Is it right to scale and log transform a variable in a lmer? I'm trying to meet the assumptions of linear mixed modeling (using lme4).
I know scaling the explanatory variables will allow a comparison of their effects on the response. However, what I don't understand is if I need to transform each variable to normality before scaling them, or if the normality assumption only matters with the response variable and not all the predictor (independent) variables? Most of my predictor variables are zero inflated and highly left skewed.
 A: Most forms of statistical analysis, including mixed modeling (and generalized linear models such as logistic regression), make few assumptions about the independent (or predictor) variables. They should in general be measured without error (there are ways to relax this assumption).
If you have continuous predictors in your model, transforming them may change the linearity of the relationships between the predictors and the response (for better or worse).  (In the generalized-linear case, this will refer to the linearity on the scale of the link function (logit, log, etc. of the expected response). It may also change the nature of interactions among predictors.
Strongly skewed predictors, outliers, or predictors with lots of zeros will in general decrease your statistical power, but there's not much you can do about that. For outliers, you should probably consider whether you expect (on a priori/subject-area grounds) those points would be representative of the same processes that are going on with the rest of the data.
