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The article focuses on a simple theory of non-cooperative games with ordinal utilities. The immediate reason for developing the present technique is in connection with an analytical theory of value. It is accepted that choice is determined by intensity of desire. The individual's intensity of desire for an object is in turn the resultant of the intensities of his separate desires. If so, the problem of an analytical theory of value (desire), becomes that of discovering how the individual's resultant intensity of desire is related to the intensities of the desires from which it is compounded--separate desires conflicting or collaborating among themselves.

The article presents information on game theory, prisoner's dilemma, and some recent discussions of the dilemma by some of those who take a "moral point of view." The term "game theory" is generally used to refer to a branch of mathematics dealing with decision-making processes through attempting to simulate mathematically a situation of decision-making so as to discover the most rational decision. The Prisoner's Dilemma is a 2-person, non-zero-sum, non-cooperative game first devised by mathematician A.W. Tucker in the early 1950's.

In the volume The Brookings Quarterly Econometric Model of the United States (Amsterdam, 1965), there are papers by C. L. Schultze and J. L. Tryon on price determination in the industrial sector, and by D. W. Jorgenson on the investment behaviour of firms in that same sector. When comparing these two contributions, one is struck by the fact that Schultze and Tryon point out that industrial firms are price makers in selling their products, whereas Jorgenson assumes that these firms are price takers. This curious fact gives rise to two questions: (1) If both price equations and investment equations occur in the same model, must then one and the same assumption with respect to producers' behaviour necessarily underlie both types of equation? (2) What is the present state of empirical research on price determination under different market forms? Ad (1): In his Economic Fluctuations in the United States, 1921–1941, L. R. Klein has proved that certain assumptions exist concerning the investment equation of either a monopolist (who is a price maker) or a price taker that are consistent with the same set of exogeneous quantities (data) for both cases. In the light of this proposition one may feel entitled to conclude that no inconsistencies exist between the assumptions made by Schultze and Tryon on the one hand and Jorgenson on the other. It should be noted that Klein proceeds on the idea that price makers are monopolists. It may, however, be better to assume that industrial firms are oligopolists. Ad (2): A good deal of research has been done with respect to production and pricing in markets that have the characteristics of homogeneous polypoly (‘pure competition’). In the field of oligopoly, however, hardly any empirical research has been done; here, theoretical constructions are practically all we have. The theory of oligopoly states that the central problem is to find out what is the best hypothesis concerning the reactions of firms on an action taken by one of them. The few investigations on price and investment decisions in oligopolistic markets that do exist (Meyer and Kuh, Meyer and Glauber, Eisner) do not allow for this circular interdependence. It may well be that the theory of oligopoly has laid too much stress on this problem. The work of J. S. Bain on the relations between market forms and market performance is qualified as an important step in the empirical research on oligopolistic price determination. [ABSTRACT FROM AUTHOR]

Copyright of Demography (Springer Nature) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Addresses the power and importance of the mean preference in a mathematical model of democratic choice. Basis of the model; Factors that affect individual preferences; Discussion on the mean preference in a model of democratic choice.

A. J. Lotka and P. R. Sharpe published their classical deterministic population model in 1911, and since that date, numerous numerical methods have been suggested for solving the integral equation inherent in the model. We consider the familiar integral equation (Equation (1)) and derive a Taylor series for r0, the unique real solution. The series is no more advantageous from the calculation point of view than many previous solutions, but it may be useful in a theoretical context. The effects on the intrinsic rate of increase of the population due to changes in the cumulants of the net maternity function are readily discernible. [ABSTRACT FROM AUTHOR]

A method to compare fertility sequences, each of which represents a cyclical fluctuation around an underlying trend, is presented. Each fertility sequence is viewed as composed of a time trend in childspacing pattern and a corresponding trend in terminal fertility rate. The procedure involved in comparing each component of one fertility sequence with the corresponding component of another is described and illustrated. Using hypothetical data it is shown, among other things, that if A and B are two cyclical fluctuations in fertility such that (i) the cycles in both are of the same length, (ii) the terminal fertility components of the two are identical, and (iii) the trend in the mean age at childbirth associated with A is higher than the corresponding trend associated with B, then, replacing B with A need not necessarily result in lowering the long-run rates of increase in the birth sequence. [ABSTRACT FROM AUTHOR]

