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From Wikipedia
An organizational structure consists of activities such as task allocation, coordination and supervision, which are directed towards the achievement of organizational aims. It can also be considered as the viewing glass or perspective through which individuals see their organization and its environment.
Many organizations have hierarchical structures, but not all.
Organizations are a variant of clustered entities.
An organization can be structured in many different ways, depending on their objectives. The structure of an organization will determine the modes in which it operates and performs.
Organizational structure allows the expressed allocation of responsibilities for different functions and processes to different entities such as the branch, department, workgroup and individual.
Organizational structure affects organizational action in two big ways. First, it provides the foundation on which standard operating procedures and routines rest. Second, it determines which individuals get to participate in which decisionmaking processes, and thus to what extent their views shape the organizationâ€™s actions.
Operational organizations and informal organizations
The set organizational structure may not coincide with facts, evolving in operational action. Such divergence decreases performance, when growing. E.g. a wrong organizational structure may hamper cooperation and thus hinder the completion of orders in due time and within limits of resources and budgets. Organizational structures shall be adaptive to process requirements, aiming to optimize the ratio of effort and input to output.
History
Organizational structures developed from the ancient times of hunters and collectors in tribal organizations through highly royal and clerical power structures to industrial structures and today's postindustrial structures.
As pointed out by Mohr (1982, pp. 102â€“103), the early theorists of organizational structure, Taylor, Fayol, and Weber "saw the importance of structure for effectiveness and efficiency and assumed without the slightest question that whatever structure was needed, people could fashion accordingly. Organizational structure was considered a matter of choice... When in the 1930s, the rebellion began that came to be known as human relations theory, there was still not a denial of the idea of structure as an artifact, but rather an advocacy of the creation of a different sort of structure, one in which the needs, knowledge, and opinions of employees might be given greater recognition." However, a different view arose in the 1960s, suggesting that the organizational structure is "an externally caused phenomenon, an outcome rather than an artifact." In the 21st century, organizational theorists such as Lim, Griffiths, and Sambrook (2010) are once again proposing that organizational structure development is very much dependent on the expression of the strategies and behavior of the management and the workers as constrained by the power distribution between them, and influenced by their environment and the outcome.
Organizational structure types
Prebureaucratic structures
Prebureaucratic (entrepreneurial) structures lack standardization of tasks. This structure is most common in smaller organizations and is best used to solve simple tasks. The structure is totally centralized. The strategic leader makes all key decisions and most communication is done by one on one conversations. It is particularly useful for new (entrepreneurial) business as it enables the founder to control growth and development.
They are usually based on traditional domination or charismatic domination in the sense of Max Weber's tripartite classification of authority.
Bureaucratic structures
Weber (1948, p. 214) gives the analogy that â€œthe fully developed bureaucratic mechanism compares with other organizations exactly as does the machine compare with the nonmechanical modes of production. Precision, speed, unambiguity, â€¦ strict subordination, reduction of friction and of material and personal costs these are raised to the optimum point in the strictly bureaucratic administration.â€� Bureaucratic structures have a certain degree of standardization. They are better suited for more complex or larger scale organizations. They usually adopt a tall structure. Then tension between bureaucratic structures and nonbureaucratic is echoed in Burns and Stalker distinction between mechanistic and organic structures. It is not the entire thing about bureaucratic structure. It is very much complex and useful for hierarchical structures organization, mostly in tall organizations.
Postbureaucratic
The term of post bureaucratic is used in two senses in the organizational literature: one generic and one much more specific . In the generic sense the term post bureaucratic is often used to describe a range of ideas developed since the 1980s that specifically contrast themselves with Weber's ideal type bureaucracy. This may include total quality management, culture management and matrix management, amongst others. None of these however has left behind the core tenets of Bureaucracy. Hierarchies still exist, authority is still Weber's rational, legal type, and the organization is still rule bound. Heckscher, arguing along these lines, describes them as cleaned up bureaucracies , rather than a fundamental shift away from bureaucracy. Gideon Kunda, in his classic study of culture management at 'Tech' argued that 'the essence of bureaucratic control  the formalisation, codification and enforcement of rules and regulations  does not change in principle.....it shifts focus from organizational structure to the organization's culture'.
