A key element in the education of youths is their sensitization to historical and artistic heritage. We analyze a field experiment conducted in Florence (Italy) to assess how appropriate incentives assigned to high-school classes may induce teens to visit museums in their free time. Noncompliance and spillover effects make the impact evaluation of this clustered encouragement design challenging. We propose to blend principal stratification and causal mediation by defining subpopulations of units according to their compliance behavior and using the information on their friendship networks as mediator. We formally define principal natural direct and indirect effects and principal controlled direct and spillover effects, and use them to disentangle spillovers from other causal channels. We adopt a Bayesian approach for inference.
AngristJ. D.ImbensG. W.RubinD. B. (1996). Identification of causal effects using instrumental variables. Journal of the American statistical Association, 91(434), 444–455.
2.
Bargagli-StoffiF. J.TortuC.ForastiereL. (2020). Heterogeneous treatment and spillover effects under clustered network interference. arXiv preprint. arXiv:2008.00707
3.
BowenD. H.GreeneJ. P.KisidaB. (2014). Learning to think critically: A visual art experiment. Educational Researcher, 43(1), 37–44.
4.
BurchenalM.GroheM. (2007). Thinking through art: Transforming museum curriculum. Journal of Museum Education, 32(2), 111–122.
5.
ChengJ.SmallD. S. (2006). Bounds on causal effects in three-arm trials with noncompliance. Journal of the Royal Statistical Society Series B: Statistical Methodology, 68(5), 815–836.
6.
CochranW. (1963). Sampling techniques (2nd ed.). John Wiley & Sons.
7.
CoxD. (1958). Planning of experiments. Wiley.
8.
Del PreteD.ForastiereL.Leone SciabolazzaV. (2019). Causal inference on networks under continuous treatment interference: An application to trade distortions in agricultural markets. http://dx.doi.org/10.2139/ssrn.3363173
9.
EshachH. (2007). Bridging in-school and out-of-school learning: Formal, non-formal, and informal education. Journal of Science Education and Technology, 16(2), 171–190.
10.
ForastiereL.AiroldiE. M.MealliF. (2021). Identification and estimation of treatment and interference effects in observational studies on networks. Journal of the American Statistical Association, 116(534), 901–918.
11.
ForastiereL.LattaruloP.MarianiM.MealliF.RazzoliniL. (2021). Exploring encouragement, treatment, and spillover effects using principal stratification, with application to a field experiment on teens’ museum attendance. Journal of Business & Economic Statistics, 39(1), 244–258.
12.
ForastiereL.MealliF.VanderWeeleT. J. (2016). Identification and estimation of causal mechanisms in clustered encouragement designs: Disentangling bed nets using Bayesian principal stratification. Journal of the American Statistical Association, 111(514), 510–525.
13.
ForastiereL.MealliF.WuA.AiroldiE. (2018). Estimating causal effects under interference using Bayesian generalized propensity scores. arXiv preprint. arXiv:1807.11038.
14.
FrangakisC. E.RubinD. B. (2002). Principal stratification in causal inference. Biometrics, 58(1), 21–29.
15.
FrangakisC. E.RubinD. B.ZhouX.-H. (2002). Clustered encouragement designs with individual noncompliance: Bayesian inference with randomization, and application to advance directive forms. Biostatistics, 3(2), 147–164.
16.
GelmanA. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Analysis, 1(3), 515–534.
17.
Goldsmith-PinkhamP.ImbensG. W. (2013). Social networks and the identification of peer effects. Journal of Business & Economic Statistics, 31(3), 253–264.
18.
GustafsonP. (2010). Bayesian inference for partially identified models. The International Journal of Biostatistics, 6(2), Article 17.
19.
HiranoK.ImbensG. W.RubinD. B.ZhouX.-H. (2000). Assessing the effect of an influenza vaccine in an encouragement design. Biostatistics, 1(1), 69–88.
20.
HongG.RaudenbushS. W. (2006). Evaluating kindergarten retention policy: A case study of causal inference for multilevel observational data. Journal of the American Statistical Association, 101(475), 901–910.
21.
HudgensM. G.HalloranM. E. (2008). Toward causal inference with interference. Journal of the American Statistical Association, 103(482), 832–842.
22.
ImbensG. W.RubinD. B. (1997). Bayesian inference for causal effects in randomized experiments with noncompliance. The Annals of Statistics, 25, 305–327.
23.
KangH.ImbensG. (2016). Peer encouragement designs in causal inference with partial interference and identification of local average network effects. arXiv preprint. arXiv:1609.04464.
24.
LattaruloP.MarianiM.RazzoliniL. (2017). Nudging museums attendance: A field experiment with high school teens. Journal of Cultural Economics, 41(3), 259–277.
25.
MatteiA.ForastiereL.MealliF. (2023). Assessing principal causal effects using principal score methods. In J. R. Zubizarreta, E. A. Stuart, D. S. Small, & P. R. Rosenbaum (Eds.), Handbook of matching and weighting adjustments for causal inference (pp. 313–348). Chapman and Hall/CRC.
26.
MatteiA.MealliF. (2007). Application of the principal stratification approach to the faenza randomized experiment on breast self-examination. Biometrics, 63(2), 437–446.
27.
MorrisS. S.FloresR.OlintoP.MedinaJ. M. (2004). Monetary incentives in primary health care and effects on use and coverage of preventive health care interventions in rural honduras: cluster randomised trial. The Lancet, 364(9450), 2030–2037.
28.
OgburnE. L.SofryginO.DiazI.Van Der LaanM. J. (2024). Causal inference for social network data. Journal of the American Statistical Association, 119(545), 597–611.
29.
PearlJ. (2001). Direct and indirect effects. In Proceedings of the seventeenth conference on uncertainty in artificial intelligence (pp. 411–420). Morgan Kaufmann Publishers Inc.
30.
RobinsJ. M.GreenlandS. (1992). Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3(2), 143–155.
31.
RubinD. B. (1980). Randomization analysis of experimental data: The fisher randomization test comment. Journal of the American Statistical Association, 75(371), 591–593.
32.
RubinD. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. The Annals of Statistics, 12(4), 1151–1172.
33.
SobelM. E. (2006). What do randomized studies of housing mobility demonstrate? Causal inference in the face of interference. Journal of the American Statistical Association, 101(476), 1398–1407.
34.
Stan Development Team. (2014). Stan: A C++ library for probability and sampling. http://mc-stan.org
35.
Ten HaveT. R.JoffeM. M. (2012). A review of causal estimation of effects in mediation analyses. Statistical Methods in Medical Research, 21(1), 77–107.
36.
VanderWeeleT. J.AnW. (2013). Social networks and causal inference. In S. L. Morgan (Ed.), Handbook of causal analysis for social research (pp. 353–374). Springer Dordrecht.
37.
VanderWeeleT. J.VansteelandtS. (2009). Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2(4), 457–468.
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