This paper arises out of the fact that place utility, a basic factor in behavioral conceptualizations of migration processes, has not been specified in operational terms. This is done here through a model that assigns intra-urban migrants to destination areal units within the city, using a normative linear programming framework based on behavioral considerations. Measures of place utilities for each areal unit and of comparative place utilities for each pair-wise permutation of areal units are provided by the shadow prices of the dual of the linear programming model. The primal of the model allocates migrants so as to maximize the household's gain from migration. This is measured by the increase in its realized aspirations with respect to a residence site, tempered by the search effort involved in acquiring the site. Implementation of the model utilizes both questionnaire and published data from Cedar Rapids, Iowa for the year 1966 to 1967. Conformity between predictions of the model and real-world characteristics is such that it is concluded that the basic form of the model is sound. It is also concluded that the posited relationships between place utility and behavior in searching for and selecting a new residential site are reasonable and can lead to valuable insights into place utility and its functioning in the intra-urban system. Due to some misallocation of migrant flows, however, we further conclude that the model should be revised into a recursive format for future use. [ABSTRACT FROM AUTHOR]

In the behavioral sciences the gap between those who try to use generally solvable mathematical models in describing the problems and those who try somehow to understand behavioral processes by simulating them--using some exact rules, usually computer programs--is getting wider and wider. It is easy to criticize the "model-makers" for the lack of any large application field for their constructs and for the oversimplifications they have made in order to get the mathematical problem solvable in practical terms, oversimplifications which often raise the question whether there are any interesting applications at all from the point of view of the serious researcher in the social science concerned. This study is an attempt to show one possible way of constructing a theory in social psychology based on as few concepts and as few assumptions as possible, while still trying to cover equally the different problem areas. One must make a tremendous number of risky decisions between different alternatives in forming such a system on this level of knowledge. Many of them may be wrong.

A study by historical comparison of the fertility trends related to mortality levels is made between Latin America and Europe. The purpose of such study is to show why Latin America did not repeat the European mortality-fertility pattern during 1930-1960. Differences between the two areas are established, and an explanation is given about the particular Latin America mortality-fertility model. The effects of such a Latin America trend are pointed out, principally in relation to population growth, city growth and labor force. Hypothetical Latin American populations are calculated under the assumption that the area has repeated the European pattern. A comparison between these hypothetical populations with the actual ones shows how different the situation of the area has actually been. Nevertheless, an analysis of the necessary fertility changes in order to reproduce the European model shows that it was impossible for Latin America to repeat the European mortality-fertility experience during 1930-1960. [ABSTRACT FROM AUTHOR]

Recent mathematical research has led to the formulation of many theorems of great interest to the economist. They permit him to judge a priori if it is possible to derive meaningful propositions of comparative statics from the system of relationships that characterize a given static model; it is not necessary for him to derive the reduced form nor to render explicit the dynamic model. The purpose of the paper is: to clarify the premises and the methodological implications of such research; to enlarge on the most significant results from the point of view of the construction of economic models; to demonstrate how the two classes of qualitatively stable models combine among themselves and to demonstrate how their intersection contains models of a causal type. The theory of qualitatively determinate systems permits the substitution (as cost of the qualitative determination) of a certain loss (though minimum and calculated) in terms of the complexity of the model for a certain loss in terms of empirical relevance. This loss may be measured by the number of the non-zero elements in the augmented matrix of the system of equations that characterize the model.

