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Imagine we estimate two sequential negative binomial regressions. In the first one, we use say 3 predictors (x1, x2,x3), and in the second, we use the same 3 plus an additional variable (x4). We are interested in whether x4 change the size of the effect of a specific variable, say x1, in the first model. We observe that incidence rate ratio of X1 is 0.74***, and when x4 included in the second model. it becomes 0.71***. There is a three percent decrease in the IRR, but is this change significant? How can we conclude that x4 reduces the effect of x1 by three percent significantly?

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