I have an outcome variable which is the score of memory function. There are two variables (say A and B, extracted from PET scans of subjects) which are significantly related to memory function. When the two variables A and B are closely correlated (Pearson's R = 0.9), how can I determine one variable is more influential(?) or better in any ways compared to another?
In summary, I have two linear models, where variable A and B are significantly related. How can I tell A is better in predicting memory function than B?
lm1 = memory ~ age + education + A
lm2 = memory ~ age + education + B
cor(A,B) = 0.9
I beg your kind advice.
Multicollinearity is a state of very high inter-correlations or inter-associations among the independent variables. Multicollinearity makes it hard to interpret your coefficients, and it reduces the power of your model to identify independent variables that are statistically significant.
Standardizing the variables can help in solving the problem and fitting your model
I would fit both models, calculate their coefficient of determination R² and perform a likelihood test to contrast both models. A significant likelihood test indicates that the models differ in terms of goodness of fit and the coefficient of determination indicates which model explain your data. Thus, considering the model with the best fit, you can infer about which variable is more likely to affect your response variable.
Standardizing (z-transformation) may help or may not - a strait forward way would be to use a non-parametric correlation testing (ranking).
For an R^2 approach I think you want something like dominance analysis:
Article The Dominance Analysis Approach for Comparing Predictors in ...
https://rdrr.io/github/clbustos/dominanceAnalysis/man/dominanceanalysis-package.html
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