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# MODEL

a set of propositions or equations describing in simplified form some aspects of our experience. Every model is based upon a theory, but the theory may not be stated in concise form. (Umpleby)

An object or process which shares crucial properties of an original, modeled object or process, but is easier to manipulate or understand. A SCALE MODEL has the same appearance as the original save for size and detail. However, increasing use is made of computer simulation: the model is a program that enables a computer to determine how key properties of the original will change over time. It is easier to change a program than to rebuild a scale model if we want to explore the effect of changes in policy or design. (Arbib)

A model is a device, scheme, or procedure typically used in systems analysis to predict the consequences of a course of action; a model usually aspires to represent the real world (to the degree needed in analysis)--for example, a relation between some observed phenomena. A model can be formal (e.g., a mathematical expression, a diagram, a table) or JUDGMENTAL (e.g., as formed by the deductions and assessments contained in the mind of an expert). Some models are causal -- i.e., they reflect cause-effect relationships. Others are CORRELATIONAL MODELS which do not necessarily reveal whether some of the observed phenomena are the cause of the others. An example is correlation models used for weather forecasting; note that the farmer who predicts rain on the basis of some observed phenomena and his past experience is using a judgmental correlation model. A deterministic MODEL generates the response to a given input by one fixed law; a stochastic MODEL picks up the response from a set of possible responses according to a fixed probability distribution (stochastic models are used to simulate the behavior of real systems under random conditions). A DYNAMIC MODEL can describe the time-spread phenomena (dynamic processes) in a system. A STATIC MODEL describes the system at a given instant of time and in an assumed state of equilibrium. Among the formal, mathematical models an ANALYTIC MODEL is formed by explicit equations. It may permit an analytic or numerical solution. An analytic model is linear if all equations in the model are linear. We speak of a simulation model if the solution, i.e., the answer to the question which the analyst has posed, is obtained by experiments on the model rather than by an explicit solution algorithm. A typical example is stochastic simulation, where one wants to obtain probabilistic properties of a system's response by evaluating the results of a large number of simulation runs on the model. In some analyses the model by which one predicts the outcome of a course of action must take into account that this outcome depends also on actions taken by other decision makers. If the assumption can be made that those decision makers optimize some defined objective functions, and all the other aspects of the system can also be formalized, an optimization model (e.g., a linear programming model) can be used to determine the system's response to a course of action. In ROLE-PLAYING MODELS those decision makers (and perhaps some other elements of the system as well) are simulated by human actors. In a MAN-MACHINE MODEL an actor or actors play roles while other parts of the model are implemented on a computer. A formal model has a structure (the form of an equation, for example) and parameters (the value of coefficients in an equation for example). Determination of both the structure and parameters is MODEL identification; determination of the parameters on the basis of experimental data is MODEL ESTIMATION. The check of a proposed model against experimental data other than those used for parameter estimation is model validation. See also verification. (IIASA)

A system that stands for or represents another typically more comprehensive system. A model consists of a set of objects, described in terms of variables and RELATIONs defined on these and either (a) embodies a theory of that portion of reality which it claims to represent or (b) corresponds to a portion of reality by virtue of an explicit homomorphism or isomorphism between the model's parameters and given DATA. Four kinds of models are distinguished: (1) Sampling models consist of a mere subset of mutually exclusive objects from a larger universe of objects. The representation is based on the assurance that each object of the universe had the same probability to be included in the sample. (2) Iconic models (see icon) are linear transforms of a configuration of objects in the universe. The representation is based on the assurance that an iconic model retains that universe's topological characteristics. E.g., scale models, photographs, the graphical representation of networks. In (3) behavioral models, the relations are transformations, equations or operating rules and the representation is based on the assurance that the behavior of the model corresponds to the behavior of the system modelled. This is established either by identifying the model's parameters and equations, or showing that the homomorph is not violated. E.g., the computer simulation of an economy, the model of a plane built into an automatic pilot. In a (4) symbolic model the set of objects are symbols and the relations are expressed in the form of algebraic, computational or algorithmic statements exhibiting no behavior of its own. Symbolic models must be realized in or coupled with a machine in order to become a behavioral model of something else. E.g., a formal statement about a social process must be translated into the algorithmic form of a program acceptable to a computer. Sampling models represent the materiality of the reality modelled. The other three do not. Their structural behavior or symbolic correspondence makes no reference to the physical nature of the objects represented in the model. (Krippendorff)
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