MODEL CHOICE BEGINS WITH THE QUESTION

Choosing Regression: A Framework for Model Selection

Regression describes how an outcome varies with one or more explanatory variables. The appropriate model depends on the outcome, data structure, and whether the goal is description, prediction, or causal inference.

OUTCOME · DESIGN · ASSUMPTIONS · INTERPRETATION

Start here:What kind of outcome are you explaining—and what claim do you want to make?

METHOD OVERVIEW

Eight common approaches

These are related tools, not interchangeable recipes. Select the design before reaching for the command.

CONTINUOUS OUTCOME

Ordinary least squares

Models the conditional mean of a continuous outcome as a linear function of explanatory variables.

regress y x1 x2, vce(robust)

CATEGORICAL OUTCOME

Logit and probit

Estimate the probability of a binary outcome; multinomial and ordered models extend the framework.

logistic y x1 x2

COUNT OUTCOME

Poisson and negative binomial

Model non-negative event counts, with negative binomial useful when variation exceeds the Poisson mean.

poisson y x, exposure(e) irr

DISTRIBUTIONAL EFFECTS

Quantile regression

Estimates how predictors relate to a chosen conditional quantile rather than only the conditional mean.

qreg y x1 x2, quantile(.5)

ENDOGENEITY · CAUSAL

Instrumental variables

Uses an exogenous instrument to isolate variation in an endogenous explanatory variable.

ivregress 2sls y x1 (x2 = z)

REPEATED OBSERVATIONS

Panel regression

Uses variation across units and over time, often accounting for time-invariant unit characteristics.

xtreg y x1 x2, fe

POLICY CHANGE · CAUSAL

Difference-in-differences

Compares outcome changes over time between a treatment group and a comparison group.

regress y i.treat##i.post

CUTOFF RULE · CAUSAL

Regression discontinuity

Estimates a local treatment effect when assignment changes discontinuously at a known threshold.

rdrobust y running, c(cutoff)

QUICK ORIENTATION

YOUR SITUATIONUSEFUL STARTING POINTKEY QUESTION

Continuous outcomeOLS or quantile regressionMean relationship or another part of the distribution?

Binary or categorical outcomeLogit, probit, multinomial or ordered modelAre categories ordered, unordered, or binary?

Non-negative event countPoisson or negative binomialIs there overdispersion or excess zeroes?

Causal policy questionIV, panel, DID or RDWhat credible source of identification is available?

PUT IT INTO PRACTICE

Work through the model decision.

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