Models And Modeling

BIBLIOGRAPHY

Social sciences rely increasingly on modeling as a result of their mathematization, the overall computerization of science, and the increase of available data. Once dubbed the “hermeneutic sciences,” the social sciences now resemble more than before the natural sciences, in which model building, testing, and comparison occupy a central role. In this development, economists have undoubtedly been pioneers among the social scientists: Since World War II, model building has become the main practice of economists. What is more, the various modeling methods adopted and developed by economists have disseminated to other social sciences. Especially, political scientists have been inspired by the rational-choice style of modeling and the associated mathematical techniques used by economists (see Morton 1999). Sociologists have, however, preferred statistical modeling, being rather skeptical about modeling social phenomena in abstract mathematical terms (Edling 2002).

Interestingly, although social scientists use in their modeling activities the same kinds of mathematical and statistical tools that natural scientists use, they often see models in a different light than do natural scientists. Whereas for social scientists models tend to be highly abstract and even unrealistic depictions of their target systems, both natural scientists and philosophers have tended to appreciate the concreteness of models as opposed to the theory. This contrast between the attitudes of social and natural scientists is partly explained by the fact that with models, social scientists often refer to what they call “formal” or “mathematical models,” which seem hopelessly plain and simple in comparison to the social phenomena they aim to explain. Although by “formal models” social scientists usually mean “mathematical models,” a model need not be mathematical to be formal. Any model that is presented symbolically or diagrammatically, allowing one to manipulate the model in order to obtain different results or predictions, can be regarded as formal. A good example of formal but not mathematical models is provided by chemical formulas (such as H₂O for water). Several philosophers, especially adherents to the semantic conception of theories (see below), distinguish between “abstract models” and the mathematical means used to express them. From their point of view, a set of mathematical equations, that is, what frequently is called a “mathematical model” by social scientists, actually should not be regarded as a model, but rather the abstract entity to which these equations refer.

Generally speaking, the most conspicuous feature of scientific models is perhaps the variety of the forms and functions they may take in scientific endeavors. The things called “models” in science make up a truly heterogeneous group: They can be diagrams, physical three-dimensional things, mathematical equations, computer simulations, model organisms, or even laboratory populations. Apart from explanation and prediction, models are used for heuristic purposes and as a tool for theory construction. Moreover, it is typical of modeling that models are often employed to explore the implications, dynamics, or internal consistency of multiple theoretical assumptions. Models can also be used as “proofs” of various theoretical possibilities.

Examples of well-known theoretical models in economics and political science include the Heckscher-Ohlin-Samuelson model, which is a general equilibrium mathematical model of international trade; the Hicks-Hansen IS-LM model, which summarizes some major features of Keynesian macroeconomics with the help of two curves; the Edgeworth-Bowley diagram, which is a geometric device defining efficient allocations in exchange situations; and the Hotelling-Downs model of two-party competition, which predicts that candidates converge to the policy preferred by the median voter. What is remarkable about these models (and is reflected, in fact, by their names) are the long histories during which they have been developed and extended by several authors. These examples exemplify also other typical features of models: their didactic value, for which the IS-LM model is especially famous, and the applicability of models as general templates to very different kinds of problems. For instance, the Edgeworth-Bowley diagram has been used for analyzing various kinds of situations in economics: consumers in exchange, production decisions of firms, welfare questions, and so on. The Hotelling-Downs model has in turn traveled from economics to political science, in which instance the original geographical dimension of the model has become merely metaphoric.

Theoretical models in the social sciences are tested either through experimentation or by estimating them by statistical methods. Often, though, the empirical models in the social sciences are based on informal theoretical reasoning, not having a formal model as a starting point. Apart from testing, integrating data, and guiding further observation and theory construction, empirical quantitative models are also constructed for predictive purposes. The statistical techniques used for predictive analysis can be grouped into different regression techniques widely used by econometrics and machine-learning approaches that originate from the research on artificial intelligence. Sharing characteristics of both theory and experiment, computer simulation offers an alternative to traditional mathematical modeling in that it allows theoreticians to experiment with more complex theoretical models than what is possible if the models are required to be analytically solvable. Moreover, the possibility provided by multiagent simulation models of exploring the emergence of macro-level behaviors from the interactions of micro-level entities in some environmental contexts seems attractive from the social science point of view.

