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In this paper, a rigorous mathematical analysis of the Krasnoshchekov model is presented. We have shown that in case a community does not contain any group of people having zero resistance to interpersonal influence, which are moreover isolated from the pressure of the rest of community, the Krasnoshchekov opinion readjustment procedure can be reduced to the Friedkin-Johnsen dynamics. In turn, if one repeats the Krasnoshchekov opinion updating rule, the corresponding dynamics forces individuals' opinions to converge eventually to some terminal opinions, which are a consensus under the same conditions as in the French-Harary-DeGroot dynamics. Otherwise, the Krasnoshchekov dynamics exhibits patterns, which are much closer to the behavior of electrons in the superconductivity state. [ABSTRACT FROM AUTHOR]

Raub and Snijders (1997) show that, under the assumption of S-shaped utility, conditions for cooperation in social dilemmas are more restrictive if outcomes represent losses than if outcomes represent gains. They neglected two interesting issues in their paper: conditions for cooperation in social dilemmas with both losses and gains as outcomes, and the effect of probability weighing on these conditions. In this paper it is shown that, under assumptions of Prospect Theory, conditions for cooperation are best if dilemmas include both positive and negative outcomes, and that these conditions improve with increasing loss aversion. Furthermore, it is shown that probability weighing can effect conditions to cooperate as well. [ABSTRACT FROM AUTHOR]

The paper presents results derived from a series of simulations of signed networks (i.e., networks containing positive and negative links) subject to a balancing process. The dynamics are followed in a space defined by variations in the proportion of positive links introduced and the tolerance to imbalance. The authors claim to have discovered boundaries in the space separating it into three distinct regions. One region probably displays the characteristics of self-organized criticality, which may have implications for the theory of extreme events. [ABSTRACT FROM AUTHOR]

This exploratory paper proposes a probabilistic approach to investigating college student attrition. Through the use of attributable risk, the top risk factors for attrition are identified and ranked. Then the issue of confounding risk between two risk factors is addressed by the means of relative attributable risk. Though it is only illustrated by the eight-year attrition data collected at a private institution, the proposed technique is comparatively simple for institutional researchers to test on their own data. [ABSTRACT FROM AUTHOR]

The folk saying, the rich get richer, the poor get poorer, implies that wealth flows from poorer to richer hands, a concentrating diffusion. Its academic statement is the Surplus Theory of Social Stratification. Angle (1986) abstracted this theory as an interacting particle system model of wealth distribution, the Inequality Process. In it, random pairs continually compete for each others wealth. The richer party has a greater chance of winning. The loser gives up a proportion of wealth. Angle (1986) found the equilibrium distribution of the Inequality Process numerically. This paper derives this distribution algebraically, showing that the Inequality Process implies that personal wealth is distributed as a mixture of negative binomial probability functions (NB pfs). The NB pf is closely related to the two parameter gamma probability density function (pdf), what Angle (1986) fitted to the equilibrium distribution of the process. The solution is given in terms of the parameters of the Inequality Process. Making wealth less fugitive by putting it into the form of human capital has the same effect on the shape of the wealth distribution as reducing the advantage of being richer in an encounter. [ABSTRACT FROM AUTHOR]

Various theoretical concerns often require researchers to answer questions of the form does co-member- ship in a group predict other ties between those individuals. Data appropriate for answering such a question often is referred to as network data Network data exhibits row-column dependencies that often invalidate traditional statistical methods for doing group comparisons such as analysis of variance and the Kruskal-Wallis Procedure. Because of the positive dependence within rows/columns the significance probabilities of such traditional methods may be exaggerated. This paper uses restricted-randomization to develop exact permutation tests for network data where co-membership in coups can be specified a priori. This enables the nonparametric estimation of the significance of standard statistics for group- difference tests and ordered-alternative tests where the group orderings have been prespecified. These methods are demonstrated by examining three different data sets: Sampson's Monastery data, Carley's Tutor Selection data, and Humana's Human Rights data. [ABSTRACT FROM AUTHOR]

In a Markov chain model of a social process, interest often centers on the distribution of the population by state. One question, the stability question, is whether this distribution converges to an equilibrium value. For an ordinary Markov chain (a chain with constant transition probabilities), complete answers are available. For an interactive Markov chain (a chain which allows the transition probabilities governing each individual to depend on the locations by state of the rest of the population), few stability results are available. This paper presents new results. Roughly, the main result is that an interactive Markov chain with unique equilibrium will be stable if the chain satisfies a certain monotonicity property. The property is a generalization to interactive Markov chains of the standard definition of monotonicity for ordinary Markov chains. [ABSTRACT FROM AUTHOR]

This paper reviews the problems of omitted variables in panel data analysis. Results obtained from previous analyses have been shown to be sensitive to the particular parametric forms assumed for the distribution of omitted variables. An alternative non-parametric approach is described in which the effects of omitted variables enter the model through the non-central moments of an error term distribution. A reparametrisation ensures that the constraints on the moments of a probability distribution are not violated. The model is applied to data on the residential mobility history of a sample of households in Cardiff, Wales. [ABSTRACT FROM AUTHOR]

