- [[240826_214237 persuasion study results|persuade harris/trump results]] Let $t_i$ be the probability of voting for trump (measured post-treatment using the lean harris/trump question); $1 - t_i$ will be probability of voting for harris. Let $p_i$ be the probability of voting (measured post-treatment). Distributions of $t_i p_i$ (trump vote) and $(1-t_i)p_i$ (harris vote), split by demrep (1: dem, 1.5: independent, 2: rep). ![[1725396338.png]] Let $\text{trump votes} = \sum{t_i \times p_i}$ and $\text{harris votes} = \sum{(1 - t_i) \times p_i}$: ```r # overall sum trump_votes harris_votes N <num> <num> <int> 1: 638.9523 906.2077 1774 # split by condition condition trump_votes harris_votes N <char> <num> <num> <int> 1: persuadeHarris 317.1532 460.2168 883 2: persuadeTrump 321.7991 445.9909 891 # split by dem/ind/rep demrep condition trump_votes harris_votes N <fctr> <char> <num> <num> <int> 1: 1 persuadeHarris 25.1424 355.2376 416 2: 1 persuadeTrump 27.4060 361.0840 435 3: 1.5 persuadeHarris 41.9590 64.2910 140 4: 1.5 persuadeTrump 52.7992 51.2008 147 5: 2 persuadeHarris 250.0518 40.6882 327 6: 2 persuadeTrump 241.5939 33.7061 309 # harris_trump_diff: harris votes minus trump votes condition harris_trump_diff <char> <num> 1: persuadeHarris 143.0636 2: persuadeTrump 124.1918 ``` Regression model where $y$ is harris vote minus trump vote, $(1-t_i)p_i - t_ip_i$ ```r > summ(feols(harris_trump_vote ~ condition, d1)) term result <char> <char> 1: (Intercept) b = 0.14 (0.03) [0.09, 0.19] p < .001 2: conditionpersuadeHarris b = 0.02 (0.04) [-0.05, 0.10] p = .555 > summ(feols(harris_trump_vote ~ condition * lean_bidentrump_1Z * topicZ, d1)) term result <char> <char> 1: (Intercept) b = 0.12 (0.01) [0.10, 0.13] p < .001 2: conditionpersuadeHarris b = 0.07 (0.01) [0.04, 0.09] p < .001 # 7%? 3: lean_bidentrump_1Z b = -0.77 (0.01) [-0.78, -0.75] p < .001 4: topicZ b = -0.01 (0.01) [-0.03, 0.00] p = .108 5: conditionpersuadeHarris × lean_bidentrump_1Z b = 0.00 (0.01) [-0.02, 0.02] p = .895 6: conditionpersuadeHarris × topicZ b = 0.02 (0.01) [0.00, 0.05] p = .032 7: lean_bidentrump_1Z × topicZ b = 0.00 (0.01) [-0.02, 0.02] p = .925 8: conditionpersuadeHarris × lean_bidentrump_1Z × topicZ b = 0.01 (0.01) [-0.02, 0.03] p = .564 # personality only > summ(feols(harris_trump_vote ~ condition * lean_bidentrump_1Z, d1[topic == "personality"])) term result <char> <char> 1: (Intercept) b = 0.13 (0.01) [0.11, 0.15] p < .001 2: conditionpersuadeHarris b = 0.04 (0.02) [0.01, 0.07] p = .010 3: lean_bidentrump_1Z b = -0.77 (0.01) [-0.79, -0.75] p < .001 4: conditionpersuadeHarris × lean_bidentrump_1Z b = -0.01 (0.02) [-0.04, 0.02] p = .616 # policy only > summ(feols(harris_trump_vote ~ condition * lean_bidentrump_1Z, d1[topic == "policy"])) term result <char> <char> 1: (Intercept) b = 0.10 (0.01) [0.08, 0.13] p < .001 2: conditionpersuadeHarris b = 0.09 (0.02) [0.06, 0.12] p < .001 3: lean_bidentrump_1Z b = -0.77 (0.01) [-0.79, -0.74] p < .001 4: conditionpersuadeHarris × lean_bidentrump_1Z b = 0.01 (0.02) [-0.03, 0.04] p = .754 # no interactions, just treatment, separately for personality and condition # personality > summ(feols(harris_trump_vote ~ condition, d1[topic == "personality"])) term result <char> <char> 1: (Intercept) b = 0.17 (0.04) [0.09, 0.24] p < .001 2: conditionpersuadeHarris b = -0.02 (0.05) [-0.13, 0.08] p = .644 # policy > summ(feols(harris_trump_vote ~ condition, d1[topic == "policy"])) term result <char> <char> 1: (Intercept) b = 0.11 (0.04) [0.04, 0.19] p = .004 2: conditionpersuadeHarris b = 0.07 (0.05) [-0.04, 0.18] p = .202 ``` # checking gord's examples/logic ```r > sim(0, 0.5) # 100% harris, 50% voting lean prob_vote harris_vote trump_vote vote_diff 0.0 0.5 0.5 0.0 0.5 # 0.5 net harris votes > sim(0.5, 1) # 50%/50% harris/trump, 100% voting lean prob_vote harris_vote trump_vote vote_diff 0.5 1.0 0.5 0.5 0.0 # 0 net votes > sim(0, 1) # 100% harris, 100% voting lean prob_vote harris_vote trump_vote vote_diff 0 1 1 0 1 # 1 net harris vote > sim(1, 1) # 100% trump, 100% voting lean prob_vote harris_vote trump_vote vote_diff 1 1 0 1 -1 # -1 net harris vote ``` What happens if we don't do net vote and use just harris vote as the outcome instead Regression model where $y$ is just harris vote, $(1-t_i)p_i$ ```r # only treatment predictor > summ(feols(harris_vote ~ condition, d1)) term result <char> <char> 1: (Intercept) b = 0.50 (0.01) [0.47, 0.53] p < .001 2: conditionpersuadeHarris b = 0.02 (0.02) [-0.02, 0.06] p = .315 # including initial lean > summ(feols(harris_vote ~ condition * lean_bidentrump_1Z * topicZ, d1)) term result <char> <char> 1: (Intercept) b = 0.49 (0.01) [0.48, 0.50] p < .001 2: conditionpersuadeHarris b = 0.04 (0.01) [0.03, 0.06] p < .001 # 4%? 3: lean_bidentrump_1Z b = -0.39 (0.01) [-0.40, -0.38] p < .001 4: topicZ b = 0.00 (0.01) [-0.01, 0.01] p = .696 5: conditionpersuadeHarris × lean_bidentrump_1Z b = -0.01 (0.01) [-0.03, 0.01] p = .342 6: conditionpersuadeHarris × topicZ b = 0.00 (0.01) [-0.02, 0.02] p = .975 7: lean_bidentrump_1Z × topicZ b = 0.01 (0.01) [0.00, 0.02] p = .197 8: conditionpersuadeHarris × lean_bidentrump_1Z × topicZ b = -0.01 (0.01) [-0.03, 0.01] p = .323 ```