Another smaller group of theorists have developed the theory of the PostBureaucratic Organization., provide a detailed discussion which attempts to describe an organization that is fundamentally not bureaucratic. Charles Heckscher has developed an ideal type, the postbureaucratic organization, in which decisions are based on dialogue and consensus rather than authority and command, the organization is a network rather than a hierarchy, open at the boundaries (in direct contrast to culture management); there is an emphasis on metadecision making rules rather than decision making rules. This sort of horizontal decision making by consensus model is often used in abstract algebra, an algebraic structure consists of one or more sets, called underlying sets or carriers or sorts, closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The notion of algebraic structure has been formalized in universal algebra.
As an abstraction, an "algebraic structure" is the collection of all possible models of a given set of axioms. More concretely, an algebraic structure is any particular model of some set of axioms. For example, the monster group both "is" an algebraic structure in the concrete sense, and abstractly, "has" the group structure in common with all other groups. This article employs both meanings of "structure."
This definition of an algebraic structure should not be taken as restrictive. Anything that satisfies the axioms defining a structure is an instance of that structure, regardless of how many other axioms that instance happens to have. For example, all groups are also semigroups and magmas.
Structures whose axioms are all identities
If the axioms defining a structure are all identities, the structure is a variety (not to be confused with algebraic variety in the sense of algebraic geometry). Identities are equations formulated using only the operations the structure allows, and variables that are tacitly universally quantified over the relevant universe. Identities contain no connectives, existentially quantified variables, or relations of any kind other than the allowed operations. The study of varieties is an important part of universal algebra.
All structures in this section are varieties. Some of these structures are most naturally axiomatized using one or more nonidentities, but are nevertheless varieties because there exists an equivalent axiomatization, one perhaps less perspicuous, composed solely of identities. Algebraic structures that are not varieties are described in the following section, and differ from varieties in their metamathematical properties.
In this section and the following one, structures are listed in approximate order of increasing complexity, operationalized as follows:
 Simple structures requiring but one set, the universe S, are listed before composite ones requiring two sets;
 Structures having the same number of required sets are then ordered by the number of binary operations (0 to 4) they require. Incidentally, no structure mentioned in this entry requires an operation whose arity exceeds 2;
 Let A and B be the two sets that make up a composite structure. Then a composite structure may include 1 or 2 functions of the form AxAâ†’B or AxBâ†’A;
 Structures having the same number and kinds of binary operations and functions are more or less ordered by the number of required unary and 0ary (distinguished elements) operations, 0 to 2 in both cases.
The indentation structure employed in this section and the one following is intended to convey information. If structure B is under structure A and more indented, then all theorems of A are theorems of B; the converse does not hold.
Ringoids and lattices can be clearly distinguished despite both having two defining binary operations. In the case of ringoids, the two operations are linked by the distributive law; in the case of lattices, they are linked by the absorption law. Ringoids also tend to have numerical models, while lattices tend to have settheoretic models.
Simple structures: No binary operation:
 Set: a degenerate algebraic structure having no operations.
 Pointed set: S has one or more distinguished elements, often 0, 1, or both.
 Unary system: S and a single unary operation over S.
 Pointed unary system: a unary system with S a pointed set.
Grouplike structures:
One binary operation, denoted by concatenation. For monoids, boundary algebras, and sloops, S is a pointed set.
 Magma or groupoid: S and a single binary operation over S.
 Steiner magma: A commutative magma satisfying x(xy) = y.
 Squag: an idempotent Steiner magma.
 Sloop: a Steiner magma with distinguished element 1, such that xx = 1.
 Semigroup: an statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions. This definition of SEM was articulated by the geneticist Sewall Wright (1921), the economist Trygve Haavelmo (1943) and the cognitive scientist Herbert Simon (1953), and formally defined by Judea Pearl (2000) using a calculus of counterfactuals.