This paper deals with a task which is typical for sociological research. In the aspect of content it was stated in the following manner: supposing there is a set of occupations; sociologists can collect questionnaire data for analysis. The task is to scale these occupations according to the subjects' answers. The matter of scaling is in replacing the object designations by numbers in such a manner that the relationships on objects might be retained in numerical relations. The measuring procedure is in assigning numerical values to the objects, and it is executed by the third element of the scale, namely by the function. Depending on arbitrary definitions of the function, the following scale types are considered: absolute, interval, differential, ordinal and nominal. Thus, constructing a scale of designations would consist merely in replacing different names of occupations by different numbers. The representatives of the same occupation would not differ from each other. In constructing mathematical models such distinction is insufficient as the proportion of studies in which the results of nominal scaling are used is very small.

Place-of-birth-by-residence data, tabulated by age and sex for the same areal units in two successive censuses, have been used to estimate intercensal net migration flows. However, a fuller use of the same data permits the estimation of place-to-place flows. This paper describes a method for estimating intercensal migration streams from place-of-birth- by-residence data and illustrates its application with data on the white female native population of the United States. [ABSTRACT FROM AUTHOR]

The growth and increasing complexity of municipal governments have been phenomenal in recent years. Thus, economic planning of the municipality has become one of the most difficult administrative functions of local government officials. Yet economic systems analysis of cities has been generally neglected by economists and management scientists. This paper presents a methodology for the effective long-range economic planning of a municipal government. More specifically, it applies the goal programming model to design optimum aggregative model for municipal economic planning. [ABSTRACT FROM AUTHOR]

To study sedimentary phenomena, we introduce random-genetic models in which genetic hypotheses and structural random elements occur for the main part. Starting from geologic hypotheses we choose principal factors which may be random functions or random variables. These factors are: depth, nature of the facies, sedimentation rate, and subsidence. Equations of evolution link the factors. Depth is a Markov process, but generally the resultant sequence does not make a Markov chain or Markov process. Three examples of such models are given with the results of simulations. [ABSTRACT FROM AUTHOR]

The natural fertility schedule of a population is the schedule of age-specific marital fertility we would observe if no birth control were being practiced. In natural fertility (no birth control) populations we can observe the natural fertility schedule directly, but in populations practicing birth control the natural fertility schedule is disguised by the marital fertility rates in those age intervals in which control is exercised, the marital fertility rates being below the natural rates. This paper elaborates a method for estimating the natural fertility schedules of populations practicing birth control. Two alternative models are presented, one nonlinear and one linear. The use of these models is then illustrated with reference to the Old Order Amish population of Lancaster County, Pennsylvania. It is shown that for Amish women born between 1860 and 1900 both the nonlinear and linear models yield an estimate of .843 as the ratio between Amish and Hutterite natural fertility schedules. [ABSTRACT FROM AUTHOR]

The article focuses on the use of models in the study of demography. Demography has made some progress in developing and applying models. This discipline has been greatly influenced by demand for prediction of future population and by efforts of its experts to satisfy that demand. Population prediction is a perpetual motion, a trisection. Except when the trends are smooth it is likely to fail. But the attempt to predict has inspired many of the demographic models that one now possesses. Such models permit experiments out of which one obtains causal knowledge; they explain data; they focus research by identifying theoretical and practical issues; they systematize comparative study across space and time; they reveal formal analogies between problems that on their surface are quite different; they even help assemble data. There may be circumstances in which the conditional prediction is more helpful than the concrete prediction of what will really happen. The main technical difficulty here arises from effects associated with the proposed change--for example, the effect that the elimination of heart disease would itself have on death rates from other causes.

Studies in factorial ecology have typically used the principal factor procedure coupled with varimax rotation. Since it can be shown that the results one obtains vary according to the factor and rotation models he employs, and since there is no one "best" way of obtaining initial and derived factor solutions, it is proposed that future research in the area adopt an approach involving the simultaneous use of several different computing algorithms for obtaining initial solutions and both orthogonal and oblique rotation procedures to avoid the possibility that the results one obtains are not method-dependent. Ideally, the factor models employed should differ maximally with respect to the principles upon which they are based. If one finds a given factor regardless of the method he uses, only then can he assert with any confidence that it is not an artifact of his method. Factorial ecologists are often interested in computing "factor scores", but "true" factor scores are not uniquely computable; they can only be estimated. Since the proposed research strategy involves using either a component or an image model, in which the corresponding scores are exact and uniquely computable, the factor score problem is, in a sense, solved. Next it is suggested that, by using orthogonal solutions, factorial ecologists may be overlooking a very important piece of information-the correlation between the factors. There is some reason to believe that this varies from city to city, and may account for the fact that some factors which emerge in studies of Western cities are sometimes not found in cities elsewhere. Some comments are also made on the value of using census tract data, and on the availability of computer programs for different initial and derived factor solutions. [ABSTRACT FROM AUTHOR]

