Is it possible to have a generic theory of error

Essentially, true score theory maintains that every measurement is an additive composite of two components: true ability or the true level of the respondent on that measure; and random error.

That is, across a set of scores, we assume that:. In more human terms this means that the variability of your measure is the sum of the variability due to true score and the variability due to random error. This will have important implications when we consider some of the more advanced models for adjusting for errors in measurement.

Why is true score theory important? For one thing, it is a simple yet powerful model for measurement. It reminds us that most measurement has an error component.

Second, true score theory is the foundation of reliability theory. Generally, a theory may be defined as a set of analytical principles or statements designed to structure our observation, understanding and explanation of the world [ 29 - 31 ]. Authors usually point to a theory as being made up of definitions of variables, a domain where the theory applies, a set of relationships between the variables and specific predictions [ 32 - 35 ]. Theories can be described on an abstraction continuum.

High abstraction level theories general or grand theories have an almost unlimited scope, middle abstraction level theories explain limited sets of phenomena and lower level abstraction theories are empirical generalizations of limited scope and application [ 30 , 36 ].

A model typically involves a deliberate simplification of a phenomenon or a specific aspect of a phenomenon.

Models need not be completely accurate representations of reality to have value [ 31 , 37 ]. Models are closely related to theory and the difference between a theory and a model is not always clear. Models can be described as theories with a more narrowly defined scope of explanation; a model is descriptive, whereas a theory is explanatory as well as descriptive [ 29 ]. A framework usually denotes a structure, overview, outline, system or plan consisting of various descriptive categories, e.

Frameworks do not provide explanations; they only describe empirical phenomena by fitting them into a set of categories [ 29 ]. Thus, five categories of theoretical approaches used in implementation science can be delineated Table 1 ; Figure 1 :.

Three aims of the use of theoretical approaches in implementation science and the five categories of theories, models and frameworks. Although theories, models and frameworks are distinct concepts, the terms are sometimes used interchangeably in implementation science [ 9 , 14 , 39 ].

A theory in this field usually implies some predictive capacity e. Frameworks in implementation science often have a descriptive purpose by pointing to factors believed or found to influence implementation outcomes e. Neither models nor frameworks specify the mechanisms of change; they are typically more like checklists of factors relevant to various aspects of implementation.

Models by Huberman [ 40 ], Landry et al. Early research-to-practice or knowledge-to-action models tended to depict rational, linear processes in which research was simply transferred from producers to users. However, subsequent models have highlighted the importance of facilitation to support the process and placed more emphasis on the contexts in which research is implemented and used.

Thus, the attention has shifted from a focus on production, diffusion and dissemination of research to various implementation aspects [ 21 ]. Action models elucidate important aspects that need to be considered in implementation practice and usually prescribe a number of stages or steps that should be followed in the process of translating research into practice.

Action models have been described as active by Graham et al. It should be noted that the terminology is not fully consistent, as some of these models are referred to as frameworks, for instance the Knowledge-to-Action Framework [ 46 ].

The how-to-implement models typically emphasize the importance of careful, deliberate planning, especially in the early stages of implementation endeavours.

In many ways, they present an ideal view of implementation practice as a process that proceeds step-wise, in an orderly, linear fashion.

Still, authors behind most models emphasize that the actual process is not necessarily sequential. Many of the action models mentioned here have been subjected to testing or evaluation, and some have been widely applied in empirical research, underscoring their usefulness [ 9 , 55 ]. The process models vary with regard to how they were developed. In contrast, models such as the Knowledge-to-Action Framework [ 45 ] and the Quality Implementation Framework [ 27 ] have relied on literature reviews of theories, models, frameworks and individual studies to identify key features of successful implementation endeavours.

Determinant frameworks describe general types also referred to as classes or domains of determinants that are hypothesized or have been found to influence implementation outcomes, e.

Some frameworks also hypothesize relationships between these determinants e. Information about what influences implementation outcomes is potentially useful for designing and executing implementation strategies that aim to change relevant determinants.

The determinant frameworks do not address how change takes place or any causal mechanisms, underscoring that they should not be considered theories. Many frameworks are multilevel, identifying determinants at different levels, from the individual user or adopter e. Hence, these integrative frameworks recognize that implementation is a multidimensional phenomenon, with multiple interacting influences.

