US GAAP taxonomy - Dimensional Modeling 1.2

In this discussion, we will consider the misconception that multiple dimensions (i.e., [Axes]) in combination can provide an aggregation (i.e., summation) or hierarchal specificity to a fact. Refer to the US GAAP taxonomy - Dimensional Modeling 1.0 posting on October 21, 2014 for background information.

There have been many discussions and statements by participants indicating that dimensions provide the ability to express numerical aggregation relationships and the modeling in the US GAAP taxonomy displays a belief that dimensions provide hierarchal organizational relationships (e.g., Segments [Axis], Subsegments [Axis]). Neither of these thoughts is correct. Numerical aggregation relationships may only be communicated by the summation-item relationship provided to items arranged in hierarchal fashion in the Calculation linkbase. Dimensions stand-alone; they are unique and independent. Dimensions intersect, but in accordance with the current Dimensions 1.0 specification, cannot be organized in a hierarchy.

To discuss this topic more fully, consider the following premises:

• XBRL is intended to provide comparable information.

• A fact once reported stands forever – no limitation to the data's persistence.

• A fact once reported cannot and should not change.

• The US GAAP taxonomy ("UGT") is dedicated to the proposition of creating a data set of financial statement information, prepared in accordance with US Generally Accepted Accounting Principles ("US GAAP"), reported by US publicly traded companies and other SEC registrants. The purpose of this data set is to improve the financial information usefulness to investors by providing standardized information that is consistent and comparable across periods and industries, which is electronically consumable and able to be processed through multiple media (individual databases, commercially available software programs, Excel, etc.).

• A dimension is each of the different aspects by which a fact may be characterized.

• Dimensions are orthogonal.

• Orthogonal, as defined by the first definition provided by Merriam-Webster (http://www.merriam-webster.com/dictionary/orthogonal) means intersecting or lying at right angles.

• For purposes of XBRL and, specifically, the UGT, dimensions being orthogonal means that each intersecting dimension is both independent and mutually exclusive.

• Independent means that no one dimension is dependent on another dimension; each dimension can exist alone and its meaning is not changed by intersection with another dimension.

• Mutually Exclusive, which is purposefully redundant, means that no one dimension should be subsumed by another dimension.

• Dimensions that are not both independent and mutually exclusive are NOT orthogonal.

• Dimensions should represent a common theme about which more detailed information is provided.

• The domain-member element provides the specific characteristic on the fact defined in an XBRL Table (i.e., Dimension = common theme, Member = specific characteristic or feature).

• Modeling dimensional structures that in combination are intended to provide hierarchal relationships or provide greater specificity in defining facts greatly diminishes the effectiveness and ability of the data to be consumed.

There are multiple facets to this discussion, which will be discussed one by one with examples and references to the UGT, which includes many instances of modeling that departs from the foregoing.

Mutually Exclusive
Assume the following two dimensions and structures exist:

Property, Plant and Equipment, Type [Axis]
	Property, Plant and Equipment, Type [Domain] - - The collection of all P,P&E [Members]
		Machinery and Equipment [Member]
Machinery and Equipment, Type [Axis]
	Machinery and Equipment, Type [Domain] - - The collection of all M&E [Members]
		Tools, Dies and Molds [Member]
		Transportation Equipment [Member]

• These two dimensions (i.e., [Axes]) are NOT orthogonal because they are not mutually exclusive.

  • Machinery & Equipment is a type of Property, Plant and Equipment. The Property, Plant and Equipment, Type [Axis] therefore subsumes the Machinery and Equipment, Type [Axis].

  • The common theme that is the Property, Plant and Equipment, Type [Axis] includes the Machinery and Equipment, Type [Axis].

  • If the [Members] placed on the Machinery and Equipment, Type [Axis] were to be placed on the Property, Plant and Equipment, Type [Axis], the fact being defined would not change.

  • The only [Member] on the Property, Plant and Equipment, Type [Axis] that the Machinery and Equipment, Type [Axis] can intersect with is the Machinery and Equipment [Member] - - another way to think about orthogonal is the ability for two dimensions to intersect with each other's [Members] without restriction.

