Skip to main content
Search form
  • 00:00


  • 00:11

    DR. HAIYAN BAI: Hello, I am Dr. Haiyan Bai, Associate Professorin the Department of Educational and Human Sciencesat the University of Central Florida.[Dr. Haiyan Bai, PhD, Associate Professor,Department of Education and Human Sciences,University of Central Florida] Today'stutorial is on the propensity scoremethod and a causal inference conceptas the first part of this tutorial.

  • 00:32

    DR. HAIYAN BAI [continued]: Our learning objectives is to understandwhy to use the propensity score method,and what is the propensity score method.When to use of propensity score method and the issueswith propensity score method.[Why use propensity score method?]

  • 00:54

    DR. HAIYAN BAI [continued]: Why we want to use the propensity score method?As we know, a lot of times in research, wewanted to derive the causal inference.[causal inference] We always liketo use treatment versus control groupsto study the causal effect.Experimental design is the best for us

  • 01:17

    DR. HAIYAN BAI [continued]: to select to use to derive the causal inferencebecause random assignment can minimizethe covariates influence in the outcome or result. However,experimental design is usually impractical in social science,human science, and educational studies.

  • 01:40

    DR. HAIYAN BAI [continued]: Therefore, most of the time, we selectto use a quasi-experimental designto control the covariates influence in the outcomevariables.However, as we know, sometimes to measureall the categorical variables and to controlthe covariates is not sufficient to reduce the group selection

  • 02:04

    DR. HAIYAN BAI [continued]: bias, which rooted in the design.In the propensity score is a methodto balance the group to reduce the selectionbias in the research design.As we can see, in the past 30 years,PSM is increasingly popular in many fields.

  • 02:27

    DR. HAIYAN BAI [continued]: [What is propensity score method?]Propensity score method was developedby Rosenbaum and Rubin, 1983, in orderto reduce the selection bias, to help to balance the groups,

  • 02:47

    DR. HAIYAN BAI [continued]: in the treatment and the control.And also, it helped design a study thatmimics experimental design.Then next, what is a propensity score?Propensity score is the probability or likelihoodof being assigned to the treatment group.It is a linear combination of covariates.

  • 03:11

    DR. HAIYAN BAI [continued]: It is often expressed as p Xi, p representingthe probability for a case to be assigned to the treatment groupbased on their covariates, Xi.Xi representing a group of covariates.

  • 03:32

    DR. HAIYAN BAI [continued]: [When to use propensity score method?]When to use the PSM for causal inference?We can say, whenever we want to derive the causal inferencefrom observational studies.Usually, in observational studies,

  • 03:54

    DR. HAIYAN BAI [continued]: researchers cannot manipulate the group assignment.However, when we use propensity score,we can balance the group assignmentto create homogeneous groups based on their covariates.Why we can use the propensity score for causal inference?

  • 04:15

    DR. HAIYAN BAI [continued]: Treatment effect usually defined as the differencebetween the individual's behaviorwhen they assigned to the treatment and the controlgroups.This is impossible because we cannot simultaneously sign

  • 04:37

    DR. HAIYAN BAI [continued]: a person into both the treatment and the control groups.This is the same with a group.We cannot assign a group of people, at the same time,both in treatment and a control group.However, we can use random assignment

  • 04:57

    DR. HAIYAN BAI [continued]: to create equal groups, like an experimental design.And with propensity score, we assumeif all the covariates to be observed in them,we can use the propensity score to make a balanced group.We can calculate the means of outcomes, of treatment,

  • 05:22

    DR. HAIYAN BAI [continued]: in the control groups to use it as the unbiased estimatorfor the Average Treatment Effect.To use the propensity score methodrequires some important assumptions.Now the first the important assumptionis Strong Ignorability in treatment assignment.

  • 05:44

    DR. HAIYAN BAI [continued]: This assumption assumes, given a group of covariates, Xi,the group assignment, r1i and r0i,representing the treatment group and the control groupsindependent to the outcome variables, zi.

  • 06:09

    DR. HAIYAN BAI [continued]: And the Strong Ignorability Assumption in that,if it is established, then it is true for a given propensityscore, calculated from the group of covariates.

  • 06:33

    DR. HAIYAN BAI [continued]: The group assignment will be independent to the outcomevariables.Another important assumption is that the Stable Unit TreatmentValue Assumption.It is that the treatment group and the control group, there'sno contaminations and interactions.

  • 06:54

    DR. HAIYAN BAI [continued]: [How to Use Propensity Score Method]Next, let's discuss about the applications of a propensityscore method.There are usually four different waysto apply propensity score method.

  • 07:14

    DR. HAIYAN BAI [continued]: We can use matching or stratification,usually also called subclassification or blocking,to create equal groups.And the others we can use under propensitycalled weighting or covariates adjustment,to use in the analysis of covariance or regression

  • 07:37

    DR. HAIYAN BAI [continued]: models.And when we apply the propensity score method,usually we also have four steps.First, we need to estimate propensity scores,and then we can use that propensity score directlyinto the analyses-- you can show them covariates.

  • 08:01

    DR. HAIYAN BAI [continued]: Or, most of the time, we use matching.When we use matching, before the final analysis,in that we should evaluate the matching quality.First, let's look at the estimation of the propensityscore.

  • 08:22

    DR. HAIYAN BAI [continued]: Most of the time, we use logistic regressionof two treatment conditions on covariates.That propensity score is the probabilityof being assigned to the treatment group.In Rubin, 2001, suggested to use the logit of a propensityscore to achieve normality so that we

  • 08:46

    DR. HAIYAN BAI [continued]: can meet most of the basic statistical analysisassumptions.Next, I would like to provide a simple example to showhow matching can be done.Now, as we can see, there are two groups-- treatmentand the comparison groups-- with their propensity scores.

  • 09:09

    DR. HAIYAN BAI [continued]: In the [INAUDIBLE] find, from the first 0.62,this score finds the closest matching to 0.61in the comparison group.The same way, we can find some other matcheson the propensity score.

  • 09:29

    DR. HAIYAN BAI [continued]: And there are two propensity scoreswe can see there's no matching.There are no match, the pairs, in the treatment group.Then we exclude them into the matched data.From the histograms, we can see, before matching,usually the two groups-- treatment and the control

  • 09:51

    DR. HAIYAN BAI [continued]: groups-- may not match very well.Or on the other word, they may notbalance on their covariates.However, after matching, we can see,we can have similar groups, balanced on their propensityscore, which is balanced on their covariates.

  • 10:13

    DR. HAIYAN BAI [continued]: In the propensity score matching,there are a lot of different ways to match the groups.In the traditional way, we have exact matchingand the Mahalanobis matching.Those matching are not perfect.To handle the limitation of the traditional matching method,

  • 10:37

    DR. HAIYAN BAI [continued]: propensity score matching was developed in that, mainly,we can categorize them into two big groups.One is greedy matching, the other is complex matching.In the greedy matching, we have a nearest neighbor match,which is the basic matching, and then caliper matching,

  • 10:59

    DR. HAIYAN BAI [continued]: Mahalanobis matching with ps.In the complex matching, we have several classificationin the optimal matching and the kernel matching.In the propensity score matching,there are four major matching methods we usually use.They are nearest neighbor matching, caliper matching,

  • 11:22

    DR. HAIYAN BAI [continued]: subclassification, and the optimal matching.In this tutorial, we would only introduce the fourcommonly used matching methods.[Nearest Neighbor Matching]I would like to use an example to demonstrate how nearest

  • 11:44

    DR. HAIYAN BAI [continued]: neighbor matching is conducted.Now when we look at the first treatment group,their propensity scores are the A, B, C, B,E. In the propensity scores for the control groupare V, W, X, Y, Z. Usually, nearest neighbor matching will

  • 12:10

    DR. HAIYAN BAI [continued]: be done in order, so the two groups of propensityscores for treatment and the control groupsshould be ranked in orders.And from the top, we find A and then findanother, the closest, propensity score in the control group

  • 12:33

    DR. HAIYAN BAI [continued]: to match it.Then we find V, with the propensity score 0.404to match it.In the same way, we go B. In the same way,we select Z in the control group-- 27.

  • 12:54

    DR. HAIYAN BAI [continued]: We select the case Z with the propensityscore 0.27 to match B, 0.29.And then we find other matches with the closest distanceto match the treatment groups.

