Often to show data that is highly dispersed one will compress the data by graphing its log. One down-side of this is that it only works if the data is all-positive or all-negative (if you use −ln(−x)). If your data contains zero and/or points in both domains then the you have to do something else. Here is a simple extension that uses a linear function around zero to smoothly connect a log function and it's opposite. x={ln(x)if x>ex/eif −e≤x≤e−ln(−x)if x<−e The function is log-linear-log ("trilog").
You can get a simple Stata utility -trilog- from here to make this transformation and create axis labels.
Another intuitive extension would be to shift the log and its opposite closer to zero, such as x={ln(x+1)if x≥0−ln(−x+1)if x<0 The downside of this is that no longer are equal proportional changes reflected as equal distance changes.
You can get a simple Stata utility -trilog- from here to make this transformation and create axis labels.
Another intuitive extension would be to shift the log and its opposite closer to zero, such as x={ln(x+1)if x≥0−ln(−x+1)if x<0 The downside of this is that no longer are equal proportional changes reflected as equal distance changes.