I understand this topic is well covered here, but having read several threads, I can't find an explicit or clear answer to my question. I looked at the following threads and can't glean an answer from any of them.
Analysing log and square-root transformed variables
Interpretation of log transformed predictor and/or response
How to interpret transformed variables in multiple regression? Interpreting transformed dependent and independent variables
I have several continuous predictor variables most of which have been square root transformed and several continuous and count response variables. I work in R using lme4. I transformed the predictors as I was receiving warnings about them being on very different scales. I also have a better model fit using the the sqrt transformations.
I know how to back-transform from sqrt transformations when the response variable has been transformed, but I am not sure if the same process applies when just the predictor is transformed. Much of the info out there on this seems to deal only with log transformations. For example on one of the linked answers above, the following example is given:
DV = Intercept + B1 * log(IV) + Error
interprets as:
"One percent increase in IV is associated with a (B1 / 100) unit increase in DV."
So I think the above example deals with my question but I can't understand it nor what to apply in the case of a square-root transformation. I don't see how B1/100 represents the log(IV). Also, my regressions do not always contain interactions as the above example does.
The data concerns forest plot attributes such as forest area, species abundance, soil acidity, tree basal area etc. Below is the output from an lmer - the predictors are all square root transformed except the pH2003(soil pH) and Y_lat predictor (latitude) and the continuous (but bounded 0-5) response variable is in it's original metric (untransformed). Do I even need to transform the estimates in this situation? They are quite different to the estimates I arrived at when the x variables were not transformed.
Scaled residuals:
Min 1Q Median 3Q Max
-2.9911 -0.6297 -0.0298 0.5843 3.6784
Random effects:
Groups Name Variance Std.Dev.
SITE (Intercept) 0.1116 0.3340
Residual 0.2628 0.5127
Number of obs: 1282, groups: SITE, 102
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -3.30833 1.08441 109.50961 -3.051 0.00286 **
MEAN_BA -0.20042 0.05024 1246.09965 -3.989 7.01e-05 ***
Y_lat 0.08411 0.02012 104.00704 4.181 6.06e-05 ***
som.s -0.04830 0.01436 1267.19067 -3.365 0.00079 ***
pH2003 0.10021 0.02173 1192.49199 4.612 4.43e-06 ***
aln.s 0.69908 0.11653 1266.43739 5.999 2.58e-09 ***
ace.s 1.05915 0.37235 1248.01543 2.844 0.00452 **
cor.s 1.23502 0.49636 1249.94876 2.488 0.01297 *
frax.s 1.44194 0.30520 1267.94172 4.725 2.56e-06 ***
que.s 0.19498 0.06028 1266.44473 3.235 0.00125 **
One or two of my response variables are log-transformed and I would also like to know if there is a different protocol if I have a sqrt transformed predictor with a log transformed response.
