Why Model? Parametric vs Nonparametric
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The Role of Models in Causal Inference
In previous chapters, we established that causal effects can be identified using the g-formula or inverse probability weighting when exchangeability, positivity, and consistency hold. In theory, these methods can be applied nonparametrically—that is, without imposing any functional form assumptions on the relationships between variables.
However, in practice, purely nonparametric approaches quickly become infeasible. This chapter explores why we need statistical models in causal inference and how to choose between different modeling strategies.
The practical challenges that necessitate modeling include:
- Curse of dimensionality: As the number of confounders increases, the number of possible combinations grows exponentially, quickly exceeding any realistic sample size
- Sparse data: Even with moderate numbers of confounders, many stratum-specific cells will contain few or no observations
- Continuous confounders: Variables like age, BMI, or blood pressure cannot be meaningfully stratified without arbitrary categorization
- Statistical efficiency: Models can "borrow strength" across similar observations, producing more precise estimates
In the NHEFS (National Health and Nutrition Examination Survey Epidemiologic Follow-up Study) analysis of smoking cessation and weight gain, we need to adjust for age, sex, race, education, baseline smoking intensity, years smoked, exercise habits, activity level, and baseline weight. Even with binary categorizations, this would create thousands of strata—far more than our sample of ~1,600 individuals can support nonparametrically.
The fundamental question we address in this chapter: When can we avoid models entirely, and when must we impose parametric assumptions?
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