THE STRUCTURAL DIAGRAM
The Structural Analysis Division of Statistics Canada has in its development of various models evolved a "Structural Diagramming"
technique t h a t allows model development to be clearly partitioned into the design and implementation phases. The design phase culminates in a structural diagram of a model t h a t can be independently implemented.
The structural diagram also serves to uniquely define all parameters and relations t h a t constitutes a complete specification of the model. This aspect of t h e s t r u c t u r a l diagram makes i t eminently useful in delineat- ing generic models36 for process descriptions. Moreover, the structural diagram enables a systematic documentation of the definition and mean- ing of all variables associated with it. All generic models in t h e Process Enyclopedia a r e t h u s documented according to this structural diagram- ming technique and a description of t h a t technique is given herein.
Models use two fundamental concepts, variables and procedures.
Variables represent information about objects defined by the model and procedures represent t h e relationships between t h e objects taking the values of variables as input and producing new values of variables as out- put.
35 TAKEN FROM JICINNES AND PAGE, 1878.
38 For the purpose of this subsection we use the terms generic model and process model in- terchangably.
Variab Les
Variables m a y be divided i n t o two groups, those t h a t a r e c a l c u l a t e d by t h e model a n d those t h a t a r e not. This is t h e familiar distinction between endogenous a n d exogenous variables.
We distinguish two kinds of endogenous o r model d e t e r m i n e d vari- ables, those representing levels o r stocks such a s population o r capital stock a n d those representing flows s u c h a s GNP o r o t h e r information such a s p e r capita consumption.
A triangle is used t o r e p r e s e n t a n endogenous stock variable a n d a circle is used t o r e p r e s e n t a n endogenous flow variable.
s t o c k o r l e v e l endogenous v a r i a b l e
f l o w o r o t h e r endogenous v a r i a b l e
We also distinguish two kinds of exogenous or p r e d e t e r m i n e d infor- mation: p a r a m e t e r s a n d exogenous variables. The distinction between exogenous variables a n d p a r a m e t e r s is n o t c l e a r c u t ; nevertheless we feel
t h a t i t is a useful distinction. Exogenous variables often represent flows (occasionally parameters) and t h u s may be expected to change over time or a r e subject t o large variations. P a r a m e t e r s represent structural con- straints and may be expected to be stable or subject to moderate trends over time. To illustrate this point consider the equation which relates the area of a circle to its radius.
Given t h e exogenous variable r a n d t h e value of the constant pararn- e t e r t h e 'model' may be used t o calculate t h e value of the endogenous variable k
A horizontal line is used t o represent a parameter and a hexagon is used for an exogenous variable.
parameter
exogenous v a r i a b l e
Procedures
Procedures are represented as four sided figures. In addition t o t h e general form which is a rectangle, two special procedures are identified.
A rhombus is used t o represent the procedure aggregation: a parallelo- gram is used to represent a procedure which is not p a r t of t h e s t r u c t u r e of t h e model but is nevertheless part of t h e code of t h e model system.
Procedures for projecting exogenous variables fall into t h e category.
s t r u c t u r a l procedure
a g g r e g a t i o n procedure
exogenous procedure
Procedures are connected t o variables (and variables to procedures) by solid directional lines. These connecting lines a r e called relational flows and represent t h e use of a particular variable in a procedure or the definition of a variable by a procedure. For example, the 'model' t o
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171-
calculate t h e a r e a of a circle may be represented a s follows :
Procedural Flows
In addition to relational flows we define procedural flows which indicate flow of control. Procedural flows a r e represented by dashed lines which join procedure to procedure.
Thus, this s e g m e n t reads "do procedure 1 which defines variable A, t h e n do procedure 2 which defines variable B".
Where procedural flows and relational flows are t h e same, we have adopted t h e convention t h a t t h e procedural flows be omitted. For exam- ple in t h e s e g m e n t
t h e dashed line would be omitted. A special symbol, namely a diamond is used t o r e p r e s e n t branching.
Branching o c c u r s when control is passed t o one procedure o r t o a n o t h e r depending upon c r i t e r i a t h a t a r e endogenous to t h e model or a r e u s e r supplied. To illustrate t h e two permissible syntaxes for branch- ing consider t h e following examples:
This segment is an example of a model-determined or endogenous branch such as 'if A is equal t o or g r e a t e r than K, do procedure 1, if A is less than 1, do procedure 2.
Note t h a t the branching symbol is not a procedure which deEines a variable, r a t h e r i t is a procedure t h a t d e t e r m i n e s t h e flow of control.
Thus, relational flows may e n t e r the diamond, b u t only procedural flows may emerge.
The following sequence demonstrates an exogenous o r user- determined branch :
i I
This segment indicates t h a t the user m u s t choose e i t h e r option 1 or option 2 for determining A. The choice of option 1 implies t h a t procedure 1 will be used t o determine A a n d the choice of option 2 t h a t procedure 2 will be used.
