I have several regression models, each with the same outcome and dependent variables. All observations are independent. I would like to test the null hypothesis: the coefficient for a specific covariate is not significantly different across the models. I have seen methods for doing multiple pairwise tests, but am looking for a single test. Any methods easily implementable in R would be appreciated.
Can you give the models and name the variable for which you are looking to have a differential effect?
I may not be understanding this fully but aMANOVA is appealing. So I would stack all the sets of variables one under each other , include a dummy variable for each separate data set and include the predictor variable and an intercation between the dummies and the predictor. You could then test whther the dummy* predictor interactions are different from each other.
Thanks for the answers. I will look into MANOVAs.
In the meantime, here is an image to clarify my question. The analysis has been stratified by smoking. I am interested in whether the association between PredictorX and Cancer is independent of smoking. In other words, I want to test whether the three lines are parallel (have the same regression coefficients for PredictorX). For consistency with the figure, I want to make sure I'm testing the difference in the three slopes and not an interaction term between the continuous smoking variable and PredictorX.
I am also interested in the generalization of this method for multiple regression models -- Instances where each model has many predictors and you are interested in testing the PredictorX coefficients for equivalence across all models (potentially more than 3 models).
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