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Unformatted text preview: Interaction effects and group comparisonsPage 1 Interaction effects and group comparisons Alternative strategy for testing whether parameters differ across groups: Dummy variables and interaction terms. We have previously shown how to do a global test of whether any coefficients differ across groups. This can be a good starting point in that it tells us whether any differences exist across groups. It may also be useful when we have good reason for believing that the models for two or more groups are substantially different. This approach, however, has some major limitations. First, it does not tell you which coefficients differ across groups. Possibilities include (a) only the intercepts differ across groups (b) the intercepts and some subset of the slope coefficients differ across groups, or (c) all of the coefficients, both intercepts and slope coefficients, differ across groups. A related problem is that running separate models for each group can be quite unwieldy, estimating many more coefficients than may be necessary. It becomes even more unwieldy if there are multiple group characteristics you are interested in, e.g. race, gender and religion. Recall that, when extraneous parameters are estimated, it becomes more difficult to detect those effects that really do differ from zero. Further, theory may give you good reason for believing that the effects of only a few variables may differ across groups, rather than all of them. In this handout, we consider an alternative strategy for examining group differences that is generally easier and more flexible. Specifically, by incorporating dummy variables for group membership and interaction terms for group membership with other independent variables, we can better identify what effects, if any, differ across groups. Preliminary Steps. If the dummy variables and interaction terms are not already in our data set, we need to compute them (or else use one of the methods described in the appendices, e.g. factor variables): Compute a DUMMY variable for group membership. Code it 1 for all members of one of the groups, 0 for all members of the others. For example, you could do something like . gen dummy = group == 1 & !missing(group) Here, dummy will equal 1 if group equals 1. It will equal 0 if group has any other nonmissing value. dummy will be missing if group is missing. Another possible approach: . tab x, gen(dummy) If x had 4 categories, this would create dummy1, dummy2, dummy3 and dummy4. You could use the rename command to create clearer names, e.g. . rename dummy1 catholic . rename dummy2 protestant . rename dummy3 jewish . rename dummy4 other Interaction effects and group comparisonsPage 2 Compute interaction terms for the dummy variable and each of the IVs whose effects you think may differ across groups. In Stata, do something like . gen dummyx1 = dummy * x1 . gen dummyx2 = dummy * x2 [NOTE: If you want, you can think of DUMMY as being an interaction term too. DUMMY = DUMMY*X0, where X0 = 1 for all cases.] DUMMY*X0, where X0 = 1 for all cases....
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