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 Macro-Simulation

Macro simulation refers to a simulation showing the effects of interventions at the macro level. In the1960s and early 1970s macro simulation was introduced to make economic analysis. Macro-simulations are quantitative models often based on control and feedback loops. They often are based on a large number of assumptions and remain at the macro level, although nowadays macro-level predictions are made by modelling at the micro level (see macro-economic models). These assumption are often critised as they proved to be wrong and backed by limited empirical evidence (e.g. Nelson & Winter, 1974). This resulted in skeptisims and a shiftt towards microsimulaton and agent-based models. In policy-making the interaction between micro and macro level has been put central. By modelling and understanding the micro-level, non-linear behavior at the macro level can be observed (Gilber & Troitzsch, 2005).
Related terms: Macroeconomic Models
References:
Gilbert, N. & K. Troitzsch (2005). Simulation and social science. Simulation for Social Scientists (2 ed.). Open University Press.

Nelson, R.R. and Winter, S.G. (1974). Neoclassical vs. Evolutionary Theories of Economic Growth: Critique and Prospectus. The Economic Journal,Vol. 84, No. 336, pp. 886-905

 Macroeconomic Models

Macroeconomic models describe the operation of the economy of a country or a region through a model who's modelling constructs and outcomes are made at the macro-level  (Yurdusev, 1993). "Macro" refers to the level of analysis. Often a distinction between the micro and macro level is made. The micro-level refers to the analysis on the level of individuals, whereas the macro-level looks over a large populations, which can be a country level. Whereas in the past these models remained at the macro level and aggregates were used to model the economy, nowadays macro-economic models are also be constructed by modelling the relationships and decisions of individual agents, which interactions results in macro-economic effects (Gilbert & Terna, 2000).
References
Yurdusev, A.N. (1993). Level of Analysis and Unit of Analysis: A Case for Distinction. Millennium: Journal of International Studies, 22(1): 77—88.
Gilbert, N. & Terna, P. (2000). How to build and use agent-based models in social science. Mind & Society, Vol 1, No. 1, pp 57-72.

 Mathematical Model

A mathematical model is an abstract model in mathematical language to describe the behaviour of a system. Eykhoff (1974) defines a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'.
Relationships and variables are the main elements included in mathematical models. Operators, such as algebraic operators, functions, etc, describe relationships. Variables play the role of abstracting systems parameter of interest that can be quantified. A mathematical model can even include operators without variables (King, 1999).
Mathematical models can be applied to construct dynamic systems, statistical models, differential equations, or game theoretic models. Davis (1996) provides a survey of mathematical models and formal approaches for decision and policy making. In his work, Davis shows how mathematics is indeed the foundation of modern decision and policy making, as it allows modeling complex systems, testing and evaluation, control and optimization (Davis, 1996).
Toshkov proposes a mathematical model for the timing and policy shift of implementation outcomes. Using a ‘decision making under institutional constraints’ framework, the model provides a number of hypotheses about the impact of  preferences, discretion, administrative capacity and policy-making constraints (Toshkov, 2007).
Related terms: Mathematical modelling
References:
Eykhoff,P. (1974) System Identification-Parameter and State Estimation. Wiley, New York.
Peter JB King (1999). Functions with no parameters
Aris, R. ( 1994 ). Mathematical Modelling Techniques, New York : Dover. ISBN 0-486-68131-9.
Davis, P. (1996). Mathematics and Decision Making. Mathematics Awareness Week 1996.
Toshkov, D. (2007).  A Formal Model of Policy Implementation in Multi-level Systems of Governance. PhD Thesis, 2007.

