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Local polynomial regression

As explained in Causal Inference for Data Science

Local polynomial regression estimates a local relationship by fitting weighted polynomial models around each prediction point.

Local polynomial regression (LPR) estimates a relationship near each prediction point by fitting a weighted polynomial model. In regression discontinuity designs, it estimates the treatment effect from the local jump at the cutoff, offering explicit formulas that are easier to inspect than many machine-learning models. section 11.2.5

A practical RDD workflow uses LPR to:

  • Fit separate local relationships on either side of the cutoff. section 11.2.5
  • Estimate the discontinuity at the cutoff as the treatment effect. section 11.2.5
  • Use rdplot for exploration and rdrobust for nonlinear estimation and confidence intervals. section 11.2.5
  • Check sensitivity to the chosen time window because different windows can change estimates and uncertainty. section 11.2.5

A time-based intervention

Suppose an algorithm begins at time T. LPR models outcomes near T on both sides, then compares their predicted values at T. An estimate of 770.05 had a confidence interval from −11.42 to 1551.52, so the data did not establish that the effect was positive. section 11.2.5

How Causal Inference for Data Science covers it

How deep it goes
Provides formulas, implementation, plots, confidence intervals, and window sensitivity, but defers detailed kernel mechanics.
Examples
Uses a time-based algorithm intervention, varying time windows, rdplot, and rdrobust output.
What it assumes
Assumes familiarity with regression discontinuity designs, treatment effects, regression, and confidence intervals.
What you can do after
Diagnose RDD estimates with rdplot and rdrobust while comparing sensitivity across local time windows.
How it connects
Connects regression discontinuity design, local linear regression, machine learning, cross-validation, kernels, and confidence intervals.
Cover of Causal Inference for Data Science
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Causal Inference for Data Science. The section links point to the parts of the book it draws on.