I have data from a randomised blocked experiment testing the effect of different crops on weeds. Each treatment was replicated in one plot in each of three blocks, on two farms, in two years (but NOT repeated measures; the blocks were in different locations on each farm each year).

Different locations of farms, different farms and different years result in different levels of crop and weed growth due to differences in soil fertility, rainfall etc. I was not interested in this, just in whether there was a consistent effect of different crop types on weeds regardless of inherent differences in mean values and variability between sites and years. I also did not just want to just crop type A, B, C etc as a predictor, but continuous characteristics of different crop types, e.g. biomass. When analysing these continuous characteristics, my approach was to standardise my continuous explanatory variables (e.g. crop biomass) AND response variable (e.g. weed biomass) by the mean and standard deviation within each block. I then used linear regression to explore the relationships.

My understanding is then that I have modelled the effect of one standard deviation increase in crop biomass on standard deviations of weed biomass. My results are displayed and discussed as 'relative crop biomass' vs 'relative weed biomass' etc.

Two questions:

1) Is this a valid approach? Can I standardise both my explanatory and response variables to the within-block mean and standard deviation to identify whether a consistent relationship exists, regardless of background differences in means and variability?

2) Could anyone direct me to any references that demonstrate/discuss this?

Yes, I know I can do this analysis with mixed models. If standardising is valid however I would prefer to use it, because it makes interpretation more straightforward in the context of my study.

I think this is a similar question to this: Standardized dependent variable and non standardized independent varaible and this: Standardized dependent variable within a group in panel data models? - but I am not clear if the replies apply to my situation.

UPDATE: This paper by Schielzeth 2010 (https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2041-210X.2010.00012.x) suggests to approach this sort of problem with mixed models. As I understand it, Schielzeth recommends to first fit a model with random intercepts, then standardising the response by the residual (within-site) standard deviation from that first model, then run a second full mixed model on the standardised response. I'm not sure why this would be better than simply standardising by each site's raw standard deviation? (given that standard deviation differs in each site). Any thoughts would be appreciated!



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