Common Errors in Statistics (and How to Avoid Them), 4th Edition

Chapter 12

Alternate Methods of Regression

Imagine how statisticians might feel about the powerful statistics programs that are now in our hands. It is so easy to key-in a set of data and calculate a wide variety of statistics—regardless what those statistics are or what they mean. There also is a need to check that things are done correctly in the statistical analyses we perform in our laboratories.

—James O. Westgard [1998]

IN THE PREVIOUS CHAPTER, WE FOCUSED EXCLUSIVELY ON ordinary least-squares linear regression (OLS) both because it is the most common modeling technique and because the limitations and caveats we outlined there apply to virtually all modeling techniques. But OLS is not the only modeling technique. To diminish the effect of outliers, and treat prediction errors as proportional to their absolute magnitude rather than their squares, one should use least absolute deviation (LAD) regression. This would be the case if the conditional distribution of the dependent variable were characterized by a distribution with heavy tails (compared to the normal distribution, increased probability of values far from the mean).

One should also employ LAD regression when the conditional distribution of the dependent variable given the predictors is not symmetric and we wish to estimate its median rather than its mean value.

If it is not clear which variable should be viewed as the predictor and which the dependent variable, as is the case when evaluating two methods of measurement, ...