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The Bradley-Terry model for a paired-comparison experiment with t treatments postulates a set of t 'true' treatment ratings π1, π2, ..., π1 such that π1 is ≥ 0, σpi;i = 1 and the probability for preferring treatment i to treatment j is π2 (π2 + πj)-1. Thus, according to this model, every comparison of two treatments results in a definite preference for one of the two. This is an unrealistic restriction since when there is no difference between the responses due to two treatments, any method of expressing preference for one over the other is somewhat arbitrary. This paper considers a modification of the Bradley-Terry model by introducing an additional parameter, called threshold parameter, into the model. This permits 'ties' in the model. The problem of estimation and tests of hypotheses for the parameters of the modified model is also dealt with in the paper. [ABSTRACT FROM AUTHOR]

This paper deals with a car-following model relating driver reaction time, temporal headway and deceleration response to accident frequency. The central goal is to assess the sensitivity of collision probability to a shift in expected reaction time. This problem reduces to determining the sensitivity of the probability of ruin to changes in the drift of the process of cumulative differences between reaction times and temporal headways. A diffusion-type approximation is used and it is shown that additive changes in mean reaction time correspond to multiplicative changes in collision probability. A numerical example is given to illustrate the potential effects of a mere 0.1 sec decrease in mean reaction time. [ABSTRACT FROM AUTHOR]

The traffic assignment and distribution problems are customarily treated as though they were independant rather than related and interacting. In this paper a combined traffic distribution-assignment model is formulated as a mathematical program, based on the equilibrium traffic distribution model and a linear programming assignment model. The behavior of this model using the DANZIG- WOLFE decomposition principle is investigated and illustrated by means of an example. A number of areas for extension are indicated and an alternative formulation that has certain advantages is also [ABSTRACT FROM AUTHOR]

Before we can construct models for multilane traffic flow, we must be able to describe single-lane traffic. This paper considers some of these methods of description including the use of headway and counting distributions. Another method of describing point processes is by means of product densities. These are essentially joint probabilities of two or more vehicles passing a point at different specified times. Product densities have been used in many fields including particle physics, ecology, and road traffic. The idea of using product densities is simple and attractive, but they do have two major disadvantages: (i) except in simple cases, headway distributions are very difficult to derive from product densities, and (ii) product density estimates for different time lags are cor- related, so that tests of hypotheses are not easy to perform. An alternative to product densities is proposed. For want of a better name these are called termination rates. The termination rate after lag τ is the probability of a vehicle passing a point in a small interval of time, divided by the length of the small interval and conditional upon the last vehicle having passed a time τ previously. These are very similar to mortality rates for humans or scrap page rates for commodities with limited life-times. The interrelations between these statistics are quoted but not derived. Various sets of data are used to illustrate the less common statistics. Some analysis is given of a sample of data from the Congress (now Eisenhower) Expressway in Chicago. Variance to mean ratios are used to show that there is a strong correlation between lanes even though the autocorrelations of headways within lanes are very small. Bivariate termination rates have been estimated for each lane. Given a vehicle in one lane, it was found that the expected number of vehicles in a neighboring lane within 2 or 3 sec was enhanced by about 10-15 percent. [ABSTRACT FROM AUTHOR]

The article describes a process for determining migration probability. A stochastic process may be defined as a process which develops over time and where events at time 2 are not independent of events at time 1. This lack of independence may be viewed in probabilistic terms. Since the application of stochastic probability processes to problems of predicting individual behavior requires data obtained from case studies where each individual can be classified with respect to a given set of categories at successive points in time, the projected analysis required a set of individual longitudinal migration histories. Consequences of the basic mechanism of the model utilized in the paper are also detailed.

Merton points out that "the most precise significance of the word function is of course found in mathematics …. " But, says Martindale, "The work of most of the recent functionalists has been at the opposite pole from this meaning." Consequently, assertions made by functionalists have not always been received with the degree of confidence that their authors might consider appropriate. It is the purpose of this paper to suggest a way in which qualitatively formulated propositions of a functional kind may be translated into a language which points to empirical referents and thus, if all goes well, leads in the end to the formulation of mathematical equations. [ABSTRACT FROM AUTHOR]

A multiple-choice item is called ideal if all its alternatives are equally attractive to every person who cannot answer the item correctly without guessing. This paper discusses reasons for attempting to construct ideal items, develops methods for testing whether items are ideal or at least more nearly ideal than other items, and presents examples of both ideal and nonideal items. [ABSTRACT FROM AUTHOR]

