Alternative Methods of Adjusting for Heteroscedasticity in Wheat Growth Data

Excerpts from the report Introduction: The purpose of this report is to suggest some techniques which are useful in adjusting for heteroscedastic disturbances common to growth data. While all the results pertain specifically to dried wheat head weights, it is hoped that the concepts involved are general enough to be of use with other types of growth data or in non-growth situations. Two basic approaches will be discussed; log transformations and weighted least squares. Several different log transformations will be developed most of which are of the form ln (Ay + B) where y is the dependent variable and A and B are derived constants based on various criteria. The last transformation discussed has four constants to be specified and the log is taken twice. The second approach is to weight the diagonal elements of the variance-covariance matrix of the dependent variable by some appropriate function which creates a homoscedastic disturbance term. A linear function is used which relates the expected value of the dependent variable to the population standard deviation.