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The article provides an explanation of sociologist Leo Goodman's paper hierarchical models for significance tests in multivariate contingency tables. In several papers Goodman presents and elaborates a system for the analysis of contingency tables that promises to be extremely useful to sociologists. The papers are however, extremely compressed, heavily complex with the cumbersome notation of contingency analysis and are not easily accessible to the student and average research worker. The aim of this article is to explain the logic and procedures of the system in terms the reader may find more comfortable. The Goodman system consists of two parts: a scheme for making significance tests by means of hierarchical models and an extensive discussion of a set of techniques known as log linear models. The two parts are logically and practically distinct. Among the important uses of hierarchical models are the following: tests for the significance of partial correlations, tests for interactions, where the control variable has as many categories as one pleases, tests for higher-order interactions, succinct statements of what is and what is not going on in a contingency table. Since none of these tools have been easily available to the average sociologist, the Goodman system is well worth learning especially because it provides considerable insight into the properties of cross-classifications and the logic of significance tests.

I am grateful to Professor Dubin for the careful attention he has given to the somewhat neglected pattern variables and for his considerable effort in exploring their potential usefulness. His article has led to a serious reconsideration of the problems he has raised-in particular, the relation between what he refers to as Model I (the pattern variables as formulated in Toward a General Theory of Action ) and Model II (the paradigm of four functional problems of systems of action from Working Papers, and later publications). Dubin suggests that the usefulness of Model II is impaired by too drastic a condensation, and that it cannot be reconciled with Model I. The Editor's invitation to comment on his paper has given me the opportunity to work out an overdue clarification of the ways in which Model II builds on and goes beyond, rather than replaces, Model I. [ABSTRACT