Given the multiplicity of models and their uses in science, it has been difficult to explicate what kind of entities models are and how they give us knowledge. Two different philosophical approaches to models can be discerned in the literature. On one hand, there have been attempts to establish, within a formal framework, what scientific models are: The earlier, syntactic view of theories and the prevailing semantic approach to models are both attempts of this kind. According to the syntactic view, the task of a model was to provide an interpretation to a skeletal axiomatized theory “in terms of more or less familiar conceptual or visualizable materials” (Nagel 1961, p. 90). The syntactic view was contested by the semantic conception of theories, which replaced the syntactic formulation of a theory with a theory's models. According to the semantic conception, theories are not assemblages of propositions or statements, but rather assemblages of models, which are taken to be structures that are defined by the use of suitable logico-mathematical language.

On the other hand, issues such as scientific reasoning, scientific discovery, and theory change have prompted philosophers to focus on the role and place of models in scientific practice (see Hesse 1966). Continuing this line of work, Margaret Morrison and Mary Morgan (1999) have suggested that models should be understood as investigative instruments that mediate between theory and data because of their autonomous nature. The autonomousness of models is due to their heterogeneous construction: Apart from theoretical notions and empirical data, they may contain also analogies, mathematical techniques, stylized facts, and policy views (Boumans 1999). As Morrison and Morgan stress that through the work of constructing and manipulating models we learn from them, their approach provides a starting point for treating models also as productive things, instead of attributing their cognitive value only to representation (Knuuttila 2005).

Indeed, the epistemic value of models has traditionally been assigned to representation. It has been claimed that models give us knowledge to the extent that they represent accurately their target phenomena. This has proven problematical, especially for the social sciences, because we usually already have some kind of preunderstanding of the social reality—which may not match with the theoretical representations of it. Of all the social sciences, economics, whose mathematization started already in the nineteenth century, has been most ridden with this problem. The most persistent philosophical problem of economics has concerned the “realisticness” of economic theories and their basic assumptions. The issue has been whether such assumptions as utility maximization, perfect information, and perfectly competitive markets “are (‘too’) unrealistic or (‘sufficiently’) realistic,” or whether that should matter at all (Mäki 1994, p. 236). Famously, the 1974 Nobel prize winner in economics, Milton Friedman, has claimed that the “unrealism” of the assumptions of economics does not matter because the goal of science is the development of hypotheses that give “valid and meaningful” predictions about phenomena (Friedman 1953). To economists themselves, however, the basic assumptions do seem to matter—being a subject of continued discussion—and thus the question is how to defend them.

Uskali Mäki has suggested that economists practice a “method of isolation,” in which a set of elements is theoretically removed from the influence of other elements in a given situation with the help of idealizing assumptions (Mäki 1992). Consequently, a theory may be true even if it is partial and involves idealizations, if it has succeeded in representing the workings of the isolated causal factors in a right way. Robert Sugden (2002) denies that economic models are made by abstracting key features of the real world. He treats economic models as (more or less) “credible worlds” whose relation to the real world is established by inferential reasoning. Moreover, he claims that we compare model systems to real systems in much the same way as we compare two real systems to each other. What the two approaches have in common is that they both conceive of economic modeling as devising plausible causal mechanisms that might produce the observable phenomena.

SEE ALSO Economics; Friedman, Milton; Game Theory; Heckscher-Ohlin-Samuelson Model; Ideal Type; IS-LM Model; Mathematics in the Social Sciences; Mundell-Fleming Model; Philosophy of Science; Positivism; Realism; Samuelson, Paul A.; Social Science

BIBLIOGRAPHY

Boumans, Marcel. 1999. Built-In Justification. In Models as Mediators: Perspectives on Natural and Social Science, ed. Mary S. Morgan and Margaret Morrison, 66–96. Cambridge, U.K.: Cambridge University Press.

