Adjusted Inertia

The usual principal inertias of a Burt table constructed from m categorical variables in MCA are the eigenvalues uk from

. These inertias provide a pessimistic indication of fit. Benzécri (1979) proposed the following inertia adjustment; it is also described by Greenacre (1984, p. 145):

for

This adjustment computes the percent of adjusted inertia relative to the sum of the adjusted inertias for all inertias greater than

Greenacre (1994, p. 156) argues that the Benzécri adjustment overestimates the quality of fit. Greenacre proposes instead to compute the percentage of adjusted inertia relative to:

for all inertias greater than

, where

is the sum of squared inertias and nc is the total number of categories across the m variables.