Data are considered to be the oil of the 21th century. They are also a rich source for many sciences, especially those that use observational data for development of an understanding behind the data. They are used to gain an insight into the discipline based on (phenotypical) observations. This insight may result in a quantitative theory offer. The main target is however a theory that explains the data. We develop a model-backed approach to theory development based on quantitative theory offers. Models are becoming the mediator between quantitative and qualitative theories. Models can be systematically developed based on a layering approach.
Data science is considered to be a new stage of scientific research. Data science is based on analysis of data resources. The analysis asks the right questions with efficient processing algorithms, machine learning and cognitive computing techniques, refined statistical models, and innovative visions of how to more effectively extract the relevant data assets and scrutinise them fast with more sophisticated results.
Sciences use all four dimensions in different proportions. We consider empirical science (describing natural phenomena and experimenting in social economics, archaeology, etc.) with a larger empirical investigation, theory-driven sciences (mainly mathematical and natural sciences) with orientation on theory-backed investigation, computation science (simulating complex phenomena, e.g. bioengineering, meteorology) with orientation on computational investigation, and data digging and exploration sciences (currently mainly data analysis and mining, partially AI) with data-oriented investigation. The last two kinds may also be considered as technology-enabled sciences.
The role of models also changes as displayed in Fig. 1:
Fig 1. Models and their functions in sciences
Data science goes beyond empirical sciences, theorydriven science, and computation science [12]. Data science discovers pattern and generates insights in data sources or data proxies. It is based on raw data and builds these insights based on knowledge from the scientific discipline and application domain. It provides models, recommendations, and potential theories on how to interpret the data. It is based on a process of organising data for analysis including data proliferation, data collection organisation, cleaning, application of tools, and analysis. It may consider huge data collections as well as small data sets. The proxy data are compiled and may become ‘smart’ quantitative data for quantitative research. Data science is essentially the ‘science’ that is turning data proxies into narrative and into quantitative data. It thus develops an understanding of the data itself. In our case, we investigate rather thin data sets. The picture is however similar to the one with very large data sets.
Explorative and investigative theory development (e.g. [1, 18, 20]) starts with an investigation of data sources and develop some proxy-based observation concepts and a theory offer. A theory offer is a scientific, explicit and systematic discussion of foundations and methods, with critical reflection, and a system of assured conceptions providing a holistic understanding. A theory offer is understood as the underpinning of technology and science similar to architecture theory [23] and the approaches by Vitruvius [32}, and L.B. Alberti [2]. Theory offers do not constitute a theory on their own, rather are some kind of collection consisting of pieces from different and partially incompatible theories, e.g. sociology theories such as the reference group theory, network theories, economic theories such as the agent, Darwinian evolution theories, subjective rationality theories, and ideology theories. Middle-range theories lie between the hypotheses space and all-inclusive efforts to develop a unified holistic theory. They guide empirical enquiry. They are close enough to observed data. A (scientific) theory is a “systematic ideational structure of broad scope, conceived by the human imagination that encompasses a family of empirical (experiential) laws regarding regularities existing in objects and events, both observed and posited. A scientific theory is a structure suggested by these laws and is devised to explain them in a scientifically rational manner. In attempting to explain things and events, the scientist employs (1) careful observation or experiments, (2) reports of regularities, and (3) systematic explanatory schemes (theories).” [6] Typically, we start with some data, e.g. proxy data. Next we (g-)derive proxy concepts (or concepts) and form some proposals for (h-)formation of a proposal of a potential explaning theory, i.e. a theory request (or request for a theory offer).
Proxy sources can be aggregated and (f-)condensed and thus become quantitative sources which are the basis for (g-)formation of quantitative concepts. These quantitative concepts are (h-)embedded into theory offers (or, resp., theory requests for proxy requests) and are the basis for a theory offer that serves as an explanation for the theory request. Quantitative concepts can be (F)mapped back to proxy concepts. Proxy-based research and quantitative research is well-integrated if the diagram is commuting. Theories can be built on the basis of theoretical concepts which are supported by sources. Quantitative concepts should be associated with qualitative concepts. The association can only be developed in the case when the association among the data has been clarified. So far, the explanations that can be generated are mainly developed for explaining the observations made on the basis of proxies.