 Mathematical Modelling

The modelling is an activity, a cognitive activity in which we thing about and make models to describe how devices or objects of interest behave. We usually use words, drawings or sketches, physical models, computer programs, or mathematical formulas (or more generally said different languages). If we use language of mathematics to make models we are providing mathematical modelling.
According to Dym and Ivey (2004) mathematical modelling is a principled activity that has principles behind it and methods that can be successfully applied. As he mentions the principles are over-arching or meta-principles phrased as questions about the intentions and purposes of mathematical modelling.
Usually mathematical modelling is the use of mathematics to describe real or conceptual world phenomena, to investigate important questions about the observed world, to explain world phenomena, to test ideas, and to make predictions about the world around or inside us. Mathematical (or equation-based modelling) is an approach to describe a system with the tools of calculus, typically in terms of systems of differential or difference equations. As mentioned in Toitzsch (1998) they usually allow only for the description on one macro level. The master equation approach can be used to describe interactions between a micro and a macro level, converting assumptions about the stochastic behaviour of micro units into statements about distributions of attributes of the macro unit or units.
According to Troitzsch (2009) only few of these mathematical models have closed solutions, thus necessitating numerical treatment, and this is kind of simulation, such that more complex systems of more complex elements profit much from agent-based models whose structural validity is often better than the structural validity of mathematical models of social and economic systems. Whereas in physics mathematical models are often sufficient and sometimes the best way of describing the interaction between fields and particles, this is only very rarely the case for social systems.
Related terms: Mathematical model
References:
Dym, C. L., Ivey, E. S. (2004). Principles of Mathematical Modeling (Computer Science and Applied Mathematics). Academic Press.
Troitzsch, Klaus G. (2009), Perspectives and Challenges of Agent-Based Simulation as a Tool for Economics and Other Social Sciences, In: Proc. of the 8th Int. Conf. on Autonomous Agents and Multi-Agent Systems (AAMAS 2009). p. 35-42.
Troitzsch, Klaus G. (1998), Multilevel Process Modeling in the Social Sciences: Mathematical Analysis and Computer Simulation, In: Liebrand, Wim B.G.; Nowak, Andrzej; Hegselmann, Rainer: Computer Modeling of Social Processes, London: Sage. p. 20--36.

 Mathematical programming

Mathematical programming (MP) is the use of mathematical (optimising) models to assist in taking decisions. The term "programming" antedates computers and means preparing a schedule of activities. It is also one of Operational Research techniques.
A static mathematical program attempts to identify the maxima or minima of a function, e.g. f(x_1,...,x_n) of n real-valued variables, called objective function, in a domain identified by a set of constraints. The constraints might take the general form of inequalities, for instance g_i(x_1,...,x_n)>-b_i. It finds the best solution to the problem as modelled. If the model has been built well, this solution should translate back into the real world as a good solution to the real-world problem. If it does not, analysis of why it is no good leads to greater understanding of the real-world problem.
As well described in Exodus Systems (2013), a Mathematical programming model answers the question "What is best?" rather than "What happened?", "What if?" (simulation), "What will happen?" (forecasting) or "What would an expert do and why?" (expert system).
According to Troitzsch (1998) the mathematical programming can be divided into linear programming, quadratic or non-linear programming, and stochastic programming.
References:
Exodus Systems (2013). Why Mathematical Programming is Useful [Online] (verified on November 23, 2013).
Troitzsch, Klaus G. (1998), Multilevel Process Modeling in the Social Sciences: Mathematical Analysis and Computer Simulation, In: Liebrand, Wim B.G.; Nowak, Andrzej; Hegselmann, Rainer: Computer Modeling of Social Processes. London: Sage. p. 20--36.

 Method

According to the Oxford dictionary, method is "a particular procedure for accomplishing or approaching something, especially a systematic or established one", for example, a method for software development/maintenance. The origin of the word is Latin through Greek (methodos, μέθοδος) meaning pursuit of knowledge and derives from -meta (expressing development) and -hodos (meaning way).
Method in terms of scientific research follows different approaches, with the main dichotomy between qualitative and quantitative research methods. At its most basic level, scientific method consists of 3 main steps: Observing, Explaining, and Testing (Carey, 2011).
The data collection methods involved in the observation step of the method include surveys, opinion polls and experiments. These data are analysed using statistical methods. These methods are used for the study of scientific phenomena, and they are not always appropriate when studying social/cultural phenomena such as those related to the social/political aspects of e-participation and people's attitude towards technologically-driven social interaction through digital media. The use of qualitative methods (Silverman, 2013) is more appropriate when we want to:

- understand peoples views, opinions and emotions from their own rather than the researchers perspective
- understand process involving peoples lives
- understand social interactions among people
- identify the social political and cultural context where people operate  
The data collection methods typically used in qualitative research are interviews, observations, focus group discussions. These data are analysed using interpretive methods.
The words method and methodology (see relevant entry in the glossary) sound similar but there is a fundamental difference between them: A method is a series of steps to achieve something; Methodology is the study of the design of the different methods used towards a goal (referred to also as research design).
Related term: Methodology
References:
Carey S.S. (2011). A Beginners guide to scientific method. Wadsworth Publishing, Boston, MA.
Silverman (2013). Doing qualitative research. Sage, London, UK.

 Methodology

A research methodology is a way that a researcher uses to systematically solve a research problem. A research methodology consists of the combination of the process, methods, and tools which are used in conducting research in a certain research domain, while research methods are means of finding truth in research domains (Nunamker et al., 1990).
Bailey describes a methodology as the philosophy of the research process which “includes the assumptions and values that serve as a rationale for research and the standards or criteria the researcher uses for interpreting data and reaching conclusion’’ (Bailey, 1982, p. 261). Hence, it becomes important for a researcher to design the methodology depending on the problem s/he is currently working on.
Related term: Method
References:
Bailey, K. D. (1982), Methods of Social Research, The Free Press
Nunamaker, J.F.,Jr; Chen, M. (1990), Systems development in information systems research, System Sciences, 1990. Proceedings of the Twenty-Third Annual Hawaii International Conference on (Volume:iii)

 Micro-Simulation

The core of micro-simulation has been defined as “a means of modelling real life events by simulating the actions of the individual units that make up the system where the events occur” (Brown and Harding, 2002), and as “computer-simulation of a society in which the population is represented by a large sample of its individual members and their behaviours” (Spielauer, 2011). This has been broadened to encompass its role in policy so that “micro-simulation models are computer programs that simulate aggregate and distributional effects of a policy, by implementing the provisions of the policy on a representative sample of individuals and families, and then summing up the results across individual units using population weights” (Martini & Trivellato, 1997, p. 84).
Micro-simulation operates at the level of individual units, for example children, each possessing a set of associated attributes as a starting point. A set of rules, typically derived from statistical analyses, is then applied in a stochastic manner to each and every individual to simulate changes in state or behaviour. The primary strength of micro-simulation techniques is their use of actual individual-level data, which allows them to reproduce social reality and the intricacy of policy structures. These data can come from various sources, which micro-simulation is able to combine into a cohesive whole. The model can then be used to estimate the outcomes of “what if” scenarios (Brown & Harding, 2002, p. 4).
Spielauer (2011) notes that micro-simulation is certainly the preferred modelling choice in three situations: (1) if population heterogeneity matters and if there are too many possible combinations of considered characteristics to split the population into a manageable number of groups; (2) if behaviours are complex at the macro level but better understood at the micro level; and (3) if individual histories matter, that is, when processes possess memory (Spielauer, 2011, pp. 6-8).
Related terms: Simulation Model
References:
Brown, L, Harding A. (2002). Social modeling and public policy: Application of microsimulation modeling in Australia. Journal of Artificial Societies and Social Simulation 5(4)6.
Martini A, Trivellato U. (1997). The role of survey data in microsimulation models for social policy analysis. Labour, 11(1), 83-112.
Spielauer M. (2011). What is social science microsimulation? Social Science Computer Review, 29(1), 9-20.