  • The Machinery and Equipment, Type [Domain], which is the full set of [Members] on the Machinery and Equipment, Type [Axis] is a duplicate of the Machinery and Equipment [Member] on the Property, Plant and Equipment, Type [Axis].

When dimensions are NOT orthogonal, the [Members] should be nested in the Definition linkbase of the [extension] taxonomy under the [Member] on the more encompassing (e.g., general, subsuming) dimension. For example, how, in this case, the UGT is modeled:

Property, Plant and Equipment, Type [Axis]
	Property, Plant and Equipment, Type [Domain]
		Machinery and Equipment [Member]
			Tools, Dies and Molds [Member]
			Transportation Equipment [Member]

The Definition linkbase hierarchy (i.e., tree) explicitly communicates that the Machinery and Equipment [Member] contains the more detailed Tools, Dies and Molds [Member] and Transportation Equipment [Member]. This hierarchy is electronically navigable and can provide integral information when accessed by a consumer.

The nesting of [Members] does not explicitly communicate a summation relationship between the [Members] because that only can be provided by the summation-item relationship assigned to numeric primary concepts in the Calculation linkbase of the [extension] taxonomy. The nesting of [Members] does however imply a summation relationship of a numeric primary concept intersecting with each of the nested [Members].

Comparable
For purposes of discussion, assume the following:

Company #1 has sales only in the USA. Company #1's sales occur in five US States. Company #1 reports sales by geography and one of those geographies is California, in which Company #1 had $1mm of sales for the nine months ended September 30, 2014.

Company #1 structures its [extension] taxonomy as follows:

All States and Provinces [Axis]
	All States and Provinces {Domain] - - The collection of all State and Province [Members]
		California [Member]

Company #1 tags its $1mm of revenues derived from sales in California as follows:

●	Value	1,000,000
Primary concept (i.e., Line Item):
●	Standard label	Revenue, Net
●	Element name	SalesRevenueNet
Contextual information:
●	All States and Provinces [Axis]	California [Member]
●	Period	2014-01-01 to 2014-09-30
●	Unit of Measure	iso4217:USD
●	Decimals	-6
●	Entity Identifer	0000000001

Company #2 has both US and International sales. Company #2's US sales occur in multiple US States. Company #2 reports sales by geography and one of those geographies is California, in which Company #2 had $3mm of sales for the nine months ended September 30, 2014.

Company #2 structures its [extension] taxonomy as follows:

All Countries [Axis]
	All Countries [Domain] - - The collection of all Country [Members]
		United States [Member]
All States and Provinces [Axis]
	All States and Provinces {Domain]
		California [Member]

Company #2 tags its $3mm of revenues derived from sales in California as follows:

●	Value	3,000,000
Primary concept (i.e., Line Item):
●	Standard label	Revenue, Net
●	Element name	SalesRevenueNet
Contextual information:
●	All Countries [Axis]	United States [Member]
●	All States and Provinces [Axis]	California [Member]
●	Period	2014-01-01 to 2014-09-30
●	Unit of Measure	iso4217:USD
●	Decimals	-6
●	Entity Identifer	0000000002

Fact Summary:

	Value	Primary Concept	Dimensional Context	Dimensional Context	Period	Unit of Measure	Decimals	Entity Identifier
Company #1	1,000,000	SalesRevenueNet	All States and Provinces [Axis] = California [Member]		2014-01-01 to 2014-09-30	iso4217:USD	-6	0000000001
Company #2	3,000,000	SalesRevenueNet	All States and Provinces [Axis] = California [Member]	All Countries [Axis] = United States [Member]	2014-01-01 to 2014-09-30	iso4217:USD	-6	0000000002

Observations:

• Both Company #1 and Company #2 are reporting the same concept - - Revenues attributable to California.

• Since both companies are using the same UGT [standard taxonomy] concept, both facts should be identically tagged.

• Note that everything about the facts line-up, except the value and the Entity Identifier, which exceptions are expected and Company #2's additional dimensional context - - All Countries [Axis] = United States [Member] - - that is marked in red.

• Since both companies tagged their facts differently, the data is not comparable and cannot be analyzed until the data set is corrected by the individual consumer.