We arrive therefore with the following research challenge: How we can close the gap between quantitative theory offers and qualitative theories within the setting of data science?
Investigative modelling at CRC 1266 [1, 16] aims at exploring and explaining transformations in societies as “processes leading to a substantial and enduring reorganisation” [1] of any or all aspects of the human social, cultural, economic, and environmental relations. 1 We restrict the mindmap in Fig. 3 to main concepts and do not display the full concept network. For details see the website of the project.
Proxies are observations for main concepts1 in Figure 3. These main concepts need however a quantitative underpinning and a number of theoretical concepts.
We develop an approach to data science based on models. Models are instruments that function in utilisation scenarios. One of these scenarios might be the development of a theory for a theory offer. We will show in the sequel how this approach can be systematically applied to development of mediating models that close the gap in Figure 5. We start with a notion of model in Section 2. Six research questions are developed which are answered in Sections 3 and 4. Next, we develop a model construction approach in Section 3. Finally, we apply this approach to data science and use models as mediators in Section 4.
Models are widely used in life, technology and sciences. Their development is still a masterpiece of an artisan and not yet systematically guided and managed. The main advantage of model-based reasoning is based on two properties of models: they are focused on the issue under consideration and are thus far simpler than the application world and they are reliable instruments since both the problem and the solution to the problem can be expressed by means of the model due to its dependability. Models must be sufficiently comprehensive for the representation of the domain under consideration, efficient for the solution computation of problems, accurate at least within the scope, and must function within an application scenario. Research question 1: Can models be used for resolving the gap between theory offers in quantitative research and theories in qualitative research? Consider for instance the CRC 1266 application: Transformation is considered in this context as a phenomenon that requires detailed description of features and hence quantitative data are necessary for descriptions by empirical models and simulations. Models mediate between quantitative theories and qualitative theories. Models are applied in hypothetical and investigative scenarios, should support causal reasoning as well as network-oriented reasoning, and are developed in an empiric framework.
Let us first briefly repeat our approach to the notion of
model: A model is a well-formed, adequate, and
dependable instrument that represents origins and that
functions in utilization scenarios [
The model should be well-formed according to some well-formedness criterion. As an instrument or more specifically an artifact a model comes with its background, e.g. paradigms, assumptions, postulates, language, thought community, etc. The background is often given only in an implicit form. The background is often implicit and hidden.
A well-formed instrument is adequate for a collection of origins if it is analogous to the origins to be represented according to some analogy criterion, it is more focused (e.g. simpler, truncated, more abstract or reduced) than the origins being modelled, and it sufficiently satisfies its purpose.
Well-formedness enables an instrument to be justified by an empirical corroboration according to its objectives, by rational coherence and conformity explicitly stated through conformity formulas or statements, by falsifiability or validation, and by stability and plasticity within a collection of origins.
The instrument is sufficient by its quality characterisation for internal quality, external quality and quality in use or through quality characteristics [26] such as correctness, generality, usefulness, comprehensibility, parsimony, robustness, novelty etc. Sufficiency is typically combined with some assurance evaluation (tolerance, modality, confidence, and restrictions). A well-formed instrument is called dependable if it is sufficient and is justified for some of the justification properties and some of the sufficiency characteristics.
Models are used as instruments in certain utilisation scenarios such as communication, reflection, understanding, negotiation, explanation, exploration, learning, introspection, theory development, documentation, illustration, analysis, construction, description, and prescription. They have to fulfil a number of specific functions in these scenarios. Typical functions of models as instruments in scenarios are (a) cognition, (b) explanation and demonstration, (c) indication, (d) variation and optimisation, (e) projection and construction, (f) control, (g) substitution, and (h) experimentation [31].
