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Barbara Guardabascio and Marco Ventura ”Estimating the dose–response function through a generalized linear model approach” The Stata Journal (2014) 14, Number 1, pp. 141–158 Presented by Gulzat Background • Rosenbaum and Rubin (1983a) -binary treatment (pscore.ado, psmatch2.ado) • Hirano and Imbens (2004)-continuous treatment normally distributed (gpscore.ado, doseresponse.ado) • Guardabascio and Ventura (2014) - continuous treatment, not necessarily normally distributed (glmgpscore.ado, glmdose.ado ) Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.3 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.4 What is a dose-response function? It is a relationship between treatment and an outcome variable e.g.: birth weight, employment, bank debt, etc Treatment Effect Function 10000 -20000 0 -10000 0 E[year6(t+1)]-E[year6(t)] 10000 15000 20000 5000 -5000 E[year6(t)] Dose Response Function 0 2 4 6 Treatment level Dose Response 8 10 Low bound Upper bound Confidence Bounds at .95 % level Dose response function = Linear prediction 0 2 4 6 Treatment level Treatment Effect 8 10 Low bound Upper bound Confidence Bounds at .95 % level Dose response function = Linear prediction Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.5 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.8 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.9 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.10 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.11 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.12 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.13 Practical implementation of GPS • • • • Estimate (1) r(t,x) (2) = , = (3) (t ) E t , r (t , X ) for Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.19 Example: The Imbens–Rubin–Sacerdote lottery sample • Survey of Massachusetts lottery winners. • The goal: to analyze the effect of the prize amount on subsequent labor earnings (from social security records). • The sample is the “winners” sample of 237 individuals who won a major prize in the lottery. Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.25 The Imbens–Rubin–Sacerdote lottery sample. Summary Variable Label Obs Mean Std. Dev. Min Max agew Age 237 46.94515 13.797 23 85 yearm1 Earnings 1 years before winning the lottery (Dollar in thousand) 237 14.46759 13.62357 0 42.258 yearm2 Earnings 2 years before winning the lottery (Dollar in thousand) 237 13.4787 12.96455 0 42 yearm3 Earnings 3 years before winning the lottery (Dollar in thousand) 237 12.8363 12.69291 0 44.291 yearm4 Earnings 4 years before winning the lottery (Dollar in thousand) 237 12.03744 12.08134 0 39.874 yearm5 Earnings 5 years before winning the lottery (Dollar in thousand) 237 12.23762 12.41131 0 68.285 yearm6 Earnings 6 years before winning the lottery (Dollar in thousand) 237 12.13228 12.37774 0 74.027 year6 Earnings six years after winning the lottery (Dollar in thousand) 202 11465.22 14338.64 0 44816 male Gender: 1 if male 237 .5780591 .4949144 0 1 tixbot Number of tickets bought 237 4.56962 3.282014 0 10 prize Variable used for treatment = Prize amount 237 55.19556 61.80347 1.139 484.79 yearw Winning year 237 6.059072 1.29401 4 8 workthen Working status after the winning 237 .8016878 .3995725 0 1 owncoll Years of college 237 1.367089 1.601196 0 5 ownhs Years of high school 237 3.603376 1.071031 0 4 The Imbens–Rubin–Sacerdote lottery sample. • Choose the quantiles of the treatment variable to divide the sample into three groups, [0-23], (23-80] and (80485]: • • • qui generate cut=23 if prize<=23 qui replace cut=80 if prize>23 & prize<=80 qui replace cut=485 if prize>80 • • • • • egen max_p=max(prize) g fraction=prize/max_p qui generate cut1=23/max_p if fraction<=23/max_p qui replace cut1=80/max_p if fraction>23/max_p & fraction<=80/max_p qui replace cut1=485/max_p if fraction>80/max_p • glmgpscore male ownhs owncoll tixbot workthen yearw yearm1 yearm2, t(fraction) gpscore(gpscore_fr) predict(y_hat_fr) sigma(sd_fr) cutpoints(cut1) index(mean) nq_gps(5) family(binomial) link(logit) detail • mat def tp1=(0.10\0.20\0.30\0.40\0.50\0.60\0.70\0.80) • glmdose male ownhs owncoll tixbot workthen yearw yearm1 yearm2, t(fraction) gpscore(gps_flog) predict(y_hat_fl) sigma(sd_fl) cutpoints(cut1) index(mean) nq_gps(5) family(binomial) link(logit) outcome(year6) dose_response(doseresp_fl) tpoints(tp1) delta(0.1) reg_type_t(quadratic) reg_type_gps(quadratic) interaction(1) bootstrap(yes) boot_reps(10) analysis(yes) detail filename("output_flog") graph("graphflog.eps") The Imbens–Rubin–Sacerdote lottery sample. Flogit glmgpscore output Flogit glmgpscore output Flogit glmgpscore output Flogit glmgpscore output Flogit glmgpscore output Flogit glmdose output Flogit glmdose output 5000 10000 Treatment Effect Function 0 -5000 -10000 -20000 -40000 E[year6(t)] 0 E[year6(t+.1)]-E[year6(t)] 20000 Dose Response Function 0 .2 .4 .6 Treatment level Dose Response .8 Low bound Upper bound Confidence Bounds at .95 % level Dose response function = Linear prediction 0 .2 .4 .6 Treatment level Treatment Effect .8 Low bound Upper bound Confidence Bounds at .95 % level Dose response function = Linear prediction Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.26 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.28 Source: PPT by Barbara Guardabascio, Marco Ventura “ESTIMATING THE DOSE-RESPONSE FUNCTION THROUGH THE GLM APPROACH”, Italian National Institute of Statistics, 7th June 2013, Potsdam, p.30