I have a dataset in which the response variable is non normal, but on log transforming, it follows the normal distribution. I constructed a mixed effect model using lme4::lmer() as below (multiple measurements within each region), where A is a continuous variable and there are 7 regions
model<-lmer(log(response)~A + (1|Region), data, REML=FALSE)
My output is
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: logresponse ~ A + (1 | Region) Data: df[, -c(6)] AIC BIC logLik deviance df.resid 151.8 159.8 -71.9 143.8 51 Scaled residuals: Min 1Q Median 3Q Max -2.24856 -0.63631 0.02206 0.59999 1.94895 Random effects: Groups Name Variance Std.Dev. Region (Intercept) 0.8611 0.9280 Residual 0.5814 0.7625 Number of obs: 55, groups: Region, 7 Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) -1.112047 0.747373 19.651457 -1.488 0.1526 A 0.008585 0.004250 29.157266 2.020 0.0526 . Correlation of Fixed Effects: (Intr) A -0.871
1) Would I infer that for A effects the response variable and the response increases by exp(0.008585) +/- exp(0.004250) (std error)? Would that be the right interpretation?
2) exp(Intercept) is not equal to the mean(log response). They are close but not equal. Why are they not equal and should I be concerned?
I know that this is a hard question to answer without knowing the dataset. So please suggest how I can improve the question.