Theoretical propositions from human ecology are used to develop a model that explains the centralization or decentralization of various types of families, such as married couples with children, in the Cleveland, Ohio, Metropolitan Area. The model shows how proximity to the Central Business District affects neighborhoods in terms of three characteristics: Age or period of development, both internal and external housing Space, and Site features such as industrial and recreational activity. These structural characteristics are seen, in turn, as the causes of the location of families in relationship to the center of Cleveland. Of the three characteristics, Space generally plays the most important and Site the least important role in determining the location of types of families. However, the location of most types of families is affected by a variety of interrelation- ships among neighborhood characteristics. [ABSTRACT FROM AUTHOR]

This paper has two principal aims: (1) to analyze and measure how the demographic variables-mortality, fertility, and immigration- affect the cost of education; (2) to evaluate what possibilities developing countries, such as those of Latin America, have for a rapid educational improvement. The paper relates demographic and educational variables of three different populations: Sweden, 1840-1965; the United States, 1850-1960; and Latin America, 1930-2000. Three educational variables are also cone sidered: (a) school attendance rates by sex and age; (b) distribution of students of same age by grade; and (c) cost of student by grade. Demographic changes in countries such as Sweden and the United States were favorable for the development of education. For the future, unless an increase of fertility occurs, mortality and fertility changes will not have a significant effect on the cost of education in these countries. In current less developed countries the demographic changes during the past were less favorable to educational development. A future reduction of fertility will significantly help them to achieve a higher educational level. [ABSTRACT FROM AUTHOR]

The reduction of population growth rates through family planning programs is being attempted in many of the developing nations of the world. This activity lends itself aptly to mathematical modeling. Building from the well-known difference equation model of population growth, a model is constructed which integrates population dynamics, program activities, and resource consumption. The model may be used predictively to assess the outcome of various program activities. Alternatively, it may be used to determine the pattern of activities which yields the greatest reduction in births under the projected resource constraints. A further use of the model is the identification of the parameters to which predictions are most sensitive; such information provides valuable insights to those gathering the input data. The model is here applied to a family planning program currently in progress. An evaluation of the feasibility of that program's goals is provided, as well as information on limiting resources, data sensitivity, and the most important ages for contraceptive acceptance. [ABSTRACT FROM AUTHOR]

This report presents, discusses and extends strategic models for representing the process of merging records from different sources when confidentiality of the records is required by law or custom. Examples and variations on the models cover simple situations, such as eliciting anonymous data from previously identified respondents, as well as more complex merge operations, such as merging files from different data archives and merging data under code linkage systems. The versatility and potential corruptibility of the models are also discussed. [ABSTRACT FROM AUTHOR]

Decision models which aspire lo generality are weak since they must be divorced from any societal environment, or assume universality for one form of society. The former is the case with normative rational models, the latter with descriptive ones such as incrementalism. To assume that decision modes vary in response to environmental factors might be a more fruitful basis for analysis. This is the point of departure for the present paper, which offers a conceptual framework independent of a priori assumptions about the decisionmaker's environment. Among hypotheses which are presented on the relationships between environmental and decision variables, is the suggestion that an important factor affecting the style of decisionmakers is their perception of change. An environment perceived as relatively stable or gradually changing will elicit incremental decision processes, while decisionmakers finding themselves subjected to rapid change in a turbulent environment may adopt a decision mode called entrepreneurial. This is distinguished from the incremental mode by, among other characteristics, its greater propensity for risk. [ABSTRACT FROM AUTHOR]

