new, as is the procedure, modified median polish, to which it refers.Google Scholar