Non-additive Models Research Articles

The Bayesian Analysis of a Nonadditive Model

Abstract A Bayesian analysis of a model for two-group experimentation is given. This model assumes that responses in one group are systematically related to responses in the other group through a general linear function using both multiplicative and additive parameters.

The Bayesian Analysis of a Nonadditive Model

The Bayesian Analysis of a Nonadditive Model

Nonadditive measures of average charge for heterogeneous questionnaires

Mechanical and logical systems admit an ‘additivity’ law of measures. However in other systems, such as biological and social systems, this may not hold. A simple non-additive model based on λ -non-additivity is considered. We characterize average charge for heterogeneous questionnaires under λ -nonadditivity and show that there are only two forms of the measure of charge, one containing one parameter and the other two. Limiting and particular cases cover those studied earlier. The average charges are shown to be bounded below by two non-additive mean value entropies of order 1, type β and order α , type β respectively.

Pyramid and Semicube Decompositions of Multiattribute Utility Functions

We apply the fractional hypercube decomposition theorem for multiattribute utility functions to the quasi-pyramid, the pyramid, and the semicube fractions. The resulting nonadditive utility models illustrate the broad range of decompositions that can be obtained with this fractional hypercube methodology. The pyramid decompositions have nonseparable interaction terms for each pair of attributes, whereas the semicube decomposition has nonseparable interaction terms for each proper subset of attributes. The computations and scaling illustrated here can be performed with other fractional hypercubes to produce various results between these two extremes.

Non-Additive Models for Policy Research: A Longitudinal Evaluation

Non-Additive Models for Policy Research: A Longitudinal Evaluation

Non-Additive Models for Policy Research: A Longitudinal Evaluation

O NE of the more active areas of political science research in recent years has been the relationship of socioeconomic and political variables to policy outputs (usually measured as expenditures) of the political system. This literature is by now quite voluminous and cannot be reviewed extensively here.1 We are interested more specifically in one recent attempt to apply an alternative means of statistical explanation to the data through the use of non-additive multiple regression.2 The vast majority of the literature on the correlates of public policies, both in the American states and cross-nationality, has been based on a linear, additive regression model.3 Strouse and Williams, however, have argued that a multiplicative regression is perhaps more appropriate to explain policy under certain conditions. They argue that

Comment on "A Non-Additive Model for State Policy Research"

P ROFESSORS STROUSE AND WILLIAMS (hereafter SW) have questioned the adequacy of the linear model and have attempted to demonstrate the utility of a nonadditive model in state policy research.1 A number of confusing aspects of the article led us to reestimate the SW data, and we reach the opposite conclusion about choice of models.2 Our major criticisms relate to the tests for significance in the proportion of variance explained (R2) appearing in the SW article. Several other troublesome aspects of the SW argument will be mentioned only in passing. For example, the graphic representations of the additive and nonadditive models are confusing. Have SW plotted three dimensions into two by holding one of the variables constant? How does a threshold effect arise in an exponential or

Simple Nonadditive Dual Resonance Model

A nonadditive model with spin degrees of freedom but no internal symmetry is studied. It is necessary to work in a space of ten or more dimensions in order to obtain a Hermitian Hamiltonian. The model possesses physical-particle creation operators and, rather surprisingly for a nonadditive model, all trajectories are linear. In ten dimensions the model appears to be equivalent to the Neveu-Schwarz model, but the trajectories with half-integral intercept are obtained even though all our operators have integral $n$. The gauge conditions associated with the $L$ and $K$ algebras are almost certainly sufficient to remove all the ghosts.

KDegeneracy in Nonadditive Dual Resonance Models

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Some statistical aspects of partitioning genotype-environmental components of variability.