The primary purpose of this paper is to analyze the "determinants" of migration between Standard Metropolitan Statistical Areas (SMSA's) in the United States. The magnitudes in which various factors have influenced inter-SMSA migration are estimated both for the country as a whole and for individual SMSA's. The "migration elasticities" estimated for individual SMSA's are in turn used to test several additional hypo- theses concerning migrant behavior. Other similar migration studies have found "wrong" signs or insignificant coefficients on certain variables a priori thought to play a crucial role in the migration process. Finally, we present clues to the causes of such "surprising" results. [ABSTRACT FROM AUTHOR]

The article presents the author's comments on the paper "On Place Utility and the Normative Allocation of Intraurban Migrants," by L.A. Brown, F.E. Horton and R.L. Wittick, previously published in a 1970 issue of the journal "Demography." He says that throughout the paper the authors have maintained that normative models of migration, which have an identifiable place utility component, may operationalize the concept of place utility. The paper also reiterates, using slightly different formulations, a statement and a model that involves a cost minimizing linear programming allocation of intraurban migrants to vacancies. The dual variables of the problem are interpreted as measures of place utility. However, the interpretation of the dual variables on which the paper is based is contradictory and untenable. The paper assumes origins and destinations containing, respectively, migrants and vacancies. Migrants are allocated to vacancies so as to minimize migration costs subject to the following conditions: one, no more migrants be shipped out of any origin than are available there and two, all vacancies be filled at all destinations.

This paper discusses a preliminary examination of the way in which a decision to use sets of ordered categories might mask relations between variables. The tentative findings showed that it would be useful to inspect the correlations between different categorizations of the same underlying variable. The interrelations between the dichotomized and trichotoanised variable's are lower than those for categorizations with higher numbers of categories. In each of the cases considered the value of r is lowest for the pair of variables that are skewed in opposite directions, which is not a surprising finding. However for the dichotomies there are instances of an r that is too low for the null hypothesis that there is no linear relation between two categorizations of the same underlying variable. The results outlined so far suggest at least three issues which need to be explored; first, one need to have some idea as to the nature and extent of the distortion caused by categorizing data, second, one need to know whether the presence of such error can lead to the rejection of models that are really consistent with the data or the acceptance of models that are not consistent with the data, and third, one need to have techniques that can allow to overcome, or compensate for, such errors.

This article focuses on the interdependent systems and factor analysis. Interdependent systems have long been extensively used within econometrics. A fairly comprehensive theory of such systems has developed. Sometimes the versatility of causal models is contrasted with the limited applicability of factor analysis, which, as a causal model is seen as a very special case with causal influences permitted only from inferred factors but never from observed variables, as in the Blalock-type recursive models and in path analysis. In sociology, assumptions seem tenable fairly seldom, i.e. the model has a rather limited sociological applicability. On the other hand, factor analysis is often assumed to apply rather widely on a descriptive level. This is somewhat unexpected, if the causal model behind the analysis is as limited as is claimed at the same time. If causal mechanisms behind observed data could follow no other model than the one just given, when factor analysis is applied, descriptions based on this kind of analysis should make sense only to the extent the necessary model can be accepted. If the model seldom applies in sociology, then factor analytical descriptions of sociological data sets should he correspondingly limited in value.

In this paper, the implications for sociological research of adopting a probabilistic model to describe the relationships among several variables, a problem presently analyzed by causal models, is explored. A mathematical statistician, then presented with the problem of determining the effect on the dependent variable of an independent variable, both directly and through an intermediate variable, would usually look at the interaction effect between an intermediate variable and an independent variable on dependent variable. Why, then, does the sociologist or economist construct a "causal chain" using linear, no-interaction models at each step, in an attempt to respond to the same problem? And what is the relationship between these two approaches? These questions will be considered in the probabilistic framework in the second half of this paper, using an example taken from research presently in progress. Before discussing in detail the problem of inter-related variables from the probabilistic viewpoint, it is necessary to inspect the various approaches currently being made to the problem in sociology, in order to determine precisely what is meant by path and chain. These approaches are, as scholar H.M. Blalock states, "mathematically equivalent." But, the methods are far from being probabilistically equivalent.

