To be more specific: my goal is to demonstrate that the effects of X1 on Y is not entirely accounted for by attitudes towards various out-groups. The latter items include measures of positivity towards racial/ethnic minorities, stereotype attribution and questions canvassing attitudes on gender-related issues. Including each of these variables individually would leave me with a 'kitchen sink' model of 20+ predictors. As I'm not interested in their effect on Y (they're only included to rule out a competing hypothesis that predicts they account for X1's effect on Y), I thought I could simply the model by combining them into an additive index. None of them are strongly correlated, and their coefficients range from 0.2 to 0.4. Would creating such an index pose any problems for answering my research question? Any help you can provide would be much appreciated. Thanks!
p.s. my sample size is roughly 2,800.
Hi Zach,
The answer to your question is both a theoretical and statistical one. From a theoretical standpoint, whether or not you combine a set of variables depends on whether you have a strong theoretical rationale for doing so. A question to ask would be: Does my theoretical framework support combining these variables together? It is not really about just wanting to minimize a large number of predictors in a model. Additionally, keep in mind that, when you include large numbers of predictors in a model, although the output will provide you with information regarding each predictor, an OLS model will nevertheless form a linear composite of the predictors. Thus, you need a reason for including them together in the first place. On a statistical note, if they are moderately correlated, that may suggest they are not the same construct but are potentially indicators of a larger construct. So if you combine them, what is the larger construct that those correlated variables comprise? These are questions to begin asking.
Cheers
Sorry this is probably too late. If I understand your problem right, not only can you combine these variables, you should. If their correlations range from .2 to .4, the composite will be highly reliable (coefficient alpha). If they are on different scales, you should standardize them before adding. And compute alpha. Your DV then will be a relatively continuous measure that should be fairly interpretable.
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