In practical applications based on widely available software, the choice to-day is between regressions with BCT (and, say, parameters beta and lambda) or with simple power transformations of variables (and, say, parameters delta and rho). The dummy variable method beats them all. We did formal tests of different ways to handle that (they are called Z-rules) in the text and in the appendices.

In that paper on rail track costs, the different types of train traffic do not use all track segments, so there are sometimes 0. The problem is that the slope coefficient is forced to be vertical.These points are discussed at length in the enclosed paper. If you use small values instead of zeroes, it works reasonably well, as an approximation, as long as the proportion of zeroes is small. This method is the only correct method of using logarithms of variables including zeroes. This must be done with care because 0 values for different explanatory variables occurring for the same observations could cause multicolinearity among the dummy variables (which can be defined as 1 if there is a 0 and 0 otherwise or the reverse). If one does this (without transforming the 0 observations), one must add a dummy variable that offsets the shift at zero for each explanatory variable that includes some zeroes. One way of dealing with observed 0 values of explanatory variables and to admit their logarithmic transformation is to use Box-Cox transformations on these explanatory variables. Josep's reply above is a good start if you want to get involved with compositional data analysis, and there is a lot more out there on the topic. I did a brief note at - its at the very end of the note. However, using untransformed data with proportional data has been criticized since Fisher! We all made the mistake in the past but no longer have to. Once transformed you can work entirely in Simplex space using something like the R 'compositions' package or, you can simply use conventional statistics. If not either throw out that record or if you are happy with it make the zero a very small number. If your data is derived from a machine then find out the limits of detection of that particular machine and substitute that value for your zero's.

proportional data you need to transform into Simplex space using log transformations before any analysis that uses normal distributions. If you are dealing with data that has the constant sum problem i.e.

Log transformation xlstat