The use of t h e ellipsis a n d the absence of relational flows into t h e diamond distinguish exogenous from endogenous branches.
a e c i u l S y m b o l s
Several additional symbols a r e needed t o complete t h e s e t . These a r e symbols t o r e p r e s e n t ' s t a r t ' , 'stop' and 'off-page connector'.
start
c 3
The off-page c o n n e c t o r s a r e u s e d a s follows:
p r o c .
0
This indicates t h a t variable A will be used in procedure 8 on page 4, a n d
indicates t h a t A has been defined by procedure 3 on page l.
By convention when connecting relational flows cross-page boun- daries the variable involved is r e p e a t e d on both pages. The off-page con- n e c t o r c a n also be u s e d t o c o n n e c t procedural flows.
lime Structure
For t h e purpose of documenting time-structured models we have adopted t h e convention of dropping time subscripts except where lead and lag relationships a r e involved. For example the equation
is r e p r e s e n t e d as:
b u t :
Time-varying parameters a r e distinguishable from parameters t h a t a r e invariant with respect t o time by placing a t t o t h e right of the horizon- tal line as follows :
VARIABLE AND PROCEDURE DOCUMENTATION
The structural diagrams are, of course, in themselves not complete model documentation: they must be complemented by information about procedures and about t h e variables t h a t a r e calculated by and used by the procedures.
The links between the structural diagrams a n d this information a r e variable and procedure names. Each variable a n d procedure is assigned a name which appears in the diagram.
The variable and procedure names a r e intended primarily to provide unique and abbreviated identifiers for each variable and procedure. A secondary objective is to convey sufhcient information about t h e vari- able o r procedure so t h a t the unique names c a n be assigned to new vari- ables or procedures without searching t h e e n t i r e list to determine whether the name is already in use.
The procedure names are used to reference t h e structural diagrams to the text which presents and explains the formula represented by t h e procedure. The variable names are the familiar 'mneumonics' which serve to label variables so that exogenous variables and parameters can
be assigned values a n d calculated variables c a n be analyzed a n d reported. The n a m e s assigned t o decisions (diamonds) a r e used i n t h e documentation of t h e available options.
A m a s t e r list of procedures is appended which contains t h e following information about procedures:
(i) procedure names;
(ii) n a m e s of variables e n t e r i n g or used in t h e procedure;
(iii) n a m e s of variables calculated or defined by t h e procedure;
(iv) procedure type - aggregation procedure o r other;
(v) English description, e.g., t h e function of t h e procedure (optional).
Analogously information about variables is appended in a m a s t e r list which consists of t h e following items:
(i) mneurnonic n a m e ;
(ii) dimension
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scalar, vector, matrix;(iii) if vector o r m a t r i x , t h e space in which t h e dimensions a r e defined a n d t h e t i t l e list for t h i s space;
(iv) variable t y p e
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exogenous endogenous, p a r a m e t e r . c o n s t a n t p a r a m e t e r ;(v) n a m e of t h e procedure which calculates o r defines t h e variable (if endogenous);
(vi) English language description of variable.
As an illustration of process model documentation using above out- lined s t r u c t u r a l diagramming technique s e e t h e example presented in Figure A-4-6 above.
A4-4: A REFERENCE
TO
S 0 E OTHER SOFTWARE TOOlS OF FELEXANCE TO THE EDSSThus, we have discussed t h e main EDSS tools, n a m e l y t h e documen- tation Language f o r the d e c i s i o n making cycLe r e p r e s e n t a t i o n (SADT for t h e "activigrams") in Chapter 3 a n d Appendix 3, the p r o c e s s i n f o m a t i o n s y s t e m , and t h e documentation Languages f o r p r o c e s s d e f i n i t i o n s ("topography" language) a n d for process m d e l d o c u m e n t a t i o n ((generic) process model s t r u c t u r e d documentation language). Also, we have t r i e d t o illustrate t h e l a t t e r ' s application for process descriptions by way of t h e study a r e a already u s e d t o illustrate t h e SADT "activigrams" docu- m e n t a t i o n language.
However, t h e EDSS will dispose OF o t h e r specific software tools t o
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(a) ease t h e s y s t e m a c c e s s t o t h e user and t o (b) provide linkage t o o t h e r formal EDP
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documentation tools for analysis a n d documentation of a particular task within t h e framework of a formal MIS system.Relating t o point (a) above we have s t a t e d i n t h e t e x t of t h i s paper t h e n e e d for a powerful, user-friendly n a t u r a l language data base m a n a g e m e n t system. However, we envisage t h e r e q u i r e m e n t for a n addi- tional tool to a s s i s t d e c i s i o n m a k e r s in the u n s t r u c t u r e d s e a r c h for d a t a in t h e intelligence phase of t h e decision making cycle. This tool shall allow t h e user to s c a n quickly t h e contents of t h e EDSS a n d enable h i m interactively t o filter o u t information, data, etc. The s y s t e m provides
t h u s a simplified form of a s y s t e m s thesaum.s and c a n be linked t o a for- mal detailed t h e s a u r u s once this becomes developed for t h e EDSS a n d for o t h e r d a t a files available. In relation t o the interactive d a t a filtering software we make reference t o t h e so-called TREE, hierarchical d a t a access and filtering software, developed a t IIASA (Medow, 1963).
