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When performing linear mixed models, I have had to square-root(log) transform the data to achieve a normal distribution. Having performed the LMMs, I now want to plot the results onto a graph, but on the original scale i.e. not square-root(log) transformed.

Apparently I can use my raw (untransformed data) on a graph, and to create the predicted regression line I can use the coefficients from my LMM output to get backtransformed predicted y-values for each of my x values. This is where I'm stuck - I have no idea how to do this. Can anyone help?

Lizzie Yarwood
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  • "I have had to square-root(log) transform the data to achieve a normal distribution." What exactly did you transform, the y values? Regression only requires normality of residuals not of data (it's unclear what you checked for the distribution). – Roland Aug 05 '20 at 09:29
  • Hi Roland - to clarify, I square-root(log) transformed my model to meet normality of residuals, e.g. : ```sqrt((log(y)~x1+x2+x3+(1|ID), data=mydata)``` – Lizzie Yarwood Aug 05 '20 at 09:46
  • Very difficult to understand what you need without a [minimal reproducible example](https://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example/5963610#5963610). However, the inverse operation of square-root-log transform (in that order) would be square then exponentiate. i.e. If `xt = sqrt(log(x))`, then `x = exp(xt^2)`. – csgroen Aug 05 '20 at 09:47

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