Causal Inference & Regression Modeling

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Abstractions about estimating causal effects and relationships from data, covering identification strategies and validity concepts (Causal Inference, External Validity, Lord's Paradox), regression frameworks (Nonlinear Least Squares, Regression, Variance Function), and specific tests or scores like the Chow Test and Continuous Individualized Risk Index.

15 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Causal Inference — Infer the effect of changing X on Y from data by fixing a causal estimand and defending an identification design or assumption that separates that effect from noncausal association, then quantify its uncertainty and scope.
• Chow Test — A classical linear-model F-test that asks whether one coefficient vector can govern two prespecified subsamples by comparing a pooled restricted fit with separate unrestricted fits.
• Continuous Individualized Risk Index — A longitudinal clinical risk score that repeatedly combines an individual's baseline risk with serial biomarker measurements to update predicted outcome risk over time.
• Dependent and independent variables — A paired modeling-role distinction between an outcome variable whose variation is explained and an input variable treated as controlled, assigned, or explanatory within a stated scope.
• Elimination Diet — A time-bounded clinical protocol that withdraws suspected dietary exposures, monitors a defined response, and selectively reintroduces them to test whether the response recurs.
• External Validity — The warrant by which an effect estimated in one study setting can be expected to hold in a target setting outside it — holding conditional on every effect-modifying feature that differs between the two being matched or adjusted.
• Fraction of variance unexplained — A regression-fit statistic equal to the proportion of dependent-variable variance left unexplained by the model's predictions.
• Least Trimmed Squares — A robust regression estimator that minimizes the sum of the h smallest squared residuals, reselecting the retained cases for each trial fit.
• Log-Linear Analysis — Fit and compare expected-count models for categorical contingency tables by using log-scale interaction terms to express joint and conditional associations.
• Lord's Paradox — Show that two arithmetically correct analyses of the same pre-post data — raw change scores versus baseline adjustment — can reach opposite verdicts about an effect, because adjustment is a causal-modeling choice and the two answer different questions depending on whether baseline is itself caused by group membership.
• Nonlinear Least Squares — Estimate parameters that enter a model nonlinearly by minimizing a residual sum of squares, usually through initialization-sensitive local iterations built from the residual Jacobian.
• Probability of Success — A model-based probability that a specified planned or ongoing study will meet its declared success criterion at a future assessment.
• Regression — The statistical method of modelling an outcome as a systematic function of explanatory variables plus specified noise, fit by minimising a loss — supporting three distinct uses (prediction, effect estimation, variance attribution) each gated by its own validity conditions.
• Residual Sum of Squares — Sum squared observed-minus-fitted response differences to obtain a nonnegative, model-relative measure of in-sample discrepancy.
• Variance function — A smooth function expressing the conditional variance of a random quantity as a function of its mean.