Our notion of a model and its functions also covers the notion of a middle-range theory. Middle-range theories have been developed for hypothetical investigation in empiric research. Models are more general and support also other functions. They provide a methodological power and allow inclusion of knowledge as long as the model (or the model suite) is still coherent. In the sequel we shall discover that models can be used as a mediator. Models may reflect qualitative as well as quantitative theories. Reflection is based on the function that is anticipated when selecting a utilisation scenario. 2.3 Model := Normal Model ₪ Deep Model A model consists of a normal model that is combined with some deep model similar to the visible (or exterior) and invisible parts of an iceberg [16, 29, 30]. The deep model reflects (α) the intentions of the problem world, (β) the accepted understanding within the community of practice, (γ) the context of the application domain, (δ) the background that is commonly accepted in the problem and application domain, and (ε) the general restrictions to the origins that might be considered. The deep model allows partial derivation of the justification and adequacy of a model.
The normal model reflects the collection of origins that are currently under consideration. Both the deep and the normal model are dependent on the functions that a model should play in application scenarios. Development of models is often restricted to development of a normal model under the assumption that the deep model is given by the modelling method, the context, the community of practice, and the function that the model has to play in a given scenario. The modelling methods also determined the methods that are used for model development. It might also include the utilization methods.
Research question 2: Can we separate the deep model from the normal model in such a way that the model can be composed of the deep model and of the normal model? If the answer to this question is positive then we might try to consider the model as an enhancement of the deep model. In this case, the development of a model can be layered.
The deep model also reflects a shared foundational set of beliefs and priorities that govern the way how a discipline handles and interprets its data. Deep models are not dominating. They are hidden and somehow form the model’s obstinacy.
Research question 3: How can be development of a model layered into the development of a deep model followed by the development of the normal model? We may now ask us whether this approach is universal. The answer will be negative if the notion of model also includes models with intractable deep models, e.g. for metaphors, parables, or physical representations. We might however concentrate on models in sciences and technology.
Models may be given as a holistic instrument that combines all aspects into one model. The approach is often too challenging. A simpler approach is the consideration of a model as a model suite (or model ensemble) [8,25] that consists of a coherent collection of models which are representing different points of view and attention. It is extended by an explicit association or collaboration schema among the models, controllers that maintain consistency or coherence of the model suite, application schemata for explicit maintenance and evolution of the model suite, and tracers for the establishment of the coherence.
Research question 4: Exists there a systematic approach to model development that is based on a co-development of normal models and deep models? Which additional models should be integrated into the model suite?
Model development does not start from scratch. We often start with generic models. A generic model [16] is a model which broadly satisfies the purpose and broadly functions in the given utilization scenario. It is later tailored to suit the particular purpose and function. Generic models can be calibrated to specific models through a process of data or situation calibration, refinement, concretization, context enhancement, or instantiation.
Research question 5: Can we develop normal models starting with a generic model and are they still capable of being integrated with the deep model? If the answer is positive then generic normal models can be calibrated to specific normal models through a process of data or situation calibration, refinement, concretization, context enhancement, or instantiation.
In [16], we developed the V-model to data mining based on a separation of the data mining process into the domain perspective with its domain world of users from a community of practice, the modelling perspective with a model world, and the data perspective in a data world.
Users are interested in solution of certain problems an application world, share the context and also the scientific and technological background. The classical data model mining process uses these perspectives for a stepwise development of a model that allows to solve their problems, e.g. (1) by modelling the problem and the issues under consideration, (2) by preparing the data world for development and enhancement of models, (3) by applying data mining algorithmics for pattern detection and model development, and (4) by using the model for development of some solution for the problems and thus augmenting the application domain world. The model development process itself can be understood a multi-iterative guided procedure that has its flow of activities.
This approach extends the classical CRISP framework [4] and other approaches to systematic data mining, e.g. [15]. Each of these approaches has its capacity and potential as well as its threats and limitations. The question is now: Research question 6: Can we generalize a data mining setting to model development for data science in such a way that models mediate between theory offers and theories? Data analysis and model suite development currently inherit success stories in a similar application. These success stories follow some kind of a meta-pattern and result in a specific data mining process as an example of a modelling method or modelling mould. Data mining starts with exploring and understanding the data mining project, its data, and a general setting of principles of modelling. After the project and the nature of the data is understood, data are preprocessed and prepared for the application of algorithms. Next pattern within the data are investigated. This pattern analysis results in clusters, maps, association rules, and some deviation analysis, i.e. we develop a model on the data space. This model is then used for development of explanations, e.g. via decision trees, (Bayesian) classifiers, regression, and (rule) learning approaches. We develop a second model on top of the first model. Next, the data space is considered in a general form by prediction analysis, e.g. nearest neighbor predictors, (artificial) neural networks, support vector machines, or other ensemble methods. The result is another model. Finally, the models are evaluated and potentially deployed. If the evaluation shows that the models satisfy quality criteria, we revise the models.
