Very generally, log(X+1) isn't a smart way to deal with X=0 cases. The really interesting point is why you get zeros in a model where you want to or have to explain multiplicative effects. Sometimes, these zeros come from a wrong treatment of background signal, a wrong treatment of control measurements, or a wrong treatment of values that are below some limit of quantification or detection. Or from a wrong understanding of the data-generating process in total. It would be better to reveal and properly solve such problems if they are the reason.

If a reason is identified but cannot be solved, you may consider other work-arounds like using a tobit-model, a zero-inflated model, or a quasi-Poisson model.

In analytical sciences, if the proportion of values below the limit of quantification (LOQ) is low, it's a usual solution to plug-in half the LOQ value.

If your variable is a count variable, use a count model (Poisson, negative binomial) that can handle zero counts.

Hello Pcl Lee. It may be that some of Jochen Wilhelm's guesses about your situation were correct. Nevertheless, it would help if you provided more information. For example:

• What is the dependent variable?
• Why did you log-transform it?
• What are the explanatory variables?
• What is your research question?

Thanks for clarifying.

Maybe I’m missing something but after the transformation your model coefficients are on the log scale. The log scale is multiplicative is it not? Therefore a coefficient less then one is a decrease. With the back transform it’s still a decrease. Your issue with this is? Cheers John