Edling, Cristofer R. 2002. Mathematics in Sociology. Annual Review of Sociology 28: 197–220.

Friedman, Milton. 1953. Essays in Positive Economics. Chicago: University of Chicago Press.

Hesse, Mary. 1966. Models and Analogies in Science. Notre Dame, IN: University of Notre Dame Press.

Knuuttila, Tarja. 2005. Models, Representation, and Mediation. Philosophy of Science 72: 1260–1271.

Mäki, Uskali. 1992. On the Method of Isolation in Economics. Poznań Studies in the Philosophy of Science and Humanities 26: 316–351.

Mäki, Uskali. 1994. Reorienting the Assumptions Issue. In New Directions in Economic Methodology, ed. Roger Backhouse, 236–256. London: Routledge.

Morrison, Margaret, and Mary S. Morgan. 1999. Models as Mediating Instruments. In Models as Mediators: Perspectives on Natural and Social Science, ed. Mary S. Morgan and Margaret Morrison, 10–37. Cambridge, U.K.: Cambridge University Press.

Morton, Rebecca M. 1999. Methods and Models: A Guide to the Empirical Analysis of Formal Models in Political Science. Cambridge, U.K.: Cambridge University Press.

Nagel, Ernest. 1961. The Structure of Science. New York: Harcourt, Brace.

Sugden, Robert. 2002. Credible Worlds: The Status of the Theoretical Models in Economics. In Fact and Fiction in Economics: Models, Realism, and Social Construction, ed. Uskali Mäki, 107–136. Cambridge, U.K.: Cambridge University Press.

Tarja Knuuttila

Modeling

The process of learning by watching others; a therapeutic technique used to effect behavioral change.

The use of modeling in psychotherapy was influenced by the research of social learning theorist Albert Bandura , who studied observational learning in children, particularly in relation to aggression . Bandura pioneered the concept of vicarious conditioning , by which one learns not only from the observed behavior of others but also from whether that behavior is rewarded or punished. Bandura concluded that certain conditions determine whether or not people learn from observed behavior. They must pay attention and retain what they have observed, and they must be capable of and motivated to reproduce the behavior. The effects of observed behavior are also stronger if the model has characteristics similar to those of the observer or is particularly attractive or powerful (the principle behind celebrity endorsements). Bandura maintained that television offered a major source of modeling, educating thousands of people to drink certain sodas or use brand name soaps. Likewise, violence and death modeled on television influenced behaviors, according to some social learning who cite the assassination attempt on President Ronald Reagan. John Hinckley made the attempt after watching Taxi Driver 15 times. Four girls testified in court that they watched Born Innocent before raping a California girl with a bottle, similar to a scene in the movie. Other theorists counter that television provides a release, rather than a modeling for aggressive behavior. In one study, researchers found that juvenile boys who watched aggressive television shows were less likely to exhibit violence than juvenile boys who did not.

Critics of modeling as an explanation for violent behavior maintain that the theory does not allow for differences in genetics, brain functioning and learning differences. Critics of the Bandura's findings on aggression maintain that the methods employed led to the outcome, including high frustration levels of children because they were not allowed to touch the toys.

As a therapeutic technique for changing one's behavior, modeling has been especially effective in the treatment of phobias. As with systematic desensitization , an individual is exposed to the feared object or situation in progressively anxiety-provoking forms. However, this series of confrontations, instead of being imagined or experienced directly, is first modeled by another person. In symbolic modeling, the person receiving treatment has also had relaxation training, and his or her task is to watch the series of modeled situations (live or on film) while remaining relaxed. As soon as a situation or action provokes anxiety, it is discontinued and the observer returns to a state of relaxation. In another effective technique, "live modeling with participation," the observer actively imitates the behavior of a live model in a series of confrontations with a feared object or situation. For example, persons being treated to overcome fear of snakes watch and imitate a model. They gradually progress from touching a snake with a gloved hand to retrieving a loose snake bare-handed and letting it crawl on their bodies.

