Estimation of Missing Values for the Analysis of Incomplete Data

Publisher Website
Google Scholar
Abstract
Equations for missing values can be formed simply by equating each unknown (for a missing value) to its estimated expectation derived from the formally complete data in which the unknowns represent the missing values. The matrix of coefficients of the missing value equations has a simple structure: each coefficient corresponds to a pair of missing values (including identical pairs) and its value is determined by the relation between the pair of missing values in the experimental design. Thus, to facilitate the formation of the equations, a table of relations for the experimental design can be set up, with the corresponding values of coefficients. Note that the inverse of the matrix of coefficients is required in computing correct Standard Errors. The paper gives a derivation of the basic result, and provides tables of coefficients for some of the standard designs. Solution of the equations by matrix inversion, in particular, is discussed in some detail, and also the solution of singular equations. A concise table for determining missing values in Randomized Blocks is presented. The procedure of forming and solving equations will generally be simpler than the older method (Yates) of applying the formula for a single missing value iteratively.

This publication has 2 references indexed in Scilit: