Counterfactuals and Program Evaluation

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Questions and Answers

What remains constant and depends only on the observable parameter P(y′ |x)∕P(y|x)?

The interval UB–LB (correct)

The confounding factor (CF)

The causal effect P(yx ) − P(yx′ )

The gap between upper and lower bounds

What must the lower bound meet for it to be considered 'more probable than not'?

It should exceed 0.5 (correct)

It must be equal to 1

It needs to be less than 0.5

It can be any value below 0.5

Under what assumption do the upper and lower bounds coincide and the gap collapses entirely?

Assumption of independence

Random sampling of data

Assumption of monotonicity (correct)

Equal expected risk ratios

What does the CF indicate in the provided content?

An estimate derived from experimental data Signup and view all the answers

Which scenario best describes when experimental data can be used to estimate counterfactuals?

When the data is drawn from the same population Signup and view all the answers

In the legal attribution example, what was the claim regarding drug x made by the manufacturer?

It has only minor effects on death rates Signup and view all the answers

What does the notation P(yx ) − P(yx′ ) refer to in the content?

The causal effect Signup and view all the answers

What is necessary for the bounds in Figure 4.5(b) to identify PN?

Monotonicity must be assumed Signup and view all the answers

What does the equation Y = bX + cH + 𝛿XH + UY represent in the context of counterfactuals?

A model with a multiplicative interaction term. Signup and view all the answers

Which parameters in Figure 4.1 can be estimated from nonexperimental data?

Parameters a, b, and c. Signup and view all the answers

What does ETT represent in the context of the model described in Eq. (4.19)?

The expected total treatment effect. Signup and view all the answers

In the recruitment example of a job training program, what was the outcome of the pilot randomized experiment?

It indicated that the program was effective. Signup and view all the answers

What was the primary motivation for offering the job training program to unemployed individuals following its success in the pilot study?

To increase enrollment and utilization of the program. Signup and view all the answers

What is the significance of the relationship between Y1 and Y0 in computing counterfactual outcomes?

It quantifies potential outcomes based on different circumstances. Signup and view all the answers

What conclusion can be drawn from the increased hiring rates observed after the job training program was offered successfully?

The program can be deemed effective in the broader population. Signup and view all the answers

What does the term 'counterfactual' typically refer to in this context?

A condition that never occurred in reality. Signup and view all the answers

What is the concluded increase in the success rate of the program?

46% Signup and view all the answers

What percentage of the increase in success rate is attributed to improved homework effort alone?

7% Signup and view all the answers

In the structural model equation y = 𝛽1 m + 𝛽2 t + uy, what does 'm' represent?

Mediator Signup and view all the answers

Which term in the equation represents the interaction effect?

𝛽3 tm Signup and view all the answers

What is NDE in the context of the structural model?

Natural Direct Effect Signup and view all the answers

According to the equations provided, what effect does treating M as the mediator help determine?

Portion of the effect requiring mediation Signup and view all the answers

What is the interaction term in the structural model?

tm Signup and view all the answers

If uy is correlated with um, what assumption about the model is being made?

They influence each other Signup and view all the answers

What does the probability of necessity (PN) indicate in legal liability cases?

It estimates the probability that damage would not have occurred if an action had not been taken. Signup and view all the answers

What is represented by E[Yx,Mx′] in the context of mediation?

The expected outcome if both treatment and mediator variables had different values. Signup and view all the answers

What does the expression P(Yx′ = y′ |X = x, Y = y) mathematically represent?

The probability that Y would take on a specific value given different treatments. Signup and view all the answers

Under which conditions can nested counterfactual expressions be estimated?

When specific criteria related to outcome consistency are met. Signup and view all the answers

What key legal criterion is captured by the probability of necessity (PN)?

The condition that damages are likely due to the defendant's action if proven. Signup and view all the answers

In the context of treatment and outcomes, what do X and Y represent?

X signifies the treatment and Y the observed outcome resulting from it. Signup and view all the answers

What does the term 'nested' in nested counterfactual expressions imply?

It indicates that multiple layers of conditioning are applied in the analysis. Signup and view all the answers

How can PN be estimated according to the content?

By using a combination of both observational and experimental data to assess likelihood. Signup and view all the answers

What is the main focus of the work by Bareinboim E and Pearl J in 2013?

Transportability of experimental results Signup and view all the answers

Which topic is NOT addressed in the research by Bollen K and Pearl J in 2013?

Data fusion techniques Signup and view all the answers

What is the contribution of Bowden R and Turkington D in 1984 to the field of statistical analysis?

Development of instrumental variables method Signup and view all the answers

The moderator-mediator variable distinction was defined by which authors?

Baron R and Kenny D Signup and view all the answers

In which publication did Judea Pearl collaborate with Glymour and Jewell?

Causal Inference in Statistics: A Primer Signup and view all the answers

What limitation of fourfold table analysis was discussed by Berkson J in 1946?

Application to hospital data Signup and view all the answers

What type of variables did Brito C and Pearl J work on in 2002?

Generalized instrumental variables Signup and view all the answers

Which of the following best describes the work of Cai Z and Kuroki M in 2006?

Variance estimators for causal probabilities Signup and view all the answers

Study Notes

Counterfactuals and Their Applications

In a model where Y = bX + cH + δXH + UY, τ (treatment effect) differs from ETT (effect of treatment on the treated) if the arrow X → H is reversed. The difference is calculable.
Parameters in causal models can be estimated from non-experimental data.
The effect of a variable (e.g., education) on a subset of the population (e.g., those with Y=1) can be computed using counterfactuals.
Counterfactuals are used to solve seemingly complex problems, improving understanding and application of causal inference.

Recruitment to a Program

A successful job training program, initially demonstrated effective via a randomized experiment, showed even higher hiring rates after a recruitment drive. This highlights the importance and complexity of evaluating program success.
Probability of necessity (PN) is expressed as P(Y0 = 0|X = 1, Y = 1), relevant to legal liability and program evaluation. It assesses the likelihood that a negative outcome would not have occurred absent a specific action.

Mathematical Results and Attribution

Probability of necessity (PN) can be estimated or bounded using observational and experimental data.
In mediation analysis, the key counterfactual expression E[Yx,Mx′] represents the expected outcome under different treatment and mediator states.
PN is defined mathematically as P(Yx′ = y′ |X = x, Y = y), representing the probability that an outcome would have been different without the treatment received. This relates to a "but for" legal criterion for cause.
Under monotonicity, upper and lower bounds of PN coincide.
Experimental data can be used to estimate counterfactuals in both experimental and observational samples.

Attribution in a Legal Setting

A lawsuit against a drug manufacturer exemplifies how counterfactuals are applicable to legal settings. Determining whether a drug caused a death uses counterfactual reasoning.

Natural Direct and Indirect Effects (NDE, NIE)

NDE and NIE analysis decomposes a total effect (TE) into direct and indirect effects via a mediator. Formulas are given to compute NDE and NIE.
Example calculations of TE, NDE, and NIE are given; showing that indirect effects may be minimal compared to direct.

Structural Models and Natural Effects

Structural models (with and without interaction terms) are used to analyze natural direct and indirect effects, with calculations illustrated. Mediation analysis is used to assess the contribution of a mediating variable.

References

A list of references is provided, covering various publications on causal inference and related methodologies.

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Description

Explore the intricate relationship between counterfactuals and program evaluation methods. This quiz delves into models that include treatment effects and their implications for causal inference. Learn how counterfactual reasoning can enhance the understanding of non-experimental data and program success metrics.