 Model

A model may be described as an abstract representation of reality constructed to fulfil a certain purpose for research or implementation activities. According to an early definition by Apostel (1960), any subject using a system A to obtain information about a system B, with A being neither directly nor indirectly interacting with B, is using A as a model for B.
According to Dietz (2006), there are three system categories: concrete, symbolic and conceptual systems. Their relationships are represented in the figure below. Referring to this figure:

- A concrete model of a concrete system is called an imitation (e.g. a scale model of an airplane or a ship or any other concrete thing).
- A conceptual model of a concrete system is called a conceptualization (e.g. the geometrical sphere as a model for celestial bodies; the Process Model as the conceptualization of the business processes in an enterprise).
- A concrete model of a conceptual system is called an implementation (e.g. the pyramids of Giza are an implementation of the geometric concept of pyramid; a business process as an implementation of the Process Model).
- A conceptual model of a conceptual system is called a conversion (e.g. the algebraic concept of a circle (x2 + y2 = r2) is a conversion of its geometric concept).
- A symbolic model of a conceptual system is called a formulation (e.g. the notion of the algebraic concept of a circle mentioned previously as a conversion model, is also a formulation model when referring to its notation).
- A conceptual model of a symbolic system is called an interpretation, which is actually the reverse of formulation (e.g. the deciphering of the Stone of Rosetta).
- A symbolic model of a symbolic system is called a transformation (e.g. from Morse to the Roman notation of letters). The term model can be equated to some graphical diagram. This is because in many fields (e.g. information systems, business processes management) most models used are graphical models. Models, however, do not necessarily have to be graphical (Op ’t Land et al, 2009). A model that is graphically displayed typically consists of three elements: (i) a collection of symbol structure types, (ii) a collection of operations that can be applied to any valid symbol structure, and (iii) a collection of inherent constraints that define the set of consistent symbol structure states, or valid changes of states (Mylopoulos and Borgida, 2009).
References:
Apostel, L. (1960) Towards the formal study of models in the non-formal sciences. Synthese, 12(2-3), pp.125–161, pdf
Dietz, J.L.G. (2006) Enterprise Ontology: Theory and Methodology. Springer, Heidelberg.
Mylopoulos, J. & Borgida, A. (2009) A Sophisticate’s Guide to Information Modeling. In: Metamodeling for Method Engineering, Jeusfeld, M.A., Jarke, M. & Mylopoulos, J. (eds.), MIT Press, Cambridge, Massachusetts, pdf
Op ’t Land, M., Proper, E., Waage, M., Cloo, J. & Steghuis, C. (2009) Enterprise Architecture: Creating Value by Informed Governance. Springer, Heidelberg.

 Modelling

Modelling is an activity aiming to make a domain of the real world easier to understand, define, quantify, visualise, and simulate. It requires identifying aspects of the domain and then developing and/or using different models for different purposes, e.g. conceptual models are used to understand, operational models to operationalise, mathematical models to quantify and graphical models to visualise the domain [Wikipedia].
Modelling is an essential part of any scientific activity, and many scientific disciplines have their own ideas about specific types of modelling (Cartwright 1983, Hacking 1983). For example, in the Information Systems (IS) discipline, the term modelling describes the elicitation and the representation of the general knowledge that any information system operating in a domain needs to know (Olive 2007, Rolland 2007).
In the policy modeling and simulation field the term modelling refers to structuring and programming a simulation model capable to produce artificial data about the structures and behaviours of a policy system (Gilbert and Doran, 1994), aiming at the prediction of policy impacts, development of new governance models and collaborative solving of complex policy problems.
Related term: Model
References:
Cartwright, N. 1983. How the Laws of Physics Lie. Oxford University Press
Hacking, I. 1983. Representing and Intervening. Introductory Topics in the Philosophy of Natural Science. Cambridge University Press
Olive, A. 2007. Conceptual Modeling of Information Systems, Springer Verlag Berlin.
Rolland, C. 2007. Capturing system intentionality with maps. Conceptual modelling in Information Systems engineering. p.141-158.
Gilbert, N. and J. Doran (eds.), 1994: Simulating Societies. The computer simulation of social phenomena. London: Routledge.