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Interpreting Interactions and Ordered Probit



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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 Iteration Iteration Iteration Iteration Iteration 0 1 2 3 4 5 log log log log log log likelihood likelihood likelihood likelihood likelihood likelihood 26 345398 20 849193 20 011675 19 917045 19 914806 19 914805 Logit estimates Log likelihood 19 914805 Number of obs LR chi2 4 Prob chi2 Pseudo R2 50 12 86 0 0120 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



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