Comparing model fits of non nested models
I am a student in Sociology at the University of Amsterdam and currently working on a paper on which I got stuck. Let me briefly introduce the outline of the paper an the statistical problem:
The idea of the paper is to compare the effcts of two individual-level variables (years of schooling measured in years (absolute measure of education) and years of schooling measured as the percentile in which a respondent falls (relative mesaure of education)) on income across several countries for several years. We would then like to take the difference in fit and relate this to educational expansion; a country level measure. Because of multicollinearity it is impossible to put both indepent variables (years of schooling and relative years of schooling) in one model.
The idea therefore is to estimate two seperate models:
income = a + b.educationinyears
income = a + b.educationrelative
We would then like to take the difference in modelfit (rsquare) between the two models and take that as the dependent variable in a model where educational expansion is the explanatory variable.
Our problem is that we can not simply take the difference in r-square since there is no significance test for this difference. If possible, we would like to weight the difference in model fit for the significance of this difference.
1) Do you have any idea if this is possible? Is there a test that compares non nested models and gives you a significance interval (which you can then use to weight the data with)?
2) How would you then weight the data, in what way?
3) Is there another solution to answer the research question with this data (I understand that the problem is solved if we take another relative measure of education, this is however not the idea of the paper).
Thanks in advance!