DFFITS

A regression influence diagnostic measuring the studentized change in an observation's fitted value when that observation is omitted from model estimation.

Version

v1 · 2026-09-08 · History

Domain-specific #

4140

Origin domain

regression diagnostics

Subdomain

influence analysis

Core Idea

DFFITS for observation i is its full-fit prediction minus its deletion-fit prediction divided by an estimated standard deviation of that fitted difference. Deleting an observation changes coefficients according to its residual and leverage; studentization makes the induced prediction change comparable across points. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

The load-bearing residual is not the broad topic of regression diagnostics. It is case-specific standardized influence on its own fitted value rather than residual extremeness alone.

Scope of Application

DFFITS belongs to regression diagnostics and is useful where the analyst can specify a fitted linear model, an observation i, full-data and leave-one-out predictions, leverage, residual variance, a studentization convention, and reference thresholds, then evaluate the diagnostic uses the same response and design with exactly observation i deleted and reports the selected internal or external variance convention. The scope is broad within that domain but bounded by the need for the diagnostic uses the same response and design with exactly observation i deleted and reports the selected internal or external variance convention. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity

The abstraction clarifies a crowded vocabulary by making the diagnostic uses the same response and design with exactly observation i deleted and reports the selected internal or external variance convention the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name DFFITS can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to DFFITS. DFFITS compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning

1. Identify the carrier. State what the elements, states, objects, or observations are: a fitted linear model, an observation i, full-data and leave-one-out predictions, leverage, residual variance, a studentization convention, and reference thresholds. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the diagnostic uses the same response and design with exactly observation i deleted and reports the selected internal or external variance convention independently of one notation or implementation.

Knowledge Transfer

Knowledge transfers strongly among subfields of regression diagnostics because they reuse a fitted linear model, an observation i, full-data and leave-one-out predictions, leverage, residual variance, a studentization convention, and reference thresholds, Deleting an observation changes coefficients according to its residual and leverage; studentization makes the induced prediction change comparable across points., and type the carrier, state every parameter and convention in the definition, test that the diagnostic uses the same response and design with exactly observation i deleted and reports the selected internal or external variance convention, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions

Current abstraction DFFITS Domain-specific

Parents (1) — more general patterns this builds on

• DFFITS is a kind of Statistical Inference Prime

  The proposed strict upward parent is prime:statistical_inference.

Hierarchy paths (4) — routes to 4 parentless roots

• DFFITS → Statistical Inference → Inductive Reasoning

Show alternative paths (3)

Neighborhood in Abstraction Space

DFFITS sits in a crowded region of the domain-specific corpus (30^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Regression Diagnostics & Model Fit (9 abstractions)

Nearest neighbors

• Regression diagnostic — 0.92
• Regression analysis — 0.92
• Working–Hotelling procedure — 0.91
• Partial residual plot — 0.90
• Best linear unbiased prediction — 0.90

Computed from structural-signature embeddings · 2026-09-08