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) 𝐸 𝑌 𝑇 = 𝑡, 𝑅 = 𝑟
(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