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# Interactions and Ordered Categorical Variables

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Thursday October 7 Interactions and Ordered Categorical Variables I Interpreting Interaction Effects also see Greene pp 123 124 A The Concept of an Interaction Remember that interactions measure how much changes on one variable affect the effect of another variable Put another way they reveal whether or not the effect of variable changes in different contexts For instance increases in ethnolinguistic fractionalization could lead to significant declines in political stability under authoritarian regimes but lead to increases in the stability of democracies If this is true there will be a strong interaction between type of political system and ethnolinguistic fractionalization B Measuring an Interaction Effect To test the hypothesis that Variable x1 influences the effect of Variable x2 and vice versa your model should include an interaction term that is the product of these two variables If the effect of one variable is altered by the other the coefficient on this interaction term x1x2 will be significant In ordinary least squares regression evaluating the effect of x1 ELF fractionalization in this example at any particular level of x2 type of political system is straightforward you add the coefficient of x1 to the product of the coefficient on x1x2 and the particular value of x2 in which you are interested For the model We can get a predicted value by y 0 1x1 2x2 3x1x2 e yhat 0 1x1 2x2 3x1x2 And we can obtain the first difference for x1 the change brought in yhat by a one unit change in x1 from x1low to x1high while all other factors are held constant by y 0 1x1high 2x2 3x1highx2 0 1x1low 2x2 3x1lowx2 y 1x1high 1x1low 3x1highx2 3x1lowx2 y 1 x1high x1low 3x2 x1high x1low y 1 3x2 C Interaction Effects in Maximum Likelihood Models If only life were so simple in the ML world In OLS this expression reduces so nicely because the predicted value yhat for a given observation is just a linear function of the coefficients and explanatory variables The contribution of 2x2 to

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