Structural Equation Models (SEM) allow both confirmatory and exploratory modeling, meaning they are suited to both theory testing and theory development. Confirmatory modeling usually starts out with a hypothesis that gets represented in a causal model. The concepts used in the model must then be operationalized to allow testing of the relationships between the concepts in the model. The model is tested against the obtained measurement data to determine how well the model fits the data. The causal assumptions embedded in the model often have falsifiable implications which can be tested against the data.
With an initial theory SEM can be used inductively by specifying a corresponding model and using data to estimate the values of free parameters. Often the initial hypothesis requires adjustment in light of model evidence. When SEM is used purely for exploration, this is usually in the context of exploratory factor analysis as in psychometric design.
Among the strengths of SEM is the ability to construct latent variables: variables which are not measured directly, but are estimated in the model from several measured variables each of which is predicted to 'tap into' the latent variables. This allows the modeler to explicitly capture the unreliability of measurement in the model, which in theory allows the structural relations between latent variables to be accurately estimated. Factor analysis, path analysis and regression all represent special cases of SEM.
In SEM, the qualitative causal assumptions are represented by the missing variables in each equation, as well as vanishing covariances among some error terms. These assumptions are testable in experimental studies and must be confirmed judgmentally in observational studies.
Steps in performing SEM analysis
Model specification
When SEM is used as a confirmatory technique, the model must be specified correctly based on the type of analysis that the researcher is attempting to confirm. When building the correct model, the researcher uses two different kinds of variables, namely exogenous and endogenous variables. The distinction between these two types of variables is whether the variable regresses on another variable or not. As in regression the dependent variable (DV) regresses on the independent variable (IV), meaning that the DV is being predicted by the IV. In SEM terminology, other variables regress on exogenous variables. Exogenous variables can be recognized in a graphical version of the model, as the variables sending out arrowheads, denoting which variable it is predicting. A variable that regresses on a variable is always an endogenous variable, even if this same variable is also used as a variable to be regressed on. Endogenous variables are recognized as the receivers of an arrowhead in the model.
It is important to note that SEM is more general than regression. In particular a variable can act as both independent and dependent variable.
Two main components of models are distinguished in SEM: the structural model showing potential causal dependencies between endogenous and exogenous variables, and the measurement model showing the relations between latent variables and their indicators. Exploratory and Confirmatory factor analysis models, for example, contain only the measurement part, while path diagrams can be viewed as an SEM that only has the structural part.
In specifying pathways in a model, the modeler can posit two types of relationships: (1) free pathways, in which hypothesised causal (in fact counterfactual) relationships between variables are tested, and therefore are left 'free' to vary, and (2) relationships between variables that already have an estimated relationship, usually based on previous studies, which are 'fixed' in the model.
A modeller will often specify a set of theoretically plausible models in order to assess whether the model proposed is the best of the set of possible models. Not only must the modeller account for the theoretical reasons for building the model as it is, but the modeller must also take into account the number of data points and the number of parameters that the model must estimate to identify the model. An identified model is a model where a specific parameter value uniquely identifies the model, and no other equivalent formulation can be given by a different parameter value. A data point is a variable with observed scores, like a variable containing the scores on a question or the number of times respondents buy a car. The parameter is the value of interest, which might be a regression coefficient between the exogenous and the endogenous variable or the factor loading (regression coefficient between a indicator and its factor). If there are fewer data points than the number of estimated parameters, the resulting model is "unidentified" , since there are too few reference points to account for all the variance in the model. The solution is to constrain one of the paths to zero, which means that it is no longer part of the model.
Estimation of free parameters
Parameter estimation is done by comparing the actual covariance matrices representing the relationships between variables and the estimated covariance matrices of the best fitting model. This is obtained through numerical maximization of a fit criterion as provided by maximum likelihood estimation, weighted least squares or asymptotically distributionfree methods. This is often accomplished by using a specialized SEM analysis program of which several exist.
Assessment of fit
Assessment of fit is a basic task in SEM modeling: forming the basis for accepting or rejecting models and, more usually, accepting one competing model over an
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