# Modeling the precision and location parameters in beta regression

Is there any technical or substantive reason to typically want to ensure the location $$\mu$$ and precision $$\phi$$ parameters in the beta regression model include the same fixed or varying predictors?

I think it's a reasonable default to assume that all predictor variables that affect the mean $$\mu$$ of the response variable actually affect its entire distribution and hence also the precision $$\phi$$.
However, it is not unusual to have predictor variables that have a clear influence on $$\mu$$ but less or virtually no influence on $$\phi$$. Also, it is conceivable that you have predictor variables that are explicitly associated with the precision $$\phi$$ (as they correspond to "uncertainty" or "ambiguity" in some way) but not (much) with $$\mu$$.