The TREE system was designed t o simplify t h e process of interaction between t h e u s e r a n d t h e computer. More specifically, t o help t h e user in t h e filtering a n d linkage of d a t a with various types of models, both stored on computer. This is achieved first, by limiting t h e n u m b e r of actions or decisions on t h e user's p a r t in predefining access, filtering a n d display methods available to h i m a n d secondly by using a hierarchi- cal t r e e as m e t h o d of structurization a n d classification. At e a c h of t h e nodes of t h e t r e e s t r u c t u r e t h e u s e r m a y access and filter d a t a and link these to t h e p a r t i c u l a r model chosen (see Figure A-4-8).
The TREE program is constructed a s a non-binary t r e e relying on linked lists a n d a special search algorithm, providing t h e u s e r with a conversational form of access t o t h e c o m p u t e r a n d serving as a "tele- scope" which can b e directed t o t h e parts of a l a r g e r s t r u c t u r e , of i n t e r e s t t o t h e user.
The actual TREE software is in FORTRAN code in order t h a t i t is independent f r o m t h e particular DBMS used for normal data access. In relation t o t h e EDSS, a main feature a n d role of a software like TREE will not only be t o provide access t o d a t a (stored in t h e Resource Data Base of t h e Process Data Base of t h e EDSS) and models (process model d a t a base of t h e EDSS) but equally t o direct t h e u s e r and t o give him an overview of
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Figure A-4-8. Anillustration of t h e TREE structure.
the contents of t h e EDSS, allowing him to access d a t a separately or in a combined form (e.g., "paradigm" representations of all d a t a relative to a particular process stored in t h e Process Data Base, etc.).
Finally, we make some comments on t h e conceptual/practical equivalences between t h e EDSS documentation languages (SADT, the pro- cess topography, etc.) a n d t h e formal EDP documentation tools in use a t towards "efficient" software development, their conceptual equivalence t o t h e functional p a r t of formal EDP documentation tools like DAFNE is
Tools are a straightfornard function of the specifics of the proposed EDSS, however, for prac- tical reasons, the advantage of tools with which the user community is already remiliar is yp-ious.
Recall here the EDSS objective of improving the effectiveness (i.e., learning, understand- ing) of the user a s opposed t o improve his efficiency or the software efficiency of e ~ a r t i c u - lar EDSS configuration.
F ~ g u r e A-4-9. Examples of DAFNE functional analysis docurnen tation using SADT for a i r pollution project a t CSI.
use of t h e EDSS itself. Thus, t h e user's perception of t h e problem changes a n d evolves (creating t h e need for additional EDSS facilities), a s a result of his u s e r of "actual" EDSS facilities. Therefore, t h e r e is nothing like a final "most efficient" s y s t e m configuration resulting from t h a t type of careful functional analysis characteristic of t h e EDP field.
The second difference relates to t h e second component of t h e DAFNE methodology, t h e d a t a analysis in addition t o t h e functional analysis a n d i t s verification feedback on the l a t t e r . The CSI performs this by using t h e Entity Relationship model (Chen. 1976) as illustrated in Fig- ure A-4-10. In view, however, of t h e evolving n a t u r e of a p a r t i c u l a r task within t h e EDSS (e.g., introduction of u n s t r u c t u r e d information flows, or formalization of previously u n s t r u c t u r e d flows), n o t only t h e functional specifications on t h e s y s t e m evolve, but equally t h e resulting d a t a requirements. This in p a r t i c u l a r , is the case with d a t a developed a d hoc within a p a r t i c u l a r task (i.e., t h e contents of t h e Resource Data Base) and i t would be in c o n t r a s t t o t h e basic EDSS objectives t o impose on the user a p a r t i c u l a r view of data. Therefore t h e adaptive design a n d imple- mentation s t r a t e g y we advocate (if t h e system is t o be called a Decision Support System), h a s t o find its equivalence equally with r e s p e c t t o t h e data, a u s e r may, a d hoc, like t o integrate into t h e system. The EDSS should respond t o t h e user's view on how t h i s d a t a should be described and s t o r e d i n t h e s y s t e m . Data introduced into t h e EDSS within t h e framework of a long-term oriented activity, s u c h a s t h e EDSS process information s y s t e m can, on t h e o t h e r hand, well be described within the Entity-Relationship model in use a t CSI (recall h e r e t h e discussion of flow attributes, a topography "owning" a number of process models, etc. i n
Chapter 4 of this paper).
Figure A-4-10. Data analysis based on entity relationship approach for air pollution project a t CSI.
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