# Why does transforming the response change the factor's influence on the response?

I ran a screening experiment for six numerical parameters to determine if they influence the response $Y$.

However, one factor, $A$, is confusing me. I visualized its effect on $Y$ and got the following plot:

However, when I plotted the effect of the parameter on $Z = \ln(1+Y)$, I got that its ifluence was quite different:

I transformed $Y$ in order to get normally distributed and homoscedasticit residuals for a mixed model for the response (and after transformation, the residuals were normally distributed and homoscedasticit).

How should I interpret this parameter's effect and why does the curve look so different for $\ln(1+Y)$? Instead of peaking and $A=0$, it drops from $A=-1$ to $A=0$ and it seems that its values at $A=1$ are almost the same as for $A=0$. Comparing to what I got for $\ln Y$, this is pretty different behavior.

EDIT 1: Here are the scatter plots for $Y$:

and $Z = \ln(1+Y)$:

• If you did literally as you claimed, then you made a numerical error, because $Z$ is a monotonic function of $Y$. If instead your plot represents some kind of summary statistics for $Y$ and you transformed the individual data values before summarizing them, then this phenomenon can be explained. Please tell us, then, what you did and what these plots actually represent. – whuber Dec 15 '16 at 19:54
• I transformed the individual data points ($Z_i = \ln(1+Y_i)$) and found their mean values and confidence intervals. $i$ is iterating over subjects. The plots represent mean values of $Y$ ($Z$) and their $95\%$ confidence intervals. :) – Milos Dec 15 '16 at 19:58
• If you would plot the individual data instead of their means, I believe you will see immediately what happened. – whuber Dec 15 '16 at 19:59
• As $(\ln(1+Y_1) + \ldots + \ln(1+Y_n)/n = \ln(1+\prod_{i=1}^n(1+Y_i))^{1/n}$, I realized that the $Z$ plot showed $\ln$ of geometric means of $Y$s. However, I could not conclude much from plotting the scatter plots. They show that $Y$ is decreasing and stabilizing as $A$ is increased, but no substantial difference could be found for $Z$. I'll include those images to the post. :) – Milos Dec 15 '16 at 20:11