The purpose of this paper is the presentation of formulae for obtaining matrix derivatives of the second order to use in making tests for maxima and minima. The theory of such second order derivatives is presented. These formulae require the rearrangment of the parameter elements in vector form and the transformed results feature Kronecker products, which have certain desirable properties. Application is made to several types of problems. [ABSTRACT FROM AUTHOR]

In this paper the first two moments of the Statistic (treatment sum of squares)/(treatment +error sums of squares) over all possible random assignments of treatments to the experimental plots are obtained for two associate PBIB designs. They are compared with the corresponding moments of a central beta distribution to study the extent to which the normal theory test may serve as an approximation to the randomization test. It is found that the approximation is reasonable for some classes of PBIB designs. [ABSTRACT FROM AUTHOR]

In many scientific investigations, it is desired to bring together, or link, two or more documents which represent the same individual, even though these documents do not contain a unique identifier and were derived from different sources. In medical and public health research and elsewhere, this problem is known as the document linkage problem. This paper considers some aspects of classifying pairs of documents into one of two populations when their items are identifying information, where each item of information can take on three distinct values correct, incorrect or missing. Section I identifies three document linkage problems. Sections 2 and 3 deal with the mathematical formulation of the multivariate document linkage problem. Section 4 gives the classification procedure and Section 5 deals with the application of the theory to a problem in the field of public health. [ABSTRACT FROM AUTHOR]

Economic statisticians do not enjoy an untarnished reputation for accurate forecasting. We have managed, over the years, to come up with some memorable failures. While we have also had our share of successes, they are not as well remembered nor as numerous as we should like. Recently, however, we have begun to pay more attention to the record, and a substantial body of evidence on forecasting performance has accumulated. In this paper I propose to review this record, try to arrive at a balanced appraisal, and offer some suggestions for improvement. [ABSTRACT FROM AUTHOR]

This paper deals with methods of "cluster analysis". In particular we attack the problem of exploring the structure of multivariate data in search of "clusters". The approach taken is to use a computer procedure to obtain the "best" partition of n objects into g groups. A number of mathematical criteria for "best" are discussed and related to statistical theory. A procedure for optimizing the criteria is outlined. Some of the criteria are compared with respect to their behavior on actual data. Results of data analysis are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper describes certain quota sampling procedures and attempts to show that they are very close to traditional probability sampling. Quotas are shown to depend on availability for interviewing and evidence is presented to show that sex, age, and employment status are reasonable predictors of availability. Quota sampling methods are not unbiased but data are presented which suggest that the bias is generally of the order of 3 to 5 per cent. It is shown, however, that the cost differentials between these quota samples and call-back samples are small. The major advantage of this new procedure may well be the speed with which interviewing may be completed during crises such as the Kennedy assassination. [ABSTRACT FROM AUTHOR]

In this paper we review the literature on the problem of handling multivariate data with observations missing on some or all of the variables under study. We examine the ways that statisticians have devised to estimate means, variances, correlations and linear regression functions from such data and refer to specific computer programs for carrying out the estimation. We show how the estimation problems can be simplified if the missing data follows certain patterns. Finally, we outline the statistical properties of the various estimators. [ABSTRACT FROM AUTHOR]

In this paper confidence bands are given for simple linear model. The confidence bands that are given are straight lines rather than curves and are either (1) parallel or (2) trapezoidal. The confidence bands are over a finite length interval. [ABSTRACT FROM AUTHOR]

A common problem in many areas is to achieve a combination of control variables which will simultaneously maximize all of the responses which are functions of the control variables. The fact that in general we can not simultaneously maximize all of the responses has led to the formulation of compromise solutions to this vector maximum problem. A point in the control variable space is better than a second point if each response at the first point is greater than or equal to the corresponding response at the second point. If a point is such that there is no better point, it is said to be admissible, or efficient. A set of points is complete if given any point not in the set there is a point in the set which is better. In this paper this formulation is used to consider the allocation of sample size to several strata when there are several characteristics of interest. [ABSTRACT FROM AUTHOR]

This paper considers some problems in the probabilistic analysis of physical evidence in criminal investigations. Two basic assumptions are made: (1) That the number of persons or objects possessing a particular set of properties can be considered as a random variable, and (2) that it is possible to estimate the probability function of this random variable. Two models (one with and one without the assumption that the suspect is a random selection from the set of possible suspects) which arc applicable to the evaluation of partial transfer evidence--an important category of physical evidence that is found in most criminal investigations--are developed. A detailed analysis of the models and an example are presented for the case when the estimated probability distribution is binomial with an expected value less than 1. As the expected value becomes smaller, the assumption of randomness in the selection of the suspect becomes immaterial to the evaluation of the evidential significance. [ABSTRACT FROM AUTHOR]