The article presents information about the styles of management inventory. At the foundation of the model operationalized by the styles of management inventory, is the typology of organizational and managerial styles suggested by scholar R. Likert. Distinguishing basically between authoritative and participative organizations, Likert posits four approaches to management, each with specified consequences for the motivation of participants, their job satisfaction, communication, decision-making, productivity and other variables. The four types, which Likert views as stages of development from ineffective and pathological to effective and healthy management, are, exploitative-authoritative, benevolent-authoritative, participative-consultative and participative-group. Scholars R.R. Blake and J.S. Mouton have extended the work of Likert into a conceptual model of managerial behavior called the managerial grid. Two concerns of major importance to the individual manager have been identified by them as a concern for production, and a concern for people. These concerns parallel the two determinants of work conditions identified by Likert as production and morale. Unlike Likert's earlier assumption, Blake and Mouton conceive of the production and people concerns as being independent of one another, that is, it is possible for a manager to have one without having the other concern.

The aim of this essay is to point out how important the connection is between the results of an analysis of the relations among variables and a classification of subjects. The problem in its most general terms can be formulated as follows: if there is a sample of n subjects xi characterized by m variable Xj, the two principal approaches for managing to obtain information from this data are, models or methods tending to individuate the relations of variables and models and methods tending to regroup the subjects xi into a certain number of homogenous classes on the basis of various criteria. In some models, such as Lazarsfeld's analysis of latent structure, analysis of latent profile and the factor analysis, in which the formation of the classes is based on the principle of "local independence," it is possible to have contemporaneously a classification of subjects xi in a certain number of classes and also an explanation of the relations of variables Xj put in relation to the underlying dimensions. However, in the majority of cases approach is altogether separated from approach, in the sense that whoever proposes to analyze the relations of variables Xj has no interest in classifying the subjects xi, even if, by choosing only one of the two approaches, much important information is eliminated resulting in the possibility of grave errors at the interpretive level.

The article presents information about a statistic for random model testing. Very often testing for the random model becomes important in the social sciences. For instance, if one has three categories of classification, he would be interested to know whether the chance of an individual falling into these categories is the same. Conventionally the test statistic used for this type of analysis is the contingency x2. Authors show here that the notion of variance, if applied to relative frequencies, yields a simple statistic for random model testing. Further-more, it is shown that the few statistic, viz. variance of relative frequencies, is related to the contingency x2. As indicated, the social scientist frequently encounters in his research the problem of testing for the random model as well as for the degree of dispersion of responses or other attributes of individuals and aggregates involving nominal data. The variance of relative frequencies can be of significant aid to the researcher in reducing his data to a convenient single measure expressing dispersion and a test for randomness. The following case should exemplify the utility of the statistic. One of the important dimensions of the division of labor in science including the social sciences, is the pattern of scientific foci or interest within different scientific disciplines.

The relation between career mobility and reproductive behavior is examined for five cities of developing Latin American nations Bogota, Columbia; San Jose, Costa Rica; Mexico City, Mexico; Panama City, Panama; and Caracas, Venezuela. The data are obtained from fertility surveys conducted between September, 1963, and August, 1964, in the above-named cities under the auspices of the Centro Latinoamericano de Demografla (CEIJADE), and the analysis is based on information from 600-800 women per city who have been married only once and married ten years or more. Career mobility is defined as an occupational change of the husband between the date of marriage and 1963-1964, based on the Hall-Jones occupational scale. Reproductive behavior is operationalized as the number of live births. The conclusion of the multiple classification analysis is that the process of career mobility in four out of five Latin American samples is not a significant factor in explaining differential reproductive behavior. These results are compatible with a variety of North American studies which stress that variation heretofore ascribed to the process of mobility is an additive composite of past and present status effects. These findings are discussed; a theoretical and methodological critique of mobility-fertility research is presented. [ABSTRACT FROM AUTHOR]

Proposes a Cobb-Douglas production function with labour of three different levels of education. Definition of the quantity of labour with primary education; Determination of income distribution over levels of education; Effects of doubled schooling on income differences.