The research questions will now be handled by specific methodological mould and hypotheses that might support a positive answer to our research challenge: 1. Models may have a number of functions. One of the functions can be the mediator function. After knowing how to develop a model, we can investigate the mediator function of models for development of a shared view on both quantitative theory offers and qualitative theories. 2. We already discovered that the deep model is somehow hidden inside the model and must be explicated. Since deep models are the intrinsic part of a model or model suite, we might try to develop deep models first before we develop normal models. 3. The layered approach has its potential and capacity.
We should also understand the limitations and the risks of this approach. 4. A model suite consists of a number of associated models. Some of them are dependent on others. If we use a layered approach then we could also use generators for models within a model suite. A typical generator is applied for generation of informative and representation models. 5. Generic and reference models combine, abstract, and generalise the experience one has gained while developing a number of models in the past. It seems thus to be a good idea to collect generic and reference model as stereotypes or pattern and then to use these models for derivation of normal models. 6. Data mining nicely demonstrates how a model can be calibrated to its real purpose. Another good example is inverse modelling where a generic model is used for refinement, calibration customi-zation, settlement, fitting, pruning, parameter instantiation, and operational adaption to origins and the world under consideration.
Let us now investigate whether our hypotheses can be supported and handled in a proper way. Models are masterpieces and would thus become work of an engineer if the model development process can be properly handled.
Engineering and software engineering (e.g. [13, 22]) distinguish between the five primary development dimensions: • Activities (‘how’) describe the way how the work is performed and the practises for the work. • Work products (‘what’) are the result of the specification and are used during specification. • Roles (‘who’) describe obligations and permissions, the involvement of actors in the specification process. • Aspects (‘where’) are used for separation of concern during the specification process. • Resources (‘on which basis’) are the basis for the specification.
Since a model (suite) is also a work product we may refine this approach to model engineering. The modelling method we will use is similar to the modelling method in mathematics [3].
The layered approach has already often and successfully been used in Computer Engineering. Most program language realisations follow this approach since COBOL and ALGOL 60 development (e.g. infrastructure definition; variable space; program space; interpreted or compiled code) and application development (e.g. application case; infrastructure; design; specialisation & tuning; deliver). Layering has also been the guiding paradigm behind text processing.
Model suite development and deployment will be based
on separation of concern into intrinsic and extrinsic parts
of models. Models typically consist from one side of a
normal model that displays all obviously relevant and
important aspects of a model and from the other side of
a deep model that intrinsically reflects commonly
accepted intentions, the accepted understanding, the
context, the background that is commonly accepted, and
restrictions for the model. The model suite will be
layered into models for initialisation, for strategic setup,
for tactic definition, for operational adaptation, and for
model delivery.
(I) The Initialisation Layer
The W*H specification pattern [9] can be applied to
model initialisation as well an includes then the
following set of statements: (i) a plan, function, and
purpose dimension (model as a conception: ‘wherefore’,
‘why’, ‘to what place or end’, ‘for when’, ‘for which
reason’) within a scenario in which the model is going to
be used as an instrument; (ii) a user or CoP dimension
(‘who’, ‘by whom’, ‘to whom’, ‘whichever’) that
describes the task portfolio in the CoP and profile of
users including beliefs, desires and intentions; (iii) an
application and a problem dimension (`in what particular
or respect’ , ‘from which’, ‘for what’, ‘where’,
`whence'); the added value dimension (evaluation). The
initialisation layer may also be enhanced by a contrast
space for user-related separation of a model and a
relevance space that is dependent on the user [11]. The
contrast and relevance spaces as a form of mind-setting
also define what is not of interest.