In individual therapy sessions, the therapist may model anxiety-producing behaviors while the client, remaining relaxed, first watches and then imitates them. In therapy involving social skills and assertiveness training, this technique may take the form of behavioral rehearsal , in which the therapist models and then helps the client practice new, more socially adaptive behaviors.

Beyond phobias, modeling has wide application in therapy. Therapists use the modeling technique to illustrate healthy behaviors that clients can learn by example and practice in session. With children, the therapist models a variety of responses to difficult situations. In the situation of dealing with a classroom bully, the therapist models alternate responses in the context of a role play , where the therapist acts as the child initially and the child assumes the role of the bully. Then roles reverse. The child practices the behavior and responses modeled while the therapist portrays the bully. In couples' therapy, modeling is used to teach listening and communications skills. With quarreling couples, the therapist models responses to facilitate resolution rather than spiral the discussion downward into name-calling. Modeling has also been used effectively in anger management and in abuse cases.

Schools offer one of the largest arenas for modeling where teachers first demonstrate the behavior they seek, be it classroom decorum or how to work a long division problem. Bandura maintains that self-efficacy may be influenced by modeling. A behavior modeled increases the student's belief about what is possible, enhancing the student's ability to accomplish the task set forth.

See also Imitation

Further Reading

Bandura, Albert. Self-Efficacy: The Exercise of Control. New York: W. H. Freeman, 1997.

Decker, Phillip J. and Nathan, Barry R. Behavior Modeling Training: Principles and Application. New York: Praeger, 1985.

mod·el / ˈmädl/ • n. 1. a three-dimensional representation of a person or thing or of a proposed structure, typically on a smaller scale than the original: a model of St. Paul's Cathedral | [as adj.] a model airplane. ∎  (in sculpture) a figure or object made in clay or wax, to be reproduced in another more durable material. 2. a system or thing used as an example to follow or imitate: the law became a model for dozens of laws banning nondegradable plastic products | [as adj.] a model farm. ∎  a simplified description, esp. a mathematical one, of a system or process, to assist calculations and predictions: a statistical model used for predicting the survival rates of endangered species. ∎  (model of) a person or thing regarded as an excellent example of a specified quality: as she grew older, she became a model of self-control | [as adj.] he was a model husband and father. ∎  (model for) an actual person or place on which a specified fictional character or location is based: the author denied that Marilyn was the model for his tragic heroine. 3. a person, typically a woman, employed to display clothes by wearing them: a fashion model. ∎  a person employed to pose for an artist, photographer, or sculptor. 4. a particular design or version of a product: trading your car in for a newer model. • v. (-eled , -el·ing ; Brit. -elled, -el·ling) [tr.] 1. fashion or shape (a three-dimensional figure or object) in a malleable material such as clay or wax: use the icing to model a house. ∎  (in drawing or painting) represent so as to appear three-dimensional: the body of the woman to the right is modeled in softer, riper forms. ∎  (model something on/after) use (esp. a system or procedure) as an example to follow or imitate: the research method will be modeled on previous work. ∎  (model oneself on) take (someone admired or respected) as an example to copy: he models himself on rock legend Elvis Presley. ∎  devise a representation, esp. a mathematical one, of (a phenomenon or system): a computer program that can model how smoke behaves. 2. display (clothes) by wearing them. ∎  [intr.] work as a model by displaying clothes or posing for an artist, photographer, or sculptor. DERIVATIVES: mod·el·er / ˈmädl-ər/ n.

model This is a term which has been given a wide variety of different meanings by sociologists. In some cases it has been used as a synonym for theory, but in others as a reference to a system of abstract concepts at a more general level than a theory. Equally, it is used to refer to a statistical model, as in causal modelling. Whichever definition is used the essence of a model is that it requires the researcher to engage with theory and thus avoid empiricism.