The usual regression approach to explaining genotype-environment interaction is considered, using a non-additive model, and the statistical validity of the analysis is discussed. An alternative approach for dividing genotype-environment interaction into components, one corresponding to each genotype, is proposed, and the optimum properties are discussed. The alternative approach is then extended to take into account a covariate. The relationship of the new approach to the regression approach is discussed, and a numerical example is given

A Multivariate Extension of Tukey's One Degree of Freedom for Non-Additivity

Abstract An extension of Tukey's one degree of freedom for non-additivity is given for the multivariate two-way cross-classification model. The hypothesis considered is that the multivariate model is additive with respect to each response (variate) against the alternative that at least one response requires a non-additive model.

A Non-Additive Model for State Policy Research

Recent research in state policy outputs has assumed the adequacy of linear models in explaining the relations between socio-economic and political variables on the one hand and state expenditures on the other. The findings of this research, that state policy outputs are largely predicated on system resources or the ability of a state to pay, are well known.' Thus political variables, such as inter-

Statistical Interaction and Parole Prediction

Many sociological theories imply interaction effects and researclh often fails to take these into account. This article relates situation, identifications and value orientations to parole outcome. Data are presented showing that distribution of parole successes and failu1res is polarized when combinations of independent variables are accounted for. any sociological theories imply interaction effects and research often fails to take these into account. Whenever it is possible to develop a rationale for predicting interaction, there should be a conscious effort to construct and test theories that explicitly take advantage of interaction effects. As to the distinct advantage of this approach, nonadditive models can generate predictions even where measurement has been very crude and while such predictions are not ordinarily incorporated in sociological theory, they are helpful in ordering what could otherwise appear to be chaotic empirical findings (see Palmore and Hammond, 1964; Blalock, 1965: 374). One particular area where such an application may be extremely useful is in predicting parole success. A rationale to demonstrate the feasibility of applying an interaction model to parole prediction can be found in the work of Albert Cohen (1955) which presents one of the major systematic theories of deviant behavior. Basically, he considers the sources of behavior to be either the situation or the frame of reference. The latter includes both internalized value orientations of the individual and reference groups which reinforce these values. Thus, according to Cohen, the world of the individual can be divided into three interdependent but analytically distinct parts. These are: (1) the situation, i.e., the external social and economic world in which the individual is located; (2) identifications, or the groups whose norms and values the individual accepts as his own; and (3) value orientations which the individual has internalized.

General models for quantal response to the joint action of a mixture of drugs

This paper is concerned with mathematical models for the representation of the joint action of mixtures of drugs. The organisms under examination are assumed to embody one or more separate physiological systems, each of which may be affected by any of the drugs in the mixture. The effect of the mixture on a given physiological system is assumed to take the form of a quantitative 'reaction', whose level is expressed as the difference between a function of the doses of the drugs (the 'effect function') and the 'tolerance' of the particular system. The tolerances of the various systems are assumed to follow a characteristic joint distribution in the population of organisms. A particular type of quantal or semi-quantal response is assumed to occur when the combined reaction of the various systems, which may be regarded as a vector quantity, falls within a prescribed region in the 'reaction space'. The probability of response may then be expressed as the integral of the joint tolerance distribution over a region whose boundaries are functions of the doses. It is emphasized that, as far as the probability of response is concerned, the choice of the number of systems and of the form of the tolerance distribution is arbitrary, in that a given situation may be expressed in terms of a variety of different representations. The derivation of various types of single and multiple system models is examined and it is shown how a group of infinite system models may be generated from the multiple system representation. The concept of interaction is discussed and a mathematical definition of non-interactive joint action is derived. The analysis of semi-quantal response data is considered and it is shown that it is impossible to determine whether one or more physiological systems is involved on the basis of quantal response data alone. The classification of models for the analysis of quantal response data is then examined. It is shown that definitions of 'similar ', 'partially similar' and 'independent' action given in the literature do not correspond to any specific properties of the probability of response. Alternative criteria for similar and independent action are put forward. A new model for the joint action of a mixture of drugs, which combines additivity of the doses with non-parallelism of the dosage-response lines for the individual drugs, is derived from the infinite system representation. An example is given of the application of this new model, in comparison with a non-additive model, to the analysis of data from surveys of lung disease in coal miners.

Interactions, Configurations, and Nonadditive Models

Interactions, Configurations, and Nonadditive Models