# Graphing interactions in linear mixed models with negative log-transformed outcome

I have performed a linear mixed model where I used Tukey's ladder of Powers to transform the outcome variable (time) to get normal residuals, which gave a negative lambda. This resulted in a vector of negative values.

I would like to represent the lmm on a graph as I have a 2-way interaction between two categorical variables. However, time obviously cannot be negative. So, I think it doesn't not really make sense to visualize the transformed values. However, if I just plot the original means and standard deviations, my error bars go below zero (probably because the data is not normal, hence the initial transformation...)

So, what is the best way to represent the interaction? Flip the log-transformed values so they are positive and plot this? Use the original scale (time) and represent the variance in some other way than standard errors?

(although this is primarily a theoretical question, for info I am using R with lme4 and cat_plot from the "interactions" package to plot the data)

• "This resulted in a vector of negative values." It is not clear how you got negative values. The transformation is just a power which is a transformation of positive numbers to positive numbers. Commented Mar 20, 2023 at 12:18
• Did you maybe compute logarithms? Commented Mar 20, 2023 at 12:21
• yes, I did a logarithmic transformation Commented Mar 20, 2023 at 14:00
• So is your question about log transformed variables? Or about power transformed variables? Commented Mar 20, 2023 at 15:25
• If I understand right, Tukey's ladder of Power's is just used to find an optimal lambda, if the lambda is positive, a power transformation is performed (x^lambda), if it is 0, a logarithmic transformation is performed (log(x)), and if it is negative an inverse power transformation is performed -1 *x^ lambda. My data was positively skewed, and to correct it I used -1 *(myvariable)^mylambda Commented Mar 20, 2023 at 15:48