Module 4 — Choice and Limited Outcomes

An outcome’s support is part of the research design. A binary variable cannot fall below zero, a count has an exposure period, and observed wages exist only after an employment decision. The model should respect these facts without turning a causal question into a distributional exercise.

Prepare

Before the workshop, classify each outcome:

Write one sentence defining the outcome, observation window and denominator. Many apparent “model failures” are outcome-definition failures.

Route

1. Binary Choice: probabilities, nonlinear effects and calibration.
2. Multinomial Choice: unordered, ordered and alternative-specific decisions.
3. Count Outcomes: rates, exposure, overdispersion and excess zeros.
4. Censoring and Selection: observed limits, participation and missing counterfactual outcomes.

Workshop: one policy, four outcomes

For the Pathways programme, compare:

• enrolment within one year: binary;
• university selected: multinomial;
• modules completed in year one: count;
• earnings five years later: continuous, but missing for people outside linked tax records.

For each, specify the estimand first. A nonlinear likelihood can improve fit; it cannot make scholarship receipt exogenous.

Follow-up deliverable

Submit a two-page marginal-effect report containing:

1. outcome support and observation process;
2. target contrast on an interpretable scale;
3. model and identifying assumptions;
4. one worked prediction or marginal effect;
5. one diagnostic and one conclusion boundary.

Postgraduate extension: derive the likelihood contribution and distinguish structural distributional assumptions from assumptions needed for causal identification.

Start with Binary Choice