Use of Models
Contents
What is a Model? - Defining (and Classifying) Models
Harper and Lim define the essence of a model thus:
a device that reflects the workings of the real-world
where the word "device" is used metaphorically to mean a "way of thinking" or "conceptual scheme" (and not literally to mean a contrived physical mechanism). Mitchell identifies two concepts of model:
1) the idea of a model as a device 2) the idea of a model as a statement of beliefs (about the modelled reality)
Striving to be philosophically precise in Chapter 7 - "The Notion Of Model" of "Enterprise Onotology", Jan Dietz quotes the Apostel definition of a model:
Any subject using a system A that is neither directly, nor indirectly interacting with a system B, to obtain information about the system B, is using A as a model for B.
It is in this sense that biologists use the term "model" to refer to individuals of one species exhibiting a disease (System A - e.g. Ovarian cancer in the Mouse) as a 'model' of individuals in another species exhibiting the same disease (System B - Ovarian cancer in the Human). This allows the researchers to perform experiments on the model to gain information (and hence understanding) on System B in order to take actions to change (including disrupting or suppressing) the behaviours of System B (possibly even curing the disease). Such experiments, even if ethical, would not be an efficient way of obtaining the information were it not for the model.
Generally, however, models will be less physical models and more symbolic models that accord with the conventions of human communication and model-making for the field.
Common to all "models", however, is an association between elements of System A (the modelled system) with elements of System B (the modelling system).
For a physical model the association may be one of "similarity" in some sense with perhaps variation in scale - hence model cars, model aeroplanes or models of machines in general.
For symbolic models, the association is between an element in the "real world" (which may be any of World 1, World 2 or World 3 in STREAMS Philosophy but will usually be either World 1 or World 3) and a symbol in the "model world". The classic example of a symbolic model with a 1-to-1 correspondence with "real-world" is the map - which may have an arbitrary scale relationship (association) with the "real world". Maps, and symbolic models however, may not be topographically accurate - merely topologically (as with the London Underground map) - and may show on the map only a small fraction of the many relationships between any two elements in the "real world".
With mathematical models real-world entities or properties are associated with variables in an equation - and the mathematical relationship(s) between the variables mirrors and models the relationships between the real-world entities. [In a similar way to which topological or topographic relationships between real-world entities and represented by similar relationships between symbols on the map (for map-like symbolic models).
Classifying Models
Harper and Lim's Model Taxonomy
Harper and Lim offer the following classificatory scheme (or multidimensional Taxonomy) for models, from Operational Research:
Models Classified by Form Of Representation
- Iconic - in which the modelled entities are represented by (and associated with) modelling entities that resemble (in some sense) them. So, for example, in working out the disposition of cars during a police operation, model cars might be used to represent the real ones.
- Analogue - in which some properties of the (entities of) the modelled system are represented by some property of the modelling system. An example might be where the height of an object (or other coordinate) is represented by a voltage in an analogue computer Biological models are examples of analogue models.
- Symbolic - in which the real world entities are represented by (mathematical) symbols. Symbolic models may be subdivided into two subcategories: qualitative and quantitative. Qualitative models indicate and illustrate some relationships between the real-world entities but make no attempt to quantify the relationships. Quantitative models describe the relationships in quantitative terms - and are usually what people mean when they refer to "mathematical models". The models produced by the various forms on Network Analysis are symbolic models and may be mathematical models.
Models Classified by Function
The function referred to here is the function of the model - what it is the model is intended to do.
- Predictive - where the model is used to predict a future reality (whether that reality is in fact realized or not).
- Evaluative - where the model is used to discriminate between alternatives (including possible "null alternatives") and evaluate them in a structured and rational 'judgement' as to which is the best option or better options. Strategic Scenario Planning may be considered a form of evaluative model-making.
- Optimising - in which the model is used to select the optimum conditions, configuration or actions.
Models Classified by the Characteristics of the Modelled Reality
Rather than being discrete categories these classificatory factors are more "spectrums of possibilities" along different dimensions:
- Deterministic -vs- Stochastic - in which any reasonably complex real-world (modelled) system can be selectively modelled as a more deterministic or stochastic model. A deterministic model is one where the transitions in the model certainly happen or do not (ie with probability of 1 or 0) as causal conditions change whereas a stochastic model is one in which the transitions and outcomes have intermediate probabilities. Clearly more deterministic real-world systems should be modelled by deterministic models and stochastic real-world systems by stochastic ones. Many real-world systems exhibit both deterministic and stochastic properties or behaviours.
- Static -vs- Dynamic - in which any reasonably complex real-world (modelled) system can be selectively modelled as a more static or dynamic model. A static model is one where there is no time-sequence of change within the model - and hence applied to "snapshots" of the real-world system at arbitrary times - whereas a dynamic model is one in which the time-sequence, change and evolution of the system is included in the model. Clearly more static (unchanging in time) real-world systems should be modelled by static models and dynamic real-world systems by dynamicones. Many real-world systems exhibit both static and dynamic properties or behaviours - and the choice of what is considered dynamic (short timescale) or static (log timescale) is situation of context dependent.
The above categories of model are not disjunctive or mutually exclusive but form a four-dimensional taxonomical space; any particular model can at once be, for example, Symbolic, Predictive, Deterministic and Dynamic - as are most of the models in Physics.
