certainty • If you want to estimate, P worse than MLE or posterior • If you want to decide, P uncalibrated • If you want to predict, P is worse than cross-validation, AIC, etc. • All of this applies to confidence intervals as well
Sad history of right-turn-on-red 496 E. Hauer / Accident Analysis and Prevention 3 Table 1 The Virginia RTOR study Before RTOR signing After RTOR signing Fatal crashes 0 0 Personal injury crashes 43 60 Persons injured 69 72 Property damage crashes 265 277 Property damage (US$) 161243 170807 Total crashes 308 337 thing and the Commissioner transmitted something entirely Table 2 Summary Crash type Treatment: Single-v Same-di Opposit Fatal Persona Property Treatment: Single-v Same-di Hauer. 2004. Accident Analysis and Prevention 36:495–500
Imagine how estimates may mislead • missing variables • sample selection • model structure • Fitting is easy; prediction is hard • Plot, plot, plot! • Embrace the uncertainty • uncertainty about parameters • uncertainty about models
add interaction. Centering disguises that fact. • Coefficient in model without interaction: • Change in outcome per unit change in predictor • e.g. change in blooms per unit change in water
add interaction. Centering disguises that fact. • Coefficient in model without interaction: • Change in outcome per unit change in predictor • e.g. change in blooms per unit change in water • Coefficient with interaction: • Change in outcome per unit change in predictor, when other predictor is zero • e.g. change in blooms per unit change in water, when shade is zero
add interaction. Centering disguises that fact. • Coefficient in model without interaction: • Change in outcome per unit change in predictor • e.g. change in blooms per unit change in water • Coefficient with interaction: • Change in outcome per unit change in predictor, when other predictor is zero • e.g. change in blooms per unit change in water, when shade is zero • Centered predictors => zero is mean value!
so use more than one plot • Here, need three plots, triptych Lewis Powell (1844–1865), before his hanging for conspiracy to assassinate Abraham Lincoln.
to interpret: “The extent to which the effect of x1 depends upon the value of x2 depends upon the value of x3 , dude.” • Hard to estimate: need lots of data, risk multicollinearity --> regularize • But you might really need them, because conditionality runs deep The Dude abides high-order interactions
• New Jersey wines vs fine French wines • Shocker: French judges preferred NJ reds to French reds • Outcome variable: score • Predictors: • region (NJ/FR) • nationality of judge (USA/FR-BE) • flight (red/white)
• Consider interactions: • Interaction of region and judge is bias. Bias depends upon flight. • Interaction of judge and flight is preference. Preference depends upon region. • Interaction of region and flight is comparative advantage. Advantage depends upon judge.
All predictors interact to some extent • Onward to multilevel models (GLMMs) • Massive interaction engines --> allow parameters to be conditional on group membership
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