Census data for area! units, SMSA's in 1960 and cities in 1940, are used to test hypotheses and estimate parameters concerning the influence of a variety of socioeconomic variables on fertility rates of ever married white and nonwhite women aged 25-29, 30-34, 35-44, and 45-49. An economic mode! of the demand for children is adopted as the theoretical framework. The principal findings are that the market earnings opportunities for wives have an important negative effect on the fertility rate and that male income, representing the income of husbands, has a small but positive effect on fertility. The implication of these results is that changes in economic variables, for example, improvements in the employment opportunities and wages for wives or the establishment of a children's allowance program, may be expected to affect fertility. [ABSTRACT FROM AUTHOR]

Focuses on risk aversion in an expenditure equation. Derivation on the consequences of uncertainty in a one-period investment model; Regulation on the marginal cost of funds; Gap between available funds and planned expenditure.

This study is one of the few multivariate analyses of the relations of several demographic and socioeconomic variables to fertility and the use of contraception. For fertility, 56 of the 92 hypothesized paths are found to be significant at the .05 level or better. The five variables having a significant and direct effect on fertility, as shown by their path coefficients (p), are: duration of marriage (p = .721), spouse's cohort (p = -.093), spouse's age at marriage (p = .052), caste (p = -.071), and number of siblings of husband (p = .050). The use of contraception is affected by, in order of importance, the spouse's education (p = .267), the husband's education (p = .099), the husband's income (p = .089), and surplus children, i.e., number of living children exceeding ideal number of children (p = .059). Child mortality, which is linked to number of living children and thus indirectly to surplus children, is affected by, in order of importance, the number of children ever born (p = .723), the husband's education (p = -.166), the spouse's absence by death or separation (p = .084), and family structure (p = .035). The advantages and disadvantages of path analysis for this type of research are briefly mentioned. [ABSTRACT FROM AUTHOR]

New procedures are developed in this article for estimating parameters of the Pearsonian Type I curve which are particularly adaptive to factors influencing the pattern of age-specific fertility rates. It is shown that with this model the number of parameters required for the graduation and simulation of these rates can be reduced to only three--total fertility rate, mean and modal ages of fertility. The reduction in the number of fertility parameters offers considerable operational and analytical advantages, and makes the Pearsonian Type I curve particularly appropriate for the construction of a parametric model for fertility projections. In light of the results of empirical tests based on fertility data for Canada, the model's potential for birth projections appears quite promising. [ABSTRACT FROM AUTHOR]

Examines the decision-making process of the charitable, professional, athletic, social and other organizations that are found throughout the U.S. society. Assumptions used as basis for the mathematical model of democratic organization; Evaluation of the improvement in decision-making efficiency that will result by restricting the voting power to the more competent members; Verification of the model.

The stable population model is used to establish formulas expressing the effects of mortality change on population growth rates, birth rates, and age composition. The change in the intrinsic growth rate is shown to be quite accurately approximated by the average decline in age-specific death rates between age zero and the mean age at childbearing in the stable population. This change is essentially independent of the initial level of fertility in the population. Changes' in birth rates and age composition are shown to be simple functions of the age pattern of cumulative changes in mortality rates relative to an appropriately defined "neutral" standard. [ABSTRACT FROM AUTHOR]

A slide rule has been devised which is based on the general mathematical models of pharmacokinetics. It permits calculation of exact dosage regimens for individual patients from certain basic parameters. First, from the patient's renal clearance, the proportionality constant characterizing renal excretion of a certain drug ( a) and its non-renal rate constant of elimination ( k), the rate constant of total elimination ( k) can be calculated. Second, from k, the apparent volume of distribution ( V) and the desired final mean concentration of a drug (c), exact values can readily be obtained for the loading dose ( D*) and the dosage schedule, which consists of the maintenance dose ( D), the dosing intervals (τ) and the infusion rate for intravenous administration. In addition the slide rule provides information about the rate at which c is reached if D alone is administered at τ, and the fluctuation in the concentration around c to be anticipated during τ. By use of this calculation, the slide rule facilitates the decision whether a loading dose should be given, and what dosage schedule is best suited to the therapeutic problem. It is possible, therefore, to calculate exact dosage regimens for individual patients, even for those with excretory dysfunction. The slide rule should also help physicians to comprehend the nature and significance of pharmacokinetic mechanisms. [ABSTRACT FROM AUTHOR]

