Have to first reduce/aggregate each subj's data to a single row - `y` (truth ratings for **false** headlines) for each subject: $\bar{y}_{repeated} - \bar{y}_{novel}$ ```r # causal effect after adjusting for 7 covariates # INDIA > average_treatment_effect(cf) estimate std.err -0.15580900 0.03798033 # highly significant # PHiLIPPINES > average_treatment_effect(cf) estimate std.err -0.15493533 0.03140944 ``` # forest feature importance ```r # india covariate imp 1: conspiracy 0.26493677 2: education 0.18423756 3: age 0.17893590 4: covid_concern 0.14513881 5: aot 0.14160492 6: income 0.06766355 7: gender 0.01748248 # philippines covariate imp 1: conspiracy 0.29870623 2: age 0.18730596 3: covid_concern 0.17562344 4: aot 0.15462638 5: income 0.12058831 6: education 0.04311698 7: gender 0.02003269 ``` # heterogeneous treatment effects (HTE) There's some evidence for HTE. If area-under-curve(AUC) in the fig below is positive, then there's HTE. ## india ![[s20220912_004234.png]] ## philippines ![[s20220912_004602.png]] # linear HTE effects ## india ```r # testing for LINEAR effects! # INDIA Best linear projection of the conditional average treatment effect. Confidence intervals are cluster- and heteroskedasticity-robust (HC3): Estimate Std. Error t value Pr(>|t|) (Intercept) 0.6935646 0.3676549 1.8865 0.05953 . age -0.0010886 0.0030696 -0.3546 0.72294 gender -0.0270749 0.0781154 -0.3466 0.72896 education -0.0630834 0.0313840 -2.0100 0.04470 * income 0.0016427 0.0122013 0.1346 0.89293 aot -0.0438045 0.0394974 -1.1090 0.26768 covid_concern -0.0026335 0.0021951 -1.1997 0.23054 conspiracy -0.0014044 0.0031584 -0.4447 0.65667 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 ``` ## philippines ```r Best linear projection of the conditional average treatment effect. Confidence intervals are cluster- and heteroskedasticity-robust (HC3): Estimate Std. Error t value Pr(>|t|) (Intercept) -3.4435e-02 3.3259e-01 -0.1035 0.9176 age -2.1658e-05 2.4380e-03 -0.0089 0.9929 gender 3.2744e-02 6.7428e-02 0.4856 0.6273 education 2.5231e-03 2.4451e-02 0.1032 0.9178 income 1.4234e-03 1.4765e-02 0.0964 0.9232 aot 6.4308e-04 2.8659e-02 0.0224 0.9821 covid_concern -2.0786e-03 1.6346e-03 -1.2716 0.2038 conspiracy -4.5896e-05 2.7823e-03 -0.0165 0.9868 ``` ## probe non-linear HTE with partial dependence plots ## india Higher education is associated with smaller treatment effects. ![[1662964988.png]] ## philippines Higher AOT is associated with weaker treatment effects. ![[1662965257.png]] ![[1662965329.png]] ![[1662965353.png]] ![[1662965384.png]]