My study is largely exploratory and looks at how environmental factors such as (physical characteristics, water quality and pesticide type and concentration) affect relative antioxidant enzyme mRNA expression. I have categorized my x variables into the 3 aforementioned categories and each category includes a 8-10 variables. Some of these variables were correlated with each other which required removal from the model. I am not 100% sure that this approach is correct in the sense that I included all variables that may have an effect on y "in theory" but not statistically (i.e. I included variables that are not independently correlated with y). This may be wrong but there is mixed info on this topic and my supervisor suggested this approach. In the end, each gene I tested did not have sig relationships with more than one variable regardless. This entire model approach was done for completeness to include all data collected since the results end up being pretty lean.
I am using a backward stepwise model selection approach (every variable is included to begin with) to analyze if explanatory (x) variables are explaining my response variable. I have dealt with multicollinearity already and am using a p value (≤ 0.05) exclusion method for the remaining variables. So I am going one by one, starting with the highest p value and dropping each non significant variable as in Chowdhury & Turin 2020.
I encountered an issue where several individually non-correlated (x and y) variables are showing to be significant when in the model together. Clearly these results are spurious. I read a few posts that suggest either multicollinearity (not the case here) or confounding variables but I can't seem to find out how to deal with this issue in a statically sound way. Do I report this issue? But how do i decide what to do next to generate the final model (even if the model is non significant in the end).
What I have done so far is just used VIF to determine which of the "sig" variables maybe were correlating with the others in a way that I was unable to detect and deleted the variable with the highest VIF. When I do this, there is no longer any significance which further convinces me that this was just an artifact. Any help would be greatly appreciated as I am trying to write up my PhD dissertation in 6 months and am very strapped for time!
Here is an example of an individual relationship between one x and my y
I removed Velocity