Cross Validated Asked by shenflow on February 21, 2021
I ran a regression model with around 10 regression coefficients.
I now want to test wether these regression coefficients are significantly different from one another.
How do I do this? Is a Wald test appropriate here?
Also, I would appreciate some reference to how to implement the respective solution (if available) in SAS, as I am required to use SAS to conduct my analysis.
EDIT: My first guess was to conduct multiple t-tests. It was pointed out that this is not correct, which is why I edited my question.
With all of your predictors on the same scale, it could make sense to test the hypothesis that all coefficients are equal with a Wald test. That's a standard way to make tests involving groups or combinations of parameter estimates. You will, however, need to be careful in how you set this up.
A Wald test is frequently set up to test the null hypothesis that all coefficients are equal to 0. That is not your hypothesis. Presumably you need to test whether any of the coefficients differs from the mean coefficient value. So be sure to read the manual before you just call for a Wald test in statistical software.
Note that there might be some extra variability here as you will be estimating the mean value from the data rather than specifying a pre-determined value. I'm not sure how much of a difference that will make, as the test only holds asymptotically in any event.
Correct answer by EdM on February 21, 2021
It is not only impractical to do t-tests for each, but most importantly wrong. Model selection based on t test is misleading. Your problem is a question of model selection. First way would be to use information criteria like AIC and BIC to compare different models which consist of different subset of variables. Regarding doing this in SAS see here.
Answered by BertHobe on February 21, 2021
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