• The data set must be the same and not require independent correction prior to consumption for the data to be usable. The data set must be normalized for everyone to have the same basis point on which to layer his or her own assumptions. Data is standard; analyses (e.g., assumptions) are individual.

• Because States and Provinces are subsumed by Countries, the dimensions in the example above are NOT orthogonal.

• Because the dimensions are not orthogonal, the dimensions should be combined into a single common theme encompassing the primary characteristic by which the fact may be characterized.

• The common theme is geography, which is why the UGT provides a single Geographical [Axis].

• The proper [extension] taxonomy structure to have been used by Company #1 is:

Geographical [Axis]
	Geographical [Domain] - - The collection of all Geography [Members]
		California [Member]

• Which would have resulted in the fact being tagged as:

●	Value	1,000,000
Primary concept (i.e., Line Item):
●	Standard label	Revenue, Net
●	Element name	SalesRevenueNet
Contextual information:
●	Geographical [Axis]	California [Member]
●	Period	2014-01-01 to 2014-09-30
●	Unit of Measure	iso4217:USD
●	Decimals	-6
●	Entity Identifer	0000000001

• The proper [extension] taxonomy structure to have been used by Company #2 is:

Geographical [Axis]
	Geographical [Domain]
		United States [Member]
			California [Member]

• Which would have resulted in the fact being tagged as:

●	Value	3,000,000
Primary concept (i.e., Line Item):
●	Standard label	Revenue, Net
●	Element name	SalesRevenueNet
Contextual information:
●	Geographical [Axis]	California [Member]
●	Period	2014-01-01 to 2014-09-30
●	Unit of Measure	iso4217:USD
●	Decimals	-6
●	Entity Identifer	0000000002

Fact Summary:

	Value	Primary Concept	Dimensional Context	Period	Unit of Measure	Decimals	Entity Identifier
Company #1	1,000,000	SalesRevenueNet	Geographical [Axis] = California [Member]	2014-01-01 to 2014-09-30	iso4217:USD	-6	0000000001
Company #2	3,000,000	SalesRevenueNet	Geographical [Axis] = California [Member]	2014-01-01 to 2014-09-30	iso4217:USD	-6	0000000002

Notice how by properly using the more general Geographical [Axis] and properly nesting the [Members], as opposed to attempting to provide specificity on the fact by using the combination of two dimensions that are NOT mutually exclusive (i.e., orthogonal), the facts are now comparable and electronically communicate exactly what both Company #1 and Company #2 reported.

A consumer can navigate the Definition linkbase hierarchy provided in Company #2's extension taxonomy and understand that Company #2 is communicating that California [Member] is contained within Untied States [Member], but the facts for both Company #1 and Company#2 are now identically reported and therefore comparable.

Additionally, note that we can humanely read the element names above and impute that the All Countries [Axis] takes hierarchal precedence over the All States and Provinces [Axis], but a machine cannot make this distinction unless programmed to do so. Making it incumbent on the consumer to program a hierarchal order of precedence for UGT (i.e., standard taxonomy) dimensions is inappropriate and inefficient. It is inappropriate because there is no hierarchal relationship between dimensions and it makes each individual consumer complete the standard data set in order to consume it - - not a standard. It is inefficient because it places additional cost and burden on the consumer.

Consistent
For this discussion, we will use Graham Holdings Company's (formerly, The Washington Post Company) Form 10-Q as of and for the quarter ended September 30, 2014 that was filed on November 5, 2014.

In footnote 13. BUSINESS SEGMENTS of its printed, published [HTML] financial statements, Graham Holdings Company states "The Company has six reportable segments: Kaplan Higher Education, Kaplan Test Preparation, Kaplan International, cable, television broadcasting and other businesses."

Graham Holdings Company then formats footnote 13. BUSINESS SEGMENTS in two parts. The first part presents one division Education (an aggregation of its Kaplan segments for PRESENTATION purposes) and three segments consisting of Cable, Television Broadcasting, and Other Businesses. The second part reports the reportable business segments that comprise the Education division, which consist of Kaplan Higher Education, Kaplan Test Preparation ("Test Preparation"), and Kaplan International. Graham Holdings Company prefaces the second part of the BUSINESS SEGMENTS disclosure as "The Company’s education division comprises the following operating segments".

