Treatment of responses below the detection limit: some current techniques compared by Factor Analysis on environmental data

Three methods of treatment of values below the detection limit (or `less-thanʹ values) are compared, in a typical case of multivariate statistical processing of environmental data. The data refer to the concentration of 14 chemical species in 42 samples of surface waters, on which a Factor Analysis is made to study the causes of pollution. Considerable effectiveness is shown, even in the presence of severe censoring, by two rather simple and widespread methods. They consist, respectively, in replacing the less-than values with a constant value and with values randomly distributed within zero and the detection limit. On the other hand, the method which estimates less-than values by means of Principal Component Analysis on the known data proves to be less effective. It is also shown that a logarithmic transformation of the original data makes the methods of treatment of less-thans less effective.