The determinant frameworks were developed in different ways. Many frameworks e. Other frameworks have relied on existing determinant frameworks and relevant theories in various disciplines, e.

Meanwhile, PARIHS Promoting Action on Research Implementation in Health Services [ 5 , 64 ] emerged from the observation that successful implementation in health care might be premised on three key determinants characteristics of the evidence, context and facilitation , a proposition which was then analysed in four empirical case studies; PARIHS has subsequently undergone substantial research and development work [ 64 ] and has been widely applied [ 65 ].

Theoretical Domains Framework represents another approach to developing determinant frameworks. It was constructed on the basis of a synthesis of constructs related to behaviour change found in 33 behaviour change theories, including many social cognitive theories [ 10 ].

The constructs are sorted into 14 theoretical domains originally 12 domains , e. Theoretical Domains Framework does not specify the causal mechanisms found in the original theories, thus sharing many characteristics with determinant frameworks. The determinant frameworks account for five types of determinants, as shown in Table 2 , which provides details of eight of the most commonly cited frameworks in implementation science.

The frameworks are superficially quite disparate, with a broad range of terms, concepts and constructs as well as different outcomes, yet they are quite similar with regard to the general types of determinants they account for. Hence, implementation researchers agree to a large extent on what the main influences on implementation outcomes are, albeit to a lesser extent on which terms that are best used to describe these determinants.

Outcomes differ correspondingly, from adherence to guidelines and research use, to successful implementation of interventions, innovations, evidence, etc. The relevance of the end users e. Determinant frameworks imply a systems approach to implementation because they point to multiple levels of influence and acknowledge that there are relationships within and across the levels and different types of determinants.

A system can be understood only as an integrated whole because it is composed not only of the sum of its components but also by the relationships among those components [ 68 ]. However, determinants are often assessed individually in implementation studies e. For instance, there could be synergistic effects such that two seemingly minor barriers constitute an important obstacle to successful outcomes if they interact. Surveying the perceived importance of a finite set of predetermined barriers can yield insights into the relative importance of these particular barriers but may overlook factors that independently affect implementation outcomes.

Furthermore, there is the issue of whether the barriers and enablers are the actual determinants i. The perceived importance of particular factors may not always correspond with the actual importance. The context is an integral part of all the determinant frameworks. Still, context is generally understood as the conditions or surroundings in which something exists or occurs, typically referring to an analytical unit that is higher than the phenomena directly under investigation.

The role afforded the context varies, from studies e. Hence, although implementation science researchers agree that the context is a critically important concept for understanding and explaining implementation, there is a lack of consensus regarding how this concept should be interpreted, in what ways the context is manifested and the means by which contextual influences might be captured in research.

The different types of determinants specified in determinant frameworks can be linked to classic theories. Implementation researchers are also wont to apply theories from other fields such as psychology, sociology and organizational theory. These theories have been referred to as classic or classic change theories to distinguish them from research-to-practice models [ 45 ]. They might be considered passive in relation to action models because they describe change mechanisms and explain how change occurs without ambitions to actually bring about change.

Theories regarding the collective such as health care teams or other aggregate levels are relevant in implementation science, e. However, their use is not as prevalent as the individual-level theories. There is increasing interest among implementation researchers in using theories concerning the organizational level because the context of implementation is becoming more widely acknowledged as an important influence on implementation outcomes.

Theories concerning organizational culture, organizational climate, leadership and organizational learning are relevant for understanding and explaining organizational influences on implementation processes [ 21 , 53 , 57 , 94 - ]. Several organization-level theories might have relevance for implementation science.

For instance, Estabrooks et al. Meanwhile, Grol et al. However, despite increased interest in organizational theories, their actual use in empirical implementation studies thus far is relatively limited. Furthermore, the Theory of Diffusion highlights the importance of intermediary actors opinion leaders, change agents and gate-keepers for successful adoption and implementation [ ], which is reflected in roles described in numerous implementation determinant frameworks e.

The Theory of Diffusion is considered the single most influential theory in the broader field of knowledge utilization of which implementation science is a part [ ]. There are also numerous theories that have been developed or adapted by researchers for potential use in implementation science to achieve enhanced understanding and explanation of certain aspects of implementation. Some of these have been developed by modifying certain features of existing theories or concepts, e.