Copyright of Medical & Biological Engineering (0025696X) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, the authors have considered some simple models for the diffusion of innovations, using as an illustration the adoption of the comprehensive school reform by Norwegian communes. The first aim was to present a kind of catalogue of models showing for which technical reasons some models tend to appear rather often and which could serve to lead, if necessary, to more complex models. The second aim was to define and limit for each model the kind of explanation it suggested. Two possible models, which have been most frequently proposed in the literature, will be emphasized. Descriptive models serve first to summarize data. The shape of the diffusion curve when fitted to a function which has a simple analytical form as well as few parameters is more easily remembered than if it had a more precise empirical description. The exact analytical form is not so important because different functions can serve the purpose of fitting the data reasonably well. Usually, analytical formulas are chosen according to the author's familiarity with them. Probabilistic models allow for more refined hypotheses than deterministic models, and, in principle, they also allow for a better judgement about the quality of fit. This, however, occurs only in the framework of a number of assumptions where control might be difficult. Probabilistic models generate a distribution of diffusion curves: the observed one being one among numerous possibilities.

The article presents abstracts of various manuscripts published in the December 1974 issue of the journal "Quality and Quantity." The article "Some Simple Mathematical Models for adoption Processes: The Case of the Comprehensive School Reform in Norway," reviews simple mathematical models which have been or may be used for adoption processes. Each model's role in the explanation process is analyzed. The case of the spread of the comprehensive school reform in Norway is used to illustrate an adoption process. The logistic, or chain-reaction model, and a normal model for independent adoption are emphasized. Another article "Models of Stratification Processes," presents certain mathematical models of the stratification process. These models are explicity concerned with the dynamics of stratification systems, and through their use it is possible to characterize time trajectories and also intra-system change. A foundation is laid for a comparative analysis of stratification systems and the analysis of historical change of any particular system. The mathematical models point to the limitation of current methodologies used in the analysis of stratification systems in that they explicitly or implicitly assume conditions of equilibrium, and employ procedures that obscure information about system change.

The present paper deals with changes over time in the sex composition of a given population. Such changes are generated by the components of population change: natality, mortality, immigration and emigration. The objective of this paper is to propose a model which provides a quantitative statement concerning the effect of each such component on the change in the sex composition of the population. It is shown that the model is applicable to the measurement of sex composition by either the masculinity proportion of the sex ratio. To demonstrate the application of the proposed model, an example based on Canadian data is given. [ABSTRACT FROM AUTHOR]

This article presents a comparison of additive and multiplicative models for qualitative data. Two distinct approaches to the analysis of qualitative data, as expressed in the form of percentages or proportions, appear in the sociological literature. The first approach involves a decomposition of the proportions or per cents in what may be called an additive model. A second approach has been introduced to sociology from statistics by researcher L.A. Goodman. This model involves a different method of decomposition, using a multiplicative model. An important feature of the multiplicative model is related to the way in which the sample is obtained. Often, fixed numbers of individuals for a sample survey are selected according to their values of the dependent variable, and then the corresponding values of the independent variable ascertained. An additive model is based on the probability theorem for mutually exclusive alternative events. In the multiplicative model, the probability of a given value of the dependent variable is explained in terms of its simultaneous occurrence with a set of other events, the values of the independent variables. Thus, the probability of the given value of the dependent variable is decomposed into a product of probabilities of given values of the independent variables occurring.

Examines the price expectations and consumer behavior Europe. Assessment on the theory of consumption function; Importance ofc psychological variables; Specification of the theories being used.