Mitchell's Model Taxonomy
Mitchell offers a similar Operational Research scheme based on a number of 'dimensions' for model characteristics:
- Dimension 1: Abstraction - "the endpoints of this dimension are actual[ity] and abstract" or 'concrete' and 'abstract'. This is the degree of abstraction in the model - and is similar to the notion of abstraction levels in Enterprise Architecture - e.g. the "Conceptual-Logical-Physical" abstraction scheme or Zachman's implicit six levels. Unlike most EA thinking, however, Mithcell considers abstraction to be not distinct, disjoint, discrete categories - but a matter of degree depending on the concepts employed - ie a large number of levels. STREAMS follows Mitchell and considers most EA thinking to be naive and simplistic in assuming or forcing models to have only a small number of abstraction levels. STREAMS admits models with as many levels of abstraction as is necessary to accurately and precisely express the concepts and beliefs in the model.
- Dimension2: Detail and Purpose - is not so much a single dimension as a 'subspace' of related model characteristics:
- Structural (White Box) -vs- Black Box - the number of components and relationships included in the model - where a 'Black Box' model has zero components (only inputs and outputs) modelled and a 'White Box' model has many or all the components and relationships modelled. (See also the discussion of White Box and Black Box models below.)
- Predictive -vs- Exploratory - a predictive model is intended to predict behaviours and outcomes accurately and precisely - and is therefore more likely to be quantitative - whereas an exploratory model is one constructed to understand the behaviour of the modelled reality in qualitative terms.
- Instrumental -vs- Realistic - and instrumental model models reality at a phenomenonological level - which means to say no-one understands the behaviour of the model or the reality modelled but the model clearly describes the behaviour of the reality. In contrast a realistic model is one underpinned by theory and the model reflects reality because the theory behind the model represents a good understanding of the reality.
- Micro - vs- Macro - where macro models exhibit the gross, large scale features of large, complex realities and keep all the details implicit whereas micro models represent the detailed view of the fundamental, atomic components. Economic models provide a useful example where macro-level models focus on the behaviours of whole countries or industries and markets and focus on large-scale aggregative measures like interest rates, growth figures, market prices, national debts and inflation whereas micro level models focus on individual transactions and small-scale exchanges of goods, services and money in the economy. In general the macro should emerge from the micro.
- Detailed -vs- Detail-free - in which the level of detail of the reality to be included in the model is consciously chosen in accordance with the purpose of the model. Modelling in detail is a time-consuming and expensive activity - and one of the mistakes of enterprise architecture practice is to model in detail (because the methodology says so?) when it is not necessary.
- Dimension 3: Abstraction - varies from standard to purpose-built. A standard model is a common, ordinary, well-known model that is used for a number of purposes, or to address a number of problems or decisions, and may have been constructed elsewhere and earlier. "Patterns" and "Reference Models" may be considered "standard models". The term "Standard Model" of course refers to the standard model of the fundamental particles and forces in Physics - and is a standard model. A custom, bespoke or purpose-built model is a model constructed to address a particular problem or understand a particular system - that has not been 'seen' elsewhere and is not addressed by any standard model.
- Dimension 4: Absolute -vs- Relative An absolute, or universal model is one that is valid anywhere and anywhen, in any situation. It may of course not be relevant but it is valid. A relative model is one that is "situation dependent" - ie one that is relative to the conditions of the context of the modelled system. Hence relative models apply to specific locales or localities - including at specific times (and not others). The contextual conditions to which the model is relative may be specified as assumptions within the model.
- Dimension 5: Action Orientation is again more of a subspace of related dimensions than a single dimension.
- Passive -vs- Normative A passive model incorporates no value-judgments or beliefs and merely deductively produces its output data from the input data according to the construction of the model. A passive model is oriented towards hypothesis making and testing - what-if scenarios - and is a tool for working out the logical implications of the input conditions. A normative model - in this sense - is one that does embody and embed value-judgments and beliefs and may be used to suggest or select "optimising" actions or constrain actions with negative consequences. An example of a normative model might be a software selection decision model - to select "the best" software available according to a set of criteria (including perhaps price/cost) that embody judgements as to what is "good".
- Passive -vs- Behavioural In this aspect, passive means the model embodies no beliefs about how people will behave or react, whereas "behavioral" will make some assumptions about how people or groups of people behave in the model. Such models may be used in policy-making and embody models of "systems of power" - or what Jackson called "Coercive Systems". For example such a model might be used to assess the political feasibility of a tax rise on a sub-population.
- Passive -vs- Interactive Again passive means that the model embodies no beliefs or value judgements - particularly about how people will behave. Interactive means that instead of making ungrounded assumptions (or beliefs) about behaviours of the system the model describes a range of possible behaviours and lets the active agents (usually people) make choices within the model; hence 'interactive'. In a sense this form of model includes not-easily-modelled agents or actors (usually people) in the model as "black-box" model elements. An interactive model is close to a role-playing game or simulation and underpinned by Drama Theory. Interactive models have been used in Defence simulations and emergency / fire-escape models and simulations for building safety assessment (particularly since September 2001)
- Dimension 6: Private -vs- Public is the degree to and scope over which the model is shared across stakeholder groups. In general models are more useful the more widely they are shared and used in decision-making at every level in an enterprise. However some models and some parts of models may have to remain private because of commercial or security implications - often models containing financial information or access controls information.
- Dimension 7: Mereological Mereology is the study of part-whole relationships. In the 'real-world' every system is a subsystem or component part of a higher-order system, or indeed several systems. Similarly every system is also the context for lower-order systems and components; 'system' is a relative concept. So every system model - a system in a different, parallel world - is a sub-model of a higher-order model or a supra-model for lower order ones. The mereological dimension judges where the model ists in this hierarchy or network.