Examples include theories such as Implementation Climate [ ], Absorptive Capacity [ ] and Organizational Readiness [ ]. The adaptation allows researchers to prioritize aspects considered to be most critical to analyse issues related to the how and why of implementation, thus improving the relevance and appropriateness to the particular circumstances at hand.

COM-B Capability, Opportunity, Motivation and Behaviour represents another approach to developing theories that might be applicable in implementation science. This theory began by identifying motivation as a process that energizes and directs behaviour. Capability and opportunity were added as necessary conditions for a volitional behaviour to occur, given sufficient motivation, on the basis of a US consensus meeting of behavioural theorists and a principle of US criminal law which considers prerequisites for performance of specified volitional behaviours [ ].

COM-B posits that capability, opportunity and motivation generate behaviour, which in turn influences the three components. Opportunity and capability can influence motivation, while enacting a behaviour can alter capability, motivation and opportunity [ 66 ]. Another theory used in implementation science, the Normalization Process Theory [ ], began life as a model, constructed on the basis of empirical studies of the implementation of new technologies [ ].

The model was subsequently expanded upon and developed into a theory as change mechanisms and interrelations between various constructs were delineated [ ]. The theory identifies four determinants of embedding i. There is a category of frameworks that provide a structure for evaluating implementation endeavours.

Both frameworks specify implementation aspects that should be evaluated as part of intervention studies. Proctor et al.

On the basis of a narrative literature review, they propose eight conceptually distinct outcomes for potential evaluation: acceptability, adoption also referred to as uptake , appropriateness, costs, feasibility, fidelity, penetration integration of a practice within a specific setting and sustainability also referred to as maintenance or institutionalization.

Although evaluation frameworks may be considered in a category of their own, theories, models and frameworks from the other four categories can also be applied for evaluation purposes because they specify concepts and constructs that may be operationalized and measured. For instance, Theoretical Domains Framework e. Furthermore, many theories, models and frameworks have spawned instruments that serve evaluation purposes, e. Implementation science has progressed towards increased use of theoretical approaches to address various implementation challenges.

While this article is not intended as a complete catalogue of all individual approaches available in implementation science, it is obvious that the menu of potentially useable theories, models and frameworks is extensive.

Researchers in the field have pragmatically looked into other fields and disciplines to find relevant approaches, thus emphasizing the interdisciplinary and multiprofessional nature of the field. This article proposes a taxonomy of five categories of theories, models and frameworks used in implementation science.

For instance, systematic reviews and overviews by Graham and Tetroe [ 25 ], Mitchell et al. However, what matters most is not how an individual approach is labelled; it is important to recognize that these theories, models and frameworks differ in terms of their assumptions, aims and other characteristics, which have implications for their use. There is considerable overlap between some of the categories.

Thus, determinant frameworks, classic theories and implementation theories can also help to guide implementation practice i. They can also be used for evaluation because they describe aspects that might be important to evaluate. A framework such as the Active Implementation Frameworks [ 68 ] appears to have a dual aim of providing hands-on support to implement something and identifying determinants of this implementation that should be analysed.

Despite the overlap between different theories, models and frameworks used in implementation science, knowledge about the three overarching aims and five categories of theoretical approaches is important to identify and select relevant approaches in various situations.

While the relevance of addressing barriers and enablers to translating research into practice is mentioned in many process models, these models do not identify or systematically structure specific determinants associated with implementation success. Another key difference is that process models recognize a temporal sequence of implementation endeavours, whereas determinant frameworks do not explicitly take a process perspective of implementation since the determinants typically relate to implementation as a whole.

Theories applied in implementation science can be characterized as middle level. Higher level theories can be built from theories at lower abstraction levels, so-called theory ladder climbing [ ].

Still, it seems unlikely that there will ever be a grand implementation theory since implementation is too multifaceted and complex a phenomenon to allow for universal explanations. There has been debate in the policy implementation research field for many years whether researchers should strive to produce a theory applicable to public policy as a whole [ 38 ].

