[R-sig-eco] AIC in R: back-transforming standardized model parameters (slopes)

[Matt Perkins]

Hi All,


I have a simple Q that I'm having some difficulty finding an answer for. I'm conducting AIC analyses in R, and I would like to be able to report 'real' slope values from my model summary output (i.e. take the slopes and report them within simple y=mx+c linear equations in my paper). However, following Greuber etal 2011, I have standardised the explanatory variables in my model by centering them to a mean of zero and and an SD of 2, using the following code and the R package "arm". My model has a normal error distribution.


stdz.model1<-standardize(model1, standardize.y=FALSE)



I do not yet know the sums behind this code in order to know how and what change has been made to my explanatory variables, in order that I could manually make back-transformations.


Therefore I wished to know (preferably) the calculation being made, and more importantly the function/code to back-transform my slope estimates to reportable 'real' slopes.


Addtionally, is it correct (or does it even matter) that I should be focusing my back-transformation on the slope estimate taken from the model summary, as opposed to instead using the model summary standardised slope estimate to calculate a y value in my linear equation (y=mx+c), and then back-transforming that y value?



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If it is useful, my model and summary tables are below.


I would like to test if treatment (kept in air or ice) affects nitrogen (N) within shrimps over time. I have repeated measures per shrimp (unique.id) that I use as a random factor to account for non-independence within an individual.


My model is a linear mixed model of the form:


model1<-lmer( N ~ time* air.ice + (1|unique.id), data=shrimp, REML=FALSE)



The two model summary tables below show the 1) un-standardised model with ready-to-use slope value ("time" = 0.008156)

and 2) standardised model with much-larger slope value ("z.time" = 0.50782)


1)

Fixed effects:
                                                  Estimate       Std. Error    t value
(Intercept)                              12.522535   0.197024      63.56
time                                           0.008156    0.001134       7.19
air.ice                                       -0.801936   0.278634      -2.88
time:air.ice                              -0.004442   0.001604     -2.77


2)

                                                   Estimate      Std. Error    t value
(Intercept)                                12.48242      0.13051      95.65
z.time                                          0.50782       0.06861       7.40
c.air.ice                                      -1.07202       0.26102      -4.11
z.time:c.air.ice                          -0.38008       0.13722     -2.77


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