Observations:

• XBRL is about tagging the DATA, NOT the PRESENTATION.

• US GAAP defines operating segments and when separate information must be reported for those operating segments (see Accounting Standards Codification ("ASC") Topic 280 and 280-10-50-10).

• US GAAP addresses the aggregation of operating segments for reporting of segment information (see ASC 280-10-50-11).

• US GAAP does not address nor mention operating divisions, nor the aggregation of separately reportable segment information for financial statement presentation purposes.

• The education division is aggregated for financial statement presentation purposes because organizationally the Kaplan entities are held by a holding company that in turn is consolidated by Graham Holdings Company - - a consolidation within a consolidation.

• Graham Holdings Company could have formatted the presentation of its HTML BUSINESS SEGMENTS financial statement disclosure in a single contiguous table combining all holding company and elimination values, but likely chose to present the printed information in two parts to more closely align with its legal structure and facilitate human readability.

• For presentation purposes, Graham Holdings Company could have aggregated Cable and Television Broadcasting into Media Operations, since that is how they refer to their operations (see footnote disclosure 1. ORGANIZATION, BASIS OF PRESENTATION AND RECENT ACCOUNTING PRONOUNCEMENTS of the Form 10-Q noted above), but likely chose not to since these operations are directly owned by the reporting entity (i.e., no subsidiary consolidation required).

Graham Holdings Company tagged $234,010,000 of operating revenues of the Test Preparation segment for the nine months ended September 30, 2014 as:

●	Value	234,010,000
Primary concept (i.e., Line Item):
●	Standard label	Revenues
●	Element name	Revenues
Contextual information:
●	Consolidation Items [Axis]	Operating Segments [Member]
●	Segments [Axis]	Education [Member]
●	Subsegments [Axis]	Test Preparation [Member]
●	Subsegments Consolidation Items [Axis]	Reportable Subsegments [Member]
●	Period	2014-01-01 to 2014-09-30
●	Unit of Measure	iso4217:USD
●	Decimals	-3
●	Entity Identifer	0000104889

In the future, if Graham Holdings Company decides to restructure the PRESENTATION of the printed, published [HTML] financial statement BUSINESS SEGMENTS disclosure to only report the operating segments, combine all holding company corporate and other amounts, and combine all elimination amounts, the $234,010,000 of operating revenues of the Test Preparation segment for the nine months ended September 30, 2014 would be tagged as:

●	Value	234,010,000
Primary concept (i.e., Line Item):
●	Standard label	Revenues
●	Element name	Revenues
Contextual information:
●	Consolidation Items [Axis]	Operating Segments [Member]
●	Segments [Axis]	Test Preparation [Member]
●	Period	2014-01-01 to 2014-09-30
●	Unit of Measure	iso4217:USD
●	Decimals	-3
●	Entity Identifer	0000104889

Fact Summary:

	Value	Primary Concept	Dimensional Context	Dimensional Context	Dimensional Context	Dimensional Context	Period	Unit of Measure	Decimals	Entity Identifier
Current Presentation	234,010,000	Revenues	Segments [Axis] = Education [Member]	Subsegments [Axis] = Test Preparation [Member]	Consolidation Items [Axis] = Operating Segments [Member]	Subsegments Consolidation Items [Axis] = Reportable Subsegments [Member]	2014-01-01 to 2014-09-30	iso4217:USD	-3	0000104889
Future Presentation	234,010,000	Revenues	Segments [Axis] = Test Preparation [Member]		Consolidation Items [Axis] = Operating Segments [Member]		2014-01-01 to 2014-09-30	iso4217:USD	-3	0000104889

Strikingly, take note that the UGT is leading Graham Holdings Company to tag its PRESENTATION, not its DATA (see Current Presentation in the Fact Summary above).

Note that the only thing that has changed is how Graham Holdings Company could change the presentation of the financial statement disclosure in printed form. Due to the UGT model provided, there now would exist two facts in the public data set that represent a single fact, yet there is no way to make that determination automatically and programmatically.