This paper proposes a statistical method to deal with multivariate ordinal polytomous data. The gamma coefficient developed by Goodman and Kruskal is extended to a partial measure of association in the framework of the log-linear model probability model. Then, this method is applied to Sewell and Armer's data on educational aspirations of high school students in order to reexamine the validity of their conclusions. [ABSTRACT FROM AUTHOR]

The paper presents a formal approach which may increase the realism and parsimony of higher-order Markov models applied to certain human behaviors. Often in behavioral applications, any improvements in fit available from increasing the order of a Markov model would be more than offset by interpretive problems caused by the very rapid increase in the number of independent parameters. The model proposed here for the higher-order process greatly reduces the number of independent parameters, replacing them with sociologically relevant effects of persistence in and reversion to previous conditions. The general model is called the "reversion model." In it, individuals are allowed to carry along some information about their pasts, for a number of periods corresponding to the order of the model. The parameters describing residence histories are constructed to give each individual an underlying set of first-order transition probabilities, which are modified by experience of the various states of the system. When an individual occupies a particular state, his relative probability of future residence there (vis-a-vis the other states as a group) is permitted to change. But occupation of a particular state is not permitted to affect the relative chances of residence among the other states. With suitable constraints, the number of parameters of this higher-order process no longer increases geometrically with the order, but only arithmetically. Maximum likelihood estimation formulas are derived for the reversion model, which is then applied to longitudinal data on the work activities of U.S. Ph.D. physicists and chemists in 1960-1966, and is found to fit well using likelihood ratio tests. [ABSTRACT FROM AUTHOR]

Holland and Leinhardt {1977a) introduced a continuous time Markov chain to model changes in a social network. Their model was further studied by Wasserman (1977) . Holland and Leinhardt (1977b) have also proposed a general class of probability measures on random networks, The purpose of this paper is to show that these probability measures may be viewed as Gibbs measures induced by a nearest neighbor potential. As such they have a Markov field property which is a natural generalization of Markov chains to spatial situations, The dynamic models are shown to fit into a general, class of Markov processes suggested by the study of interacting particle systems. A related "voter model" is discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a continuous time version of a diffusion model introduced by Gray and von Broembsen (1974). The new formulation allows a deeper analysis of the stochastic aspects of the diffusion process and, in particular, of the threshold effect which occurs in the absence of an outside transmitting source. Attention is drawn to important similarities and differences between the stochastic and the deterministic versions of the model. Simple approximations for the distribution of the ultimate number of hearers axe given as well as the exact distribution. Some generalizations are suggested and it is shown that their analysis in deterministic terms is relatively easy. [ABSTRACT FROM AUTHOR]

Markov chains, and various generalizations of them, almost universally assume that the transition probabilities applying to a single individual are independent of the behavior of other individuals in the population. That is, there is no interaction among individuals. This is an extremely limiting assumption in modelling social processes. This paper concerns interactive Markov chains, defined as Markov chains in which transition probabilities are functions of population frequencies in the states. [ABSTRACT FROM AUTHOR]

This paper considers the statistical inference of structural properties in organizations. Specifically, the sampling probability distributions of the number of links and the cumulative distribution of the number of components are determined. Probability estimates of both the number of links and the number of components are then found. [ABSTRACT FROM AUTHOR]

This paper compares three methods (sequel, cardinal, maximal) for constructing a weak order from a partial order on a finite set. The constructed weak orders include the partial order. To evaluate the methods, several different selection disciplines were used to stochastically generate partial orders from a fixed linear order. The error of a weak order which includes a generated partial order is a function of the number of ordered pairs added to the partial order to get the weak order which are the reverse of ordered pairs in the fixed linear order. In all cases, the sequel and cardinal mean errors were much lower than the maximal mean error. In most but not all cases, the cardinal mean error was lower than the sequel mean error. [ABSTRACT FROM AUTHOR]

This paper examines Caplow's model of coalitions in the triad and identifies several shortcomings. Retaining the basic structure of Caplow's arguments, it recasts the problem as one of interdependent rational decision making. The reformulation allows increased generality in several directions, including a more general notion of strength, relaxation of the additivity assumption about strength, and the adoption of probabilistic choice to allow predictions about the relative frequencies of the various coalitions. [ABSTRACT FROM AUTHOR]

The intent of this paper is to provide a definition of a sociometric clique in the language of graph theory. This problem is viewed from two perspectives: maintaining fidelity to the intuitive notion of a clique; and providing adequate computational mechanics for large bodies of data. Luce's (1950) concept of an n-clique is used, but further qualifications are added. Two statistics or measures with associated probability distributions are defined for testing the adequacy of a subgraph which qualifies according to the definition. [ABSTRACT FROM AUTHOR]