Part I. Output for an interaction effect. (All in Courier font, size 9), suppose I want to predict whether Senate committees in the 50 states are required to report legislation that they are assigned. I begin with a model that attempts to explain the presence of a reporting rule (senhear=1) by using the three components of legislative professionalism, the house’s session length, staffing levels, and salaries, along with a measure of the “moralism” of the state’s political culture. I run the following logit model, using Clarify. . estsimp logit senrepor totalday salary staffup moral Iteration 0: log likelihood = -26.345398 Iteration 1: log likelihood = -20.849193 Iteration 2: log likelihood = -20.011675 Iteration 3: log likelihood = -19.917045 Iteration 4: log likelihood = -19.914806 Iteration 5: log likelihood = -19.914805 Logit estimates Number of obs = 50 LR chi2(4) = 12.86 Prob > chi2 = 0.0120 Log likelihood = -19.914805 Pseudo R2 = 0.2441 ------------------------------------------------------------------------------ senrepor | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- totalday | -.0141113 .0099893 -1.41 0.158 -.0336899 .0054674 salary | .0000921 .0000477 1.93 0.053 -1.33e-06 .0001856 staffup | -2.492502 1.392717 -1.79 0.074 -5.222177 .2371723 moral | 2.617587 1.120754 2.34 0.020 .4209504 4.814224 _cons | -2.046383 .9856179 -2.08 0.038 -3.978159 -.1146075 ------------------------------------------------------------------------------ Simulating main parameters. Please wait.... % of simulations completed: 20% 40% 60% 80% 100% Number of simulations : 1000 Names of new variables : b1 b2 b3 b4 b5 Now I can look at the effects increasing the salary level from Maine’s value ($12,900) to California’s ($99,250), holding other variables constant at their means: setx mean simqi fd(pr) changex(salary 12900 99250) First Difference: salary 12900 99250 Quantity of Interest | Mean Std. Err. [95% Conf. Interval] ---------------------------+-------------------------------------------------- dPr(senrepor = 0) | -.842876 .2485586 -.9939116 -.0548535 dPr(senrepor = 1) | .842876 .2485586 .0548535 .9939116 This tells me that moving from Maine’s salary to California’s salary, all other factors being equal, increase the chances of requiring Senate committees to report bills by 0.84, with a confidence interval of (0.05 to 0.99).Now suppose I want to test whether the effect of salary is different in moralistic and nonmoralistic states, and estimates those two context-bound effects. I create the interaction variable salary_moral (the product of the two, by using the Stata command genx salary_moral=salary*moral), and estimate another logit model with this interaction term included. But first, I have to get rid of the simulated parameters from the last model. drop b* estsimp logit senrepor totalday salary staffup moral salary_moral Iteration 0: log likelihood = -26.345398 Iteration 1: log likelihood = -20.45492 Iteration 2: log likelihood = -19.315403 Iteration 3: log likelihood = -19.150856 Iteration 4: log likelihood = -19.144103 Iteration 5: log likelihood = -19.144086 Logit estimates Number of obs = 50 LR chi2(5) = 14.40 Prob > chi2 = 0.0132 Log likelihood = -19.144086 Pseudo R2 = 0.2733 ------------------------------------------------------------------------------ senrepor | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- totalday | -.0093382 .0097495 -0.96 0.338 -.0284469 .0097705 salary | .0001326 .0000596 2.22 0.026 .0000157 .0002495 staffup | -2.422675 1.377301 -1.76 0.079 -5.122136 .2767861 moral | 4.598178 2.281156 2.02 0.044 .1271951 9.069161 salary_moral | -.0000673 .0000575 -1.17 0.242 -.0001801 .0000454 _cons | -4.184283 2.295119 -1.82 0.068 -8.682634 .3140674 ------------------------------------------------------------------------------ Simulating main parameters. Please wait.... % of simulations completed: 16% 33% 50% 66% 83% 100% Number of simulations : 1000 Names of new variables : b1 b2 b3 b4 b5 b6 Although it is not statistically significant, this interaction term tells me that salary has a smaller affect on committee reporting requirements in states with moralistic political cultures. To get a sense of the scale of the “slope shift,” I can look at first differences. Maybe I wasn’t listening to my own lectures, and I set all of the variables at their means. This sets the interaction term at the mean of the product of the two variables: setx mean simqi fd(pr) changex(salary 12900 99250) First Difference: salary 12900 99250 Quantity of Interest | Mean Std. Err. [95% Conf. Interval] ---------------------------+-------------------------------------------------- dPr(senrepor = 0) | -.917242 .1888489 -.9980687 -.2803625 dPr(senrepor = 1) | .917242 .1888489 .2803625 .9980687But now I know that I need to hold the interaction term constant at the product of their means. sum salary if moral!=. Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- salary | 50 25376.64 19829.32 200 99250 . sum moral Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- moral | 50 .5 .5050763 0 10 setx mean setx salary_moral 25376*0.5 This would be the syntax I needed in order to correctly estimate the effect of some other variable, like