Observations:

• The Segments [Axis] subsumes the Subsegments [Axis] and, because these are not mutually exclusive dimensions, should therefore be combined into the Segments [Axis].

• The Consolidation Items [Axis] subsumes the Subsegments Consolidation Items [Axis] and, because these are not mutually exclusive dimensions, should therefore be combined into the Consolidation Items [Axis].

• Any time the prefix "SUB" is attached to a word, it is a strong indication that the "SUB" component is contained within the larger "non-SUB" component.

• The $234,010,000 of Current Presentation Revenues qualified by the Segments [Axis] = Education [Member] is inappropriate because by Graham Holdings Company's own financial statement representation it only has six reportable segments and the "education division" is not one of the six. The existing taxonomy model is encouraging an invalid [Member] (i.e., not a reportable segment) on the Segments [Axis], which is a data quality issue affecting consumption.

• Note that the UGT defines:

  • Operating Segments [Member] as "Identifies components of an entity that engage in business activities from which they may earn revenue and incur expenses, including transactions with other components of the same entity."

  • Reportable Subsegments [Member] as "Identifies division of a component of an entity that engage in business activities from which they may earn revenue and incur expenses, including transactions with other components of the same entity."

  • US GAAP does not refer to a "reportable division". In fact, US GAAP uses the word "division" as a means to distinguish between a component of a public company that is clearly an operating segment and a component of a public company that possibly is not an operating segment (see ASC 280-10-55-3 to 55-5). US GAAP does not imply that a division is subsumed or subsumes an operating segment.

  • The Operating Segments [Member] and Reportable Subsegments [Member] substantively have the same definition, which is another strong indication that there is a problem with the dimensional model provided in the UGT.

• Due to the dimensional model provided, a change in presentation changes the fact. This duplication of a fact in the data set does not achieve consistency, which is a primary benefit and intention of XBRL. The model ignores the underlying premise that a fact once reported cannot and should not change.

Had Graham Holdings Company modeled its [extension] taxonomy nesting the [Members] on the more inclusive Segments [Axis] and Consolidation Items [Axis] as follows:

Segments [Axis]
	Segments [Domain]
		Education [Member]
			Test Preparation [Member]
Consolidation Items [Axis]
	Consolidation Items [Domain]
		Operating Segments [Member]

and in the future modified its HTML financial statement presentation as described above, changing its [extension] taxonomy to:

Segments [Axis]
	Segments [Domain]
		Test Preparation [Member]
Consolidation Items [Axis]
	Consolidation Items [Domain]
		Operating Segments [Member]

In both Instances, the $234,010,000 of operating revenues of the Test Preparation segment for the nine months ended September 30, 2014 would be tagged as:

Fact Summary:

	Value	Primary Concept	Dimensional Context	Dimensional Context	Period	Unit of Measure	Decimals	Entity Identifier
Current Presentation	234,010,000	Revenues	Segments [Axis] = Test Preparation [Member]	Consolidation Items [Axis] = Operating Segments [Member]	2014-01-01 to 2014-09-30	iso4217:USD	-3	0000104889
Future Presentation	234,010,000	Revenues	Segments [Axis] = Test Preparation [Member]	Consolidation Items [Axis] = Operating Segments [Member]	2014-01-01 to 2014-09-30	iso4217:USD	-3	0000104889

Note that the current and future fact now exactly line-up. By nesting the [Members] on the more inclusive dimension, as opposed to trying to use a combination of dimensions that are NOT orthogonal in an attempt to provide a hierarchal relationship, the XBRL premise that a fact once reported should not and cannot change and that a fact once reported stands forever is achieved.

Observations:

• Modeling dimensions that are NOT orthogonal and attempting to combine them to properly define and communicate facts diminishes the consistency of the data.

• If dimensions are NOT orthogonal, nesting the [Members] on a single, more inclusive dimension (i.e., common theme) in a Definition linkbase hierarchy, communicates the relationship of the [Members] one to the other without diminishing the consistency or quality of the data.

• Graham Holdings Company employed the modeling in the UGT as published and followed the UGT Implementation Guide Version 2.1 June 2014 Segment Reporting ("Implementation Guide"), with the exception that the Consolidation Items [Axis] with the Operating Segments [Member] should not have been applied to the $234,010,000 of revenues qualified by (i.e., intersecting with) the Test Preparation [Member].