(II) The Enabling Setup Layer
The enabling intrinsic setup layer defines the
opportunity space and the infrastructure for the model.
The results will be from one side a deep model and from
the other side a modelling framework or modelling
mould that guides and govern next activities. We define
the context and the most of the background (the
grounding (paradigms, postulates, restrictions, theories,
culture, foundations) and the basis (assumptions, concept
world, practices, language as carrier, thought
community and thought style, methodology, pattern,
routines, common sense)) of the model. The context,
extrinsic, and strategic dimension answers question like
‘at or towards which’, ‘where about’, ‘to what place or
situation’, and ‘when’. Additionally, we decide which
methodology and environment seem to be the most
effective and purposeful. The development and
deployment dimension (‘how’, ‘whence’, ‘what in’,
‘what out’, ‘where’) defines the modelling methodology,
i.e. the modelling mould.
(III) The Extrinsic Source Reflection Layer
We separate the deep model elements from elements of
the normal model at the extrinsic source reflection layer.
According to the model function, the normal model
represents extrinsic elements of potential origins based
on their content and thus answers questions such as
‘what’, ‘with which’, and ‘by means of which’. It reflects
the extrinsic theory essentials that are necessarily to be
represented, e.g. conceptions or pre-conceptions from
the theory that is underpinning the application. The
normal model can be built from scratch (‘greenfield’
modelling). It is more usual based on the experience
gained so far. The latter case thus starts with a generic or
reference model that might incorporate parameters. The
extrinsic source reflection layer can be understood as a
tactical layer.
(IV) The Operational Customisation Layer
Generic or general normal models are adjusted to those
that a best fitted to those origins that are considered for
the application in the operational customisation layer.
This layer is sometimes holistically handled with
extrinsic reflection. Inverse modelling uses this layer for
adaptation of the model to the observational data (e.g.
data adaption in astrophysics or parameter instantiation
in most data mining processes). In some cases, this layer
seems to be trivial. It is not trivial in the general case
however. It instantiates parameters, adapts the normal
model to those origins (or data sources) that are really
under consideration, prepares the model for the special
use and to the special - most appropriate - solution, and
integrates the deep model with the normal model. The
normal model is typically pruned in order to become
simpler based on Solomonoff and Occam principled
deviation [
Model-backed reasoning is thus some kind of revisable reasoning depending on the stages of knowledge. Modelling becomes now a process that starts with deep models and continues with suites of generic models and revisable refinement according to data on hand. It should support handling of uncertainties and incompleteness of any kind and must thus make use of an integrated data management. Therefore, model-backed reasoning is properly based on layered model development.
Models can be used to render the theory offer. At the same time models may also render a theory. We claim that these two views can be integrated. The model functions thus as mediator [17]. The rendering procedures are however different. We envision that this integration can be based on the mappings in Figure 4.
Fig. 4 Models as integrating and mediating instruments Models can be understood as being composed of model concepts that are supported by data sources. We can now distinguish f-mappings at the same level, g-mappings between sources and concept, G--mappings from concepts to supporting sources, and h-embedding mappings from concepts to theory offers, models, or theories. Fig. 4 shows how the gap displayed in Fig. 2can be closed. A model consists of concepts which are derived from quantitative or theoretical concepts. The association between these two kinds is either handled similar to associations in a model suite or is directly integrated similar to integration of structural components from different database schemata.
Quantitative concepts are indicators or general quantitative properties. Model concepts are already abstractions from those quantitative concepts. Theoretical concepts in Fig. 3 are elements of a theory that is currently under development. The research task to be accomplished is the harmonisation of these mappings. This harmonisation can be based on the mappings for supporting resources if some commuting diagram properties are valid for model concepts and the model. For instance, quantitative concepts used in the CRC 1266 for support of reasoning as displayed in Fig. 3 are typicality of a property for the proxy concept, distribution (plants, ...) of properties within the proxies, the concept of a village (with an understanding from medieval times), evolution pattern that can be observed for proxies, exchange pattern, society and their members (within a modern interpretation), the variety of concepts of a center, concepts characterizing social structures and gender relations, and concepts characterizing architecture. Accepted hypotheses are, for example, are the existence of diachrony pattern for changes, chromatography of time series in the proxies, the existence of periods of dark ages, the human as a driver of development, the existence of gift exchange between societies (reciprocity), pattern of ritualistic behavior in 3 phases, pattern of kinds and styles of collaboration, and pattern of interaction among centers.
