The Foundations Department as a Dependency Map

Seventeen entries, eighteen dependencies, and the structures they define

Foundations
ontology
knowledge base
An engineering drawing of the Journal’s Foundations entries (Vol. 1 Nos. 1–2): which entry depends on which, and where each concept is defined, generated from the department’s knowledge base.
Author

William Bert Craytor

Published

October 5, 2026

Working paper · not peer reviewed

The Foundations department of the Valuation Engineer Journal now holds seventeen entries across two issues, and they are not independent: an entry on endogeneity assumes the reader has the conditional expectation function; the basis of value assumes the purposes of valuation; terminological divergence assumes both the scheme and the basis of value. The department’s knowledge base records these dependencies as facts — depends_on/2 and related/2 — and each entry’s cross-references repeat them in prose. This page draws the facts.

The drawing is generated, not hand-made: a script reads every entry’s number, title, version and DOI from its source, reads the dependency facts from the knowledge base, and lays the result out as an engineering sheet. When Issue 3’s entries are added, the sheet is redrawn by running the script again. A dependency that names a concept with no entry of its own is reported in the audit box at the foot of the sheet rather than drawn; at the time of writing there are none.

How to read the sheet

  • Blocks are entries, in three columns: Issue 1’s hedonic vocabulary; Issue 2’s statistical ladder, with the MARS supplement beside it; and Issue 2’s four legal-conceptual entries. Each block shows the entry’s number and version; its DOI appears on hover.
  • Solid arrows mean depends on: the entry at the tail uses vocabulary the entry at the head establishes, so read the head first.
  • Dashed arrows mean related: a concept the entry discusses without depending on it. Related concepts that have no entry of their own (multicollinearity, instrumental variable, mass appraisal, …) are listed in small type under the block that refers to them.
  • Click a block to light its wiring and list, beneath the drawing, what it depends on, what depends on it, and its related concepts. Press Esc to clear.
  • The parts list below the drawing is the concept ontology: the structures the entries define — the classification of practice, the price decomposition, condition and the remodel, confounder and mediator, the residual and the Journal’s method, the scheme and the value effect — each with the entry that owns the definition and the entries that use it.

Foundations — dependency map and concept ontology

The Valuation Engineer Journal · Foundations, Vol. 1 Nos. 1–2
drawn from the knowledge base: 18 dependencies, 17 relations, 17 entries
sheet 1 of 1 · generated by scripts/foundations-graph.py
depends on (read that entry first)related conceptselected entry and its wiringclick or focus a block; Esc clears
Issue 1 — the hedonic vocabularyIssue 2 — the statistical ladderIssue 2 — the legal-conceptual fourThe Basis of Value and the Approach depends on The Scheme, and Effects on ValueThe Basis of Value and the Approach depends on The Purposes of ValuationCharacteristics Space depends on Heterogeneous GoodConditional Expectation depends on Hedonic RegressionEndogeneity depends on Conditional ExpectationEndogeneity depends on Omitted Variable BiasHedonic Price Function depends on Characteristics SpaceHedonic Price Function depends on Heterogeneous GoodHedonic Regression depends on Hedonic Price FunctionHedonic Regression depends on Implicit PriceParameter Identification depends on Conditional ExpectationParameter Identification depends on EndogeneityImplicit Price depends on Hedonic Price FunctionLatent Variable depends on Characteristics SpaceOmitted Variable Bias depends on Conditional ExpectationOmitted Variable Bias depends on Hedonic RegressionOmitted Variable Bias depends on Implicit PriceTerminological Divergence depends on The Basis of Value and the Approach001 · v1.0.0Heterogeneous GoodHeterogeneous Good — Vol. 1 No. 1, DOI 10.67330/s1scsv65002 · v1.0.0Characteristics SpaceCharacteristics Space — Vol. 1 No. 1, DOI 10.67330/3yymh010003 · v1.0.0Hedonic Price FunctionHedonic Price Function — Vol. 1 No. 1, DOI 10.67330/9x1a0489004 · v1.0.0Implicit PriceImplicit Price — Vol. 1 No. 1, DOI 10.67330/md6wke17related: marginal value, sales comparison adjustment005 · v1.0.0Hedonic RegressionHedonic Regression — Vol. 1 No. 1, DOI 10.67330/ams1t139related: automated valuation model, mass appraisal006 · v1.0.0Latent VariableLatent Variable — Vol. 1 No. 1, DOI 10.67330/11n3g168related: proxy variable, residual signal, unobserved heterogeneity001 · v1.1.0The Barrier to Human Understanding of MAThe Barrier to Human Understanding of MARS — Vol. 1 No. 2, DOI 10.67330/qmnctv78007 · v1.1.0Conditional ExpectationConditional Expectation — Vol. 1 No. 2, DOI 10.67330/99hhbc69related: ordinary least squares, residual008 · v1.1.0Omitted Variable BiasOmitted Variable Bias — Vol. 1 No. 2, DOI 10.67330/460smg10related: adjustment, comp selection, multicollinearity009 · v1.1.0EndogeneityEndogeneity — Vol. 1 No. 2, DOI 10.67330/z9feps66related: instrumental variable, selection bias, simultaneity010 · v1.1.0Parameter IdentificationParameter Identification — Vol. 1 No. 2, DOI 10.67330/xjszh949related: falsifiability, robustness011 · v1.0.0The Scheme, and Effects on ValueThe Scheme, and Effects on Value — Vol. 1 No. 2, DOI 10.67330/30ncvp43012 · v1.1.0The Purposes of ValuationThe Purposes of Valuation — Vol. 1 No. 2, DOI 10.67330/g9knsr34013 · v1.1.0Terminological DivergenceTerminological Divergence — Vol. 1 No. 2, DOI 10.67330/symwrt78014 · v1.1.0The Basis of Value and the ApproachThe Basis of Value and the Approach — Vol. 1 No. 2, DOI 10.67330/jp7pr043
Select an entry to see what it depends on, what depends on it, and the structures it defines.