At root, models seek to simplify phenomena, as an aid to conceptualization and explanation. In sociology structural-functionalism is a model in the first two senses suggested above, since it provides a broad frame of reference (a meta-theory which states that society is like an organism) and a set of conceptual propositions (a theory showing how the parts of society are integrated and make a contribution to the functioning of the whole). Where a hypothesis about the relationship between concepts is specified, and the concepts can be measured, we may speak of an operational model. These models are sometimes expressed diagrammatically, and may be set out more formally in mathematical terms, as for example in a regression model or loglinear model. Model building, a key aspect of mathematical sociology, involves the refinement of models from the stage of a flow diagram to a formal mathematical expression. Causal models may be of either type. Whatever form it takes, a model is an aid to complex theoretical activity, and directs our attention to concepts or variables and their interrelationships. See also MULTI-LEVEL MODELS; MULTIVARIATE ANALYSIS.

model and modeling in painting, the use of light and shade to simulate volume in the representation of solids. In sculpture the terms denote a technique involving the use of a pliable material such as clay or wax. As opposed to carving, modeling permits addition as well as subtraction of material and lends itself to freer handling and change of intention. The technique is exemplified also by those works in cast metal and plaster that are made from the mold of a clay original. The mold is made by the process of cire perdue . The noun model is used to describe such an original and also any three-dimensional scale model for a larger or more elaborate project in architecture, landscaping, or industry. It also denotes a person or object used as an aid to representation in painting.

model A simplified representation of something (the referent). The representation may be physical or abstract, and may be restricted to certain properties of the referent. In computing, models are usually abstract and are typically represented in a diagramming notation, such as dataflow diagrams (in functional design), ERA diagrams (for a data model), or state-transition diagrams (for a model of behavior); in the case of the relational model the referent is the target system while in the waterfall model, V-model, and spiral model the referent is the development process. In computer graphics, models are used to create realistic images of objects and their attributes (see color model, lighting model, reflectance model).

modeling The act of creating a model of something for a particular purpose, such as to describe it, understand it, or derive some properties. The process involves deciding which simplifications, idealizations, or abstractions to make, what kinds of representations to adopt, and how to express the selected properties of the referent. The context of a prospective system may be modeled as part of the systems analysis. A program or software-based system may be modeled to produce an abstract design or for nonfunctional properties such as performance.

model † architect's plans; design, make XVI; representation or figure in three dimensions; exemplar, pattern XVII. — F. † modelle, now modèle — It. modello: Rom. *modellus, for L. modulus, dim. of modus (see prec.).
Hence vb. XVII.

model A representation of reality in which the main features of some aspect of the real world are presented in simplified terms in order to make that aspect easier to comprehend, and often to facilitate the making of predictions.

model A representation of reality in which the main features of some aspect of the real world are presented in simplified terms in order to make that aspect easier to comprehend, and often to facilitate the making of predictions.

model Representation of reality in which the main features of some aspect of the real world are presented in simplified terms in order to make that aspect easier to comprehend, and often to facilitate the making of predictions.

model •addle, paddle, saddle, skedaddle, staddle, straddle •candle, Coromandel, dandle, Handel, handle, mishandle, Randall, sandal, scandal, vandal •manhandle, panhandle •packsaddle • side-saddle •backpedal, heddle, medal, meddle, pedal, peddle, treadle •Grendel, Kendall, Lendl, Mendel, Rendell, sendal, Wendell •cradle, ladle •beadle, bipedal, credal, needle, wheedle •diddle, fiddle, griddle, kiddle, Liddell, middle, piddle, riddle, twiddle •brindle, dwindle, kindle, spindle, swindle, Tyndale •paradiddle, taradiddle •pyramidal • apsidal •bridal, bridle, fratricidal, genocidal, germicidal, homicidal, idle, idol, infanticidal, insecticidal, intertidal, matricidal, parricidal, patricidal, pesticidal, regicidal, sidle, suicidal, tidal, tyrannicidal, uxoricidal •coddle, doddle, model, noddle, swaddle, toddle, twaddle, waddle •fondle, rondel •mollycoddle •caudal, chordal, dawdle •poundal, roundel •Gödel, modal, yodel •crinoidal •boodle, caboodle, canoodle, doodle, feudal, noodle, poodle, strudel, udal •befuddle, cuddle, fuddle, huddle, muddle, puddle, ruddle •bundle, trundle •prebendal • synodal •antipodal, tripodal •citadel •curdle, engirdle, girdle, hurdle •dirndl