  • The Implementation Guide would indicate that the Consolidation Items [Axis] with the Operating Segments [Member] should only be applied to the aggregation for PRESENTATION purposes of the revenues for the education division of Graham Holdings Company.

  • There are multiple problems with this, as aforementioned, but it demonstrates the convoluted nature of the model when NOT orthogonal dimensions are combined in an attempt to provide hierarchal specificity or summation relationships.

• If the UGT were modeled so that dimensions were orthogonal (i.e., independent and mutually exclusive), then Graham Holdings Company would have nested the [Members] as indicated above, thereby achieving the goal of consistency, as well as the other desired characteristics of the XBRL US public company data set.

Alternatives:

• Dimensional Hierarchy

  • Dimensions are not hierarchal, but if it is desired to provide some inference as to the hierarchal order of precedence of dimensions or that one dimension subsumes another dimension, a general-special relationship could be provided.

  • The general-special relationship could be provided in the UGT, so that it is transparent to the financial statement issuer, but programmatically available to the consumer.

  • The financial statement issuer would need to be aware of the general-special relationship, as all relationships are important to understanding the nature and intended implementation of standard taxonomy dimensional concepts (or any UGT concept).

  • For extended dimensions, the financial statement issuer would need to provide the general-special relationship for the source (i.e., subsuming) and target (i.e., subsumed) dimensions, as appropriate.

  • This is another task for which the financial statement issuer would be responsible.

  • Every additional task for which the financial statement issuer is responsible increases the degree of difficulty of creating the [extension] taxonomy and introduces greater potential for human error.

  • Dimensions do not provide hierarchal relationships and introducing another task is neither cost-effective nor guaranteed to improve the quality of the data.

• Aggregation (summation)

  • Dimensions do not and cannot provide summation relationships.

  • Definition linkbase hierarchies consisting of [Members] nested within [Members] on a given dimension do imply that the domain-member child roles up into the domain-member parent.

  • If it were desired to explicitly communicate that a numerical concept (i.e., Line Item) intersecting with domain-members on a given dimension are intended to roll-up, then a label role could be used to communicate such intention.

  • An Axis Roll Up label role could be added to the UGT or extended dimension concepts to communicate that the [Members] intersecting with a  numerical concept in an XBRL table is intended to sum. For example, facts in an Instance tagged with the Revenues Line Item intersecting with the Geographical [Axis] and each of the fifty US States [Members] nested under the US [Member] with the Axis Roll Up label role on the Geographical [Axis] would communicate that each of the US State [Member] Revenues aggregates to total US [Member] Revenues.

  • This is another task for which the financial statement issuer would be responsible.

  • Every additional task for which the financial statement issuer is responsible increases the degree of difficulty of creating the [extension] taxonomy and introduces greater potential for human error.

  • Dimensions do not provide summation relationships and, introducing another task is not cost-effective; although something like an Axis Roll Up label role could improve the analytical quality of the data.

Conclusion
Dimensions should be orthogonal (i.e., independent and mutually exclusive). If dimensions are NOT orthogonal, then, in the Definition linkbase, the domain-member elements (i.e., [Domains], [Members]) should be nested under one another to form hierarchal relationships on the more inclusive dimension. Dimensions should not be used to provide specificity, which is the purpose of [Members] (i.e., each of the possible (specific) characteristics or features by which a fact may be qualified (defined)). The UGT should be corrected to rationalize redundant dimensions and dimensions that are subsumed by other dimensions, in order to achieve comparability and consistency of the public data set.

It brings to mind an automobile from the 1970s to the 1980s, which was the basis for a movie starring Gene Hackman. In the movie, the automobile was prone to exploding in flames if hit in the rear while engaging the left turn signal. What if the manufacturer had inserted instructions in the owner's manual (e.g., Implementation Guide) that stated "Avoid using left turn signal because doing so while being rear ended may result in grave bodily harm." Most, if not all, of us would find the manufacturer's actions wholly inadequate. The lesson: No degree of instructions corrects bad design.