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Different types of models
The overarching goal of science is to explain the world: the nature, the life, or the society. These explanations oftentimes come in the form of models. But there are different types of models, aimed at different goals. I wanted to draw a distinction between different types of models, and got inspired by two papers [1,2] in my search. This is a starter to built upon regarding the notion of modeling in science.
Theories are the primary tools by which scientists make sense of observations and make predictions. Science is a pragmatic process through which we solve empirical problems and answer questions about observable phenomena. Scientific problems may be ill-defined, because the search space and solution criteria are not explicitly stated. We can thus define a scientific explanation as a proposed solution to an empirical problem, and scientific theories to be the ideas we use to form explanations.
Conceptual framework: a language within which explanations are proposed. It is a set of foundational theories upon which the further theories are built.
Descriptive models: what is the phenomenon? Which variables to observe and how to relate them? It is a selective account of phenomenological data.
Mechanistic models aim to answer: how does this phenomenon arise? Mechanistic explanations explain a phenomenon in terms of its component parts and interactions. They build upon assumptions of which parts and processes are relevant. Sometimes mechanistic models can give rise to causal explanations. Mathematically, one often studies mechanistic models as dynamical systems in which a set of variables represent the temporal evolution of component processes or their equilibrium conditions.
Normative models aim to answer: why does this phenomenon exist? Normative models explain the phenomenon in terms of its function. When quantified, normative models formalize the goal of the phenomenon in an objective function (also known as a utility or cost function), which defines what it means for a system to perform “well”. These models are founded on an assumed statement of a goal and the constraints under which the system operates. Normative modeling is a computational approach to characterize the behavior of a biological, psychological or other variable under physiological normative conditions.[1]