Theories of qualitative research use, for instance, concepts of evolution change, of climate change, of influence of climate change, of climate reactions, of sedimentation, concepts expressed as big man theories, and a number of concepts that might characterize the neolithication.
We thus use the model as some kind of twofold medium which has ‘Janus’ head behavior: it is both (I) a view of the theory-offer and (II) a view of the theory. It is a model (i) for the theory offer as a reflective “epistemic thing” [21] of discovery and a presupposition and (ii) of a theory as a specific viewpoint representation. It thus comprehends what has been developed for theory offers and supports explanations of the theory.
The development of a model has, however, also a feedback turn both on the theory offer and the theory. The model is then at the same time an instrument, a mediator, a companion, a middle, and a medium in the sense of [5]. The model itself thus becomes an investigation instrument.
Let us finally discuss an obstacle of quantitative research
that results in some obstinacy of models. Theory and
model development are in both cases evidence-based due
to the way how they are derived from proxies. The
O(bservation)-C(laims/Hypotheses)-E(vidence)R(easoning) pattern [7] starts with some observations
and detection of hypotheses about these observations.
Hypotheses are transformed into claims and research
questions that form a research agenda. Evidences are
then either systematically elicited from data, from
previous investigations, or from the belief and
knowledge space. Reasoning should then connect
evidences to the claims. The results are some kind of
Bayesian formulas representing the claim with the
evidence. Evidence-based reasoning combines therefore
inductive and abductive reasoning. It is enhanced by
Occam's razor approaches [19] that allow to finalize the
model development. It can be combined with
Solomonoff induction [
OCER pattern are the basis for evidence-based proxy reasoning (e.g. in the CRC 1266 [1]) that follow positive evidences. Evidence-based reasoning is based on the following principles: Models represent only acceptable possibilities (each model captures a distinct set of possibilities to which the current description refers) which are consistent with the premises and the knowledge gained so far what makes them intrinsically uncertain because they mirror only some properties they represent.
Models are proxy-driven (the structure of the model corresponds to the proxies it represents. They might also include abstractions such as negation. Models represent only what has been observed and not what is false in contrast to fully explicit models (that represent too what is false). The accuracy of the world view depends on the accuracy of proxies that are considered and the richness those.
We use pragmatic reasoning schemata (e.g. A causes B; B prevents C; therefore, A prevents C). Evidence-based reasoning thus makes a difference between deterministic conclusions (A cause B to occur: given A then B occurs) and ordered sets of possibilities (A enables B to occur: given A then it is possible for B to occur).
Models and model suites are one of the main instruments in science and technology. They support reasoning in various forms, e.g. by systematic revisable modelling based on data and as an associated collection of models. This paper develops an approach for development of fully fledged models (a) with extrinsic parts similar to usual (normal) models and (b) with intrinsic parts which are typically hidden in the modelling approach, in the background and context of the model, and in the intentions behind the model. While making this explicit, we are able to use a model as a problem description and to compute the solution of the problem under consideration directly from the model. The paper presents the first methodological part of this solution. The development of corresponding tools and the implementation are topics of a forthcoming paper. The presented layered approach should not be applied as a 1-2-3-4-5 waterfall sequence of activities. Rather, model development and model utilisation use an evolutionary approach that returns to previous steps whenever sufficiency characteristics of models become problematic within the application domain. The layers can however be considered as phases of development. We notice that our layered approach also supports model revision and model evolution. It can also be used for model migration and model reengineering.
The layered approach seems to be combinable with modelling cultures, e.g. those that can be observed for our first case study [14]. The approach is based on a separation of concern within an initialisation layer, within an intrinsic and this implicit setup layer, within an extrinsic and thus explicit source reflection layer, within an operational customisation layer, and finally with a model delivery layer.
CRC 1266. Scales of transformation - Humanenvironmental interaction in prehistoric and