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I am interested in the relationship between religiosity and religious distrust (would you dislike having as neighbours people of different religions).

One of my main goals is to make the role of each individual religion insignificant; according to my argument monotheism leads to distrust, regardless of the particular religion. However, religions explain about 53% of my variation in religious distrust according to the R-squared. I wanted to include variables that would 'take away' from this influence of religion in terms of explanatory variable. For example, economic inequality in most Muslim countries might be a reason for differences in distrust, or the number of times people pray, which is less in Protestant countries. So I added as independent variables: Economic inequality, urbanization, separation church/state, number of times people pray, and education. When I include these in a model without religion I get an R-squared of about 37%.

When I include all these independent variables + religion, religion becomes significant again, I think because religion incorporates much more explanation than either single one of my other independent variables. My R-squared in this model is, again, 53. My question is, is there any way to support the claim that although religion might matter, my independent variables 'take away' at least some of its explanatory value?

So:

  • religion alone explain 53%;
  • my independent variables explain 37% alone;
  • together they explain 53% again

Could I say that of the 53% religion used to explain, 37% / 53% is now explained by my other independent variables? So in a sense, I took away about 2/3 of the explanatory value of religion by introducing other variables? Or is this not statistically valid, because they might for example explain different parts of the variation in my dependent variable?

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I assume you are doing some sort of a linear regression since you're using R-squared? Keep in mind that the order in which variables are added to your model might make a difference. Particularly if any of your variables are correlated and/or collinear (the latter you can test by calculating the Variance Inflation Factor (VIF)). Ideally you'd want to include explanatory variables that are independent.

However, if you want to keep all your explanatory variables, an idea would be to try models with the variables added in different orders, and then look at your ANOVA table, as well as the significance of your coefficients.

Maybe you can share the type of model and type of data that you're using as it will probably help in answering your question.

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  • $\begingroup$ Thanks! My model is indeed linear. My variables are all numerical, except for religion which is categorical ( Sunni, Shia.. etc) . I have checked for multicollinearity and the only variables that really correlate are education and how many times people pray (inversely) , which makes sense, as modern countries tend to have better education and are less religious. I have found the 'relaimpo' package which tells me this: Relative Importance Metrics Religion 0.30024710; urbanization 0.06477207 ; Separation C/S 0.10016121; Pray; 0.10701489; Education 0.04267369 Inequality 0.03112785 $\endgroup$ – Daan Schouten Mar 25 '16 at 15:49
  • $\begingroup$ My regular R-squared ( not adjusted) is 64%, so from this I read that about half of that is explained by religion, and the rest by my other independent variables $\endgroup$ – Daan Schouten Mar 25 '16 at 15:52
  • $\begingroup$ What method did you apply to check for multicollinearity? Because it is strange that your R^2 does not increase when you add more explanatory variables. That in itself points to collinearity. $\endgroup$ – Geraldine Mar 25 '16 at 16:01
  • $\begingroup$ Other options are to examine the partial R^2 for your different explanatory variables, or compare the RMSEs from your different models (the latter is more to try and better understand how well your model fits, beyond just R^2) $\endgroup$ – Geraldine Mar 25 '16 at 16:05
  • $\begingroup$ Oh, and yeah, I do like the relaimpo package myself too. What does it tell you for the model without religion? $\endgroup$ – Geraldine Mar 25 '16 at 16:08

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