Have to first reduce/aggregate each subj's data to a single row (so will lack statistical power to detect treatment effects and doesn't account for item effects)
- `y` (truth ratings for **false** headlines) for each subject: $\bar{y}_{repeated} - \bar{y}_{novel}$
- only 275 rows/subjects
As with results from mixed-effects models, adjusting for covariates matters.
```r
# causal effect after adjusting for 11 covariates
> average_treatment_effect(cf)
estimate std.err
-0.08206909 0.08725634 # huge SE, but correct sign
# explore/compare: causal effect adjusting for just age and gender
> average_treatment_effect(cf)
estimate std.err
-0.001629907 0.084440179 # no treatment effect at all, so adjusting for covariates indeed mattered
```
# forest feature importance
```r
covariate imp
1: tenuredays 0.275882666 # most predictive of treatment effect
2: gap_days 0.205919552
3: conspiracy 0.133391372
4: age 0.105974972
5: aot 0.101171554
6: covid_concern 0.060441118
7: genderMale 0.030862710
8: domainMedia & Ent 0.022562396
9: domainProfessional Services / Industry 0.012170469
10: domainSocial Media 0.010141687
11: regionSEA 0.007875551
12: countryGR 0.007493924
13: domainHi-Tech 0.006852252
14: countryPH 0.005138410
15: roleTeam Leader 0.003737543
16: roleTeammate 0.002965230
17: regionLATAM 0.002025386
18: countryTW 0.001920672
19: regionIN 0.001754025
20: countryIN 0.001718512
21: domainSupport 0.000000000
covariate imp
```
# 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.
![[s20220801_115003.png]]
# linear HTE effects
```r
# testing for LINEAR effects!
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) 1.7795e-01 7.6960e-01 0.2312 0.817317
age -2.5360e-03 1.2565e-02 -0.2018 0.840198
tenuredays -9.0839e-05 1.9319e-04 -0.4702 0.638596
aot 5.7687e-02 6.6946e-02 0.8617 0.389622
covid_concern -1.3539e-01 6.4589e-02 -2.0961 0.037011 *
conspiracy -6.0817e-03 5.4675e-02 -0.1112 0.911514
gap_days 1.0507e-01 3.4180e-02 3.0741 0.002329 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
```
## probe non-linear HTE with partial dependence plots
Subjs who have been moderators for longer show **weaker** treatment effects.
![[1659376370.png]]
The longer the no. of days between wave1 and wave2 complete, the weaker the treatment effect.
![[1659376440.png]]
Higher AOT associated with weaker treatment effects.
![[1659376557.png]]
Greater COVID concern associated with stronger treatment effects.
![[1659376595.png]]