Your interpretations of the red and blue lines are, indeed, correct. The red line tells you that the difference in OUT differs significantly between GRPs 1 and 0 when CONCEN = 0. Only you can say what that means in the real world. The blue line is an omnibus hypothesis test. The null hypothesis for this test is that the expected value of OUT in GRPs 0 and 1 are the same at all values of CONCEN--and that hypothesis is resoundingly rejected.
For your second concern, because CONCEN was entered into the model as a continuous variable (c.CONCEN), you cannot use it in that way with the -margins- command, nor its near-relatives. But you can get the contrast you are seeking (OUT at CONCEN = 3 vs CONCEN = 0 in GRP 0) using -lincom- instead. To do this correctly you have to back to the two-equation interpretation of the model that I showed in #12. In GRP 0 at CONCEN = 3, the model predicts an expected value of _cons + _b[CONCEN]*3. At CONCEN = 0, it is _cons + _b[CONCEN]*0 = _cons. So the difference, when we subtract, is just _b[CONCEN]*(3-0) = 3*_b[CONCEN]. To get an estimate of this difference along with a standard error and confidence interval and p-value, you can just issue the command
Now, in this case, using -lincom- is, in a sense, overkill: you could just multiply the coefficient, standard error, and CI bounds for CONCEN from the regression table output by 3, and the p-value is identical to that in the regression table. But I wrote out all those steps because there may be more complicated contrasts you are interested in that won't reduce to a simple multiple of a line in the regression table. This -lincom- approach is what we used to use before -margins- was created.
Finally, you raise the question of what, if anything, to do about multiple comparisons. This is a very thorny issue, and if you ask a dozen statisticians you will probably get 25 different answers. In some fields there are strong traditions that dictate how this must be done to get your result published. My experience as an epidemiologist who publishes mostly in clinical and public health journals is that pretty much anything is acceptable provided you state in your methods section what you have (or haven't) done. My personal practice, absent a rebuke by a reviewer, is to do no adjustment for multiple comparisons and say so up front. (I have my reasons for this, but I don't really want to digress into an area of discussion that typically generates much heat and little light). But if you have a particular audience or journal in mind for your results, you should check to see what the conventions are there and follow that.
For your second concern, because CONCEN was entered into the model as a continuous variable (c.CONCEN), you cannot use it in that way with the -margins- command, nor its near-relatives. But you can get the contrast you are seeking (OUT at CONCEN = 3 vs CONCEN = 0 in GRP 0) using -lincom- instead. To do this correctly you have to back to the two-equation interpretation of the model that I showed in #12. In GRP 0 at CONCEN = 3, the model predicts an expected value of _cons + _b[CONCEN]*3. At CONCEN = 0, it is _cons + _b[CONCEN]*0 = _cons. So the difference, when we subtract, is just _b[CONCEN]*(3-0) = 3*_b[CONCEN]. To get an estimate of this difference along with a standard error and confidence interval and p-value, you can just issue the command
Code:
lincom 3*CONCEN
Finally, you raise the question of what, if anything, to do about multiple comparisons. This is a very thorny issue, and if you ask a dozen statisticians you will probably get 25 different answers. In some fields there are strong traditions that dictate how this must be done to get your result published. My experience as an epidemiologist who publishes mostly in clinical and public health journals is that pretty much anything is acceptable provided you state in your methods section what you have (or haven't) done. My personal practice, absent a rebuke by a reviewer, is to do no adjustment for multiple comparisons and say so up front. (I have my reasons for this, but I don't really want to digress into an area of discussion that typically generates much heat and little light). But if you have a particular audience or journal in mind for your results, you should check to see what the conventions are there and follow that.
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