Classification of practice (012)

  1. Purpose — why the valuation is needed (eight purposes)
  2. settled together, in no fixed order: property interest · governing law · basis of value
  3. Methodology — how the figure is reached

defined in 012 The Purposes of Valuation; used by 014 The Basis of Value and the Approach, 011 The Scheme, and Effects on Value, 013 Terminological Divergence

What a regression estimates (007)

  1. P = E[P | Z] + ε, E[ε | Z] = 0 always (the CEF and its deviation)
  2. u = P − fitted equation: the structural error, which may move with the regressors
  3. rate = slope of the CEF in one feature; adjustment = contribution difference

defined in 007 Conditional Expectation; used by 008 Omitted Variable Bias, 009 Endogeneity, 010 Parameter Identification, 001 The Barrier to Human Understanding of MARS

Condition, score and remodel (008)

  1. Condition — a state of the house (latent)
  2. Condition score — its estimate, 0.00–10.00: share of the market area in worse condition
  3. Remodel — an event; its value is the condition and quality it produced

defined in 008 Omitted Variable Bias; used by 009 Endogeneity, 010 Parameter Identification, 006 Latent Variable

Which variables to hold fixed (009)

  1. Confounder — causes both regressor and price → hold fixed
  2. Mediator — the channel from regressor to price → do not hold fixed for the total effect
  3. Treatment — any intervention asked about; a remodel is one, not randomly assigned

defined in 009 Endogeneity; used by 010 Parameter Identification

Residual and the Journal's method (006, RCA)

  1. Regression on measured features only; residual ≈ 20 % in a California market
  2. Latent contributions (condition, quality, …) assigned by the appraiser, summing to the residual
  3. Proof II: how the residual is divided does not change the value conclusion

defined in 006 Latent Variable; used by 007 Conditional Expectation, 008 Omitted Variable Bias

The scheme and its effect on value (011 → 013)

  1. Scheme / project — the undertaking whose effect on value is disregarded
  2. Value effect — a counterfactual quantity; law fixes the form, a tribunal its extent
  3. Directional pair — increase / decrease named separately; verb in Russian; none in China (surveyed)

defined in 011 The Scheme, and Effects on Value; used by 013 Terminological Divergence, 012 The Purposes of Valuation, 014 The Basis of Value and the Approach

Audit — dependencies naming a concept without an entry (drawn nowhere):
  • none — every dependency names an entry

What the sheet shows

Three things are easier to see drawn than read.

First, the department has a spine. Everything in Issue 2’s statistical ladder descends from Conditional Expectation (007), and everything in Issue 1 descends from Heterogeneous Good (001) through Characteristics Space (002); the two spines meet at Hedonic Regression (005), on which both Conditional Expectation and Omitted Variable Bias depend. A reader new to the department can follow the solid arrows backwards from any entry to the two or three it rests on.

Second, the legal-conceptual four are wired differently from the statistical four. The ladder is a chain, each entry depending on the one before; the four of the second movement form a small web around The Basis of Value and the Approach (014), which depends on both The Scheme (011) and The Purposes of Valuation (012), and on which Terminological Divergence (013) depends in turn. That is why a change to 012’s classification, as in its version 1.1.0, had to be carried into 014 and the Overview.

Third, the parts list shows where a term is owned. Condition is defined in Omitted Variable Bias (008) and used by Endogeneity and Identification; confounder and mediator are defined in Endogeneity (009) and used by Identification; the residual and the rule that its division does not change the value conclusion belong to Latent Variable (006) and the RCA paper, and are used by 007 and 008. An entry that uses a term it does not own should cite the owner, and the sheet makes the omissions visible.

Source

The generator is scripts/foundations-graph.py in the Journal’s publishing repository; it writes this page’s drawing (graph.html) and a standalone sheet. The facts it draws are the ones the entries’ Prolog companions are tested against, so the drawing and the department’s machine-checkable claims cannot drift apart.