Determinant frameworks in implementation science clearly suggest that many different theories are relevant for understanding and explaining the many influences on implementation. The use of a single theory that focuses only on a particular aspect of implementation will not tell the whole story. Choosing one approach often means placing weight on some aspects e. The extension of the methods developed in the present paper to this class of problems could bring out some new features that deserve being identified.

Finally, another direction for extending the present work would be to address error dynamics arising both from sensitivity to the initial conditions and from the model uncertainties within a unified formalism. Citation: Journal of the Atmospheric Sciences 60, 17; Sign in Sign up.

Advanced Search Help. Journal of the Atmospheric Sciences. Sections Abstract 1. Introduction 2. Deterministic dynamics of model error: Formulation 3. Probabilistic dynamics of model error 4. Model error in bifurcating and bistable systems a. Periodic behavior b. Quasi-periodic behavior c. Model error in the presence of chaotic dynamics: Two case studies 6. Export References. Vannitsem , and J-F. Webster , and E. Export Figures View in gallery Time evolution of the model mean-square error in a bistable system [ Eq.

Close View raw image Time evolution of the model mean-square error in a bistable system [ Eq. View raw image a Typical time evolution of a single realization of the square error and b a two-dimensional phase plot along its y and x components as obtained from model I. View raw image Probability density of the mean-square error at increasing times as obtained from model I and 10 5 realizations.

Chart I. Tracks of Centers of Anticyclones, December, Author: P. Previous Article Next Article. Editorial Type: Article. Nicolis 1. CO;2 Page s : — Article History. Download PDF. Full access. Introduction Natural complex systems like the atmosphere are believed to be robust on the grounds that they are the results of a long evolution, during which they have adapted to the environmental conditions.

The behavior of the system changes qualitatively, in the sense that the previously prevailing solution loses its stability and new stable regimes are taking over.

This phenomenon of bifurcation reveals the existence of a second kind of sensitivity associated to a temporary loss of structural stability that, in view of the foregoing discussion, can be referred to as sensitivity to the parameters. In atmospheric and climate dynamics this scenario may account for the sudden events associated with the glaciation—deglaciation cycles, or for possible switchings of circulation patterns that could arise from, among others, anthropogenic effects. The qualitative behavior remains the same, but the structure of the attractor and, hence, other dynamical properties such as mean values, characteristic times, predictability, etc.

If the reference regime is a simple one, like a steady state, the effect of this kind of parameter sensitivity is expected to be mild.

But when superposed to the sensitivity to initial conditions characteristic of the real-world atmosphere it may have some far reaching consequences and complicate further the issue of prediction Leith Deterministic dynamics of model error: Formulation A first question pertains to the short time evolution of model error averaged over the underlying attractor of the exact dynamics.

The model equations thus have the form. First, multiplying Eq. On the other hand, using Eq. A full answer to the role of the Lyapunov exponents in model error growth can be given for the simple example. Probabilistic dynamics of model error In this section we explore the probabilistic structure of model errors. Using Eq. Model error in bifurcating and bistable systems In this and the following section we analyze the dynamical and statistical aspects of model error in some generic classes of deterministic dynamical systems of relevance in atmospheric physics.

Periodic behavior The dynamics reduces to the normal form of the Hopf bifurcation:. We define the normalized error in this case as. Suppose finally that the time evolution of nature contains an additional contribution of the form [cf.

Quasi-periodic behavior The dynamics reduces to the normal form. Bistable systems The canonical form of evolution equation for a bistable system is.

Thanks to the simplicity of Eq. Utilizing the explicit form of the exact solution one obtains after a standard calculation:. Model error in the presence of chaotic dynamics: Two case studies In this section we carry out numerical experiments on error growth dynamics in the light of the analysis of sections 2 and 3 , in two representative low-order models giving rise to chaotic dynamics: Lorenz's three-mode truncation of the Boussinesq equations of thermal convection Lorenz ,.

For illustrative purposes we shall address the effect of these latter terms for model I only. That compiles for me Your code doesn't match the error message. Is there a reason that Foo doesn't have where T : Concrete?

ZaidMasud thanks; with that edit: there is no regular way to do that. You can hack it with reflection MakeGenericMethod etc , but that is not a good answer. Show 3 more comments. Active Oldest Votes. CreateInstance generic ; Don't let it the chance to do it. Improve this answer. LightStriker LightStriker Add a comment.

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