  • 13:14

    DR. HAIYAN BAI [continued]: As we can see, the global distance is 0.39.Nearest neighbor matching is the basic propensity scorematching method.In the [INAUDIBLE] nearest neighbor matching,we can see there are some limitations

  • 13:35

    DR. HAIYAN BAI [continued]: because some matching may have large differencesbetween the control group and the treatment group cases.And to solve the problem, caliper matching was developed.[Caliper Matching]

  • 13:56

    DR. HAIYAN BAI [continued]: Caliper matching is the matching methodto set up the bandwidth or range of the score.The bandwidth is defined as 0.25 timesthe standard deviation of the group of propensity scores.Only two cases found that in the control group

  • 14:21

    DR. HAIYAN BAI [continued]: to match the treatment group.Because we used the bandwidth, anything beyond-- any caseswith the propensity score beyond the bandwidth,we exclude them from the matching data.In nearest neighbor matching, D and the Y

  • 14:42

    DR. HAIYAN BAI [continued]: were matched with the distance of 0.18.However, in the caliper matching,the case B and Z matched with the distance of 0.02,which is a much more reduced with the difference

  • 15:02

    DR. HAIYAN BAI [continued]: between the two propensity scores.The global distance of 0.4 in caliper matchingis much more smaller than the global distance in the nearestneighbor matching.As we can see, in caliper matching,we have the sample size significantly reduced.

  • 15:26

    DR. HAIYAN BAI [continued]: [Optimal Matching]In optimal matching, all the casesmatched in the optimal way in termsof reducing the global distance.As we can see, the global distancewas 0.37 in the nearest neighbor matching.

  • 15:48

    DR. HAIYAN BAI [continued]: X was matched with C in the nearest neighbor matchingand the distance is 0.15.And Y was matched with D in nearest neighbor matchingand the distance is 0.18.In the full optimal matching, there'sno restrictions, as in the nearest neighbor matching,

  • 16:11

    DR. HAIYAN BAI [continued]: for the ranking order.And also, there's no restrictionsof the bandwidth in the caliper matching.[Subclassification]There is another type of matching, subclassification.

  • 16:32

    DR. HAIYAN BAI [continued]: Some researchers do not categorizethe subclassification matching as one of the matching methods.However, as we know subclassification stillused the matching for groups other than finding the matchingpairs on the individual basis.And usually, we have five strata used in the quantile.

  • 16:58

    DR. HAIYAN BAI [continued]: In them, match the cases in groups basedon their propensity score.[Issues With Propensity Score Method]Next, let's look at the issues with propensity score matching.As other statistical methods, propensity score matching

  • 17:22

    DR. HAIYAN BAI [continued]: is on limitations.First, it is harder to ensure that weselect all the covariates, that there's no hidden bias.And the next, we would like to knowwhen it is a properly used, the matching waysare without a replacement.

  • 17:44

    DR. HAIYAN BAI [continued]: How we are going to deal with remaining significant selectionbias and then, how to evaluate the matching quality.Also, sensitivity analysis is a big topic for further research.[Conclusion]

  • 18:05

    DR. HAIYAN BAI [continued]: Regarding to these issues, I suggestedthat you use the newly published book by Pan and Bai in 2015.That is named The Propensity Score Analysis,Fundamentals and Developments.You will find some issues and the solutions in this book.

  • 18:30

    DR. HAIYAN BAI [continued]: And I would like to suggest the other references attached.[Further Reading][Bai (2015), Methodological considerationsin implementing propensity score matching][Brookhart, Schneeweiss, Rothman, Glynn, Avorn,and Sturmer (2006), Variable Selection for Propensity ScoreModels.American Journal of Epidemiology][Rosenbaum and Rubin (1983), The CentralRole of the Propensity Score in Observational Studiesfor Causal Effects.Biometrika.][Rubin (2001), Using Propensity Scoresto Help Design Obervational Studies-- Applicationto the Tobacco Litigation.Heath Services and Outcomes Research Methodology][MUSIC PLAYING]

Video Info

Publisher: SAGE Publications Ltd

Publication Year: 2017

Video Type:Tutorial

Methods: Experimental design, Causation

Keywords: issues and controversies; mathematical applications; mathematical formulas; mathematics; practices, strategies, and tools; treatment ... Show More

Segment Info

Segment Num.: 1

Persons Discussed:

Events Discussed:



Dr. Haiyan Bai discusses propensity score methods and why to use them. The propensity score method reduces selection bias, balances groups, and gives a propensity score of the likelihood of being assigned to the treatment group. Bai discusses when the method is used, how to use the method, and what issues the method has.

Looks like you do not have access to this content.

An Introduction to Propensity Score Methods

Dr. Haiyan Bai discusses propensity score methods and why to use them. The propensity score method reduces selection bias, balances groups, and gives a propensity score of the likelihood of being assigned to the treatment group. Bai discusses when the method is used, how to use the method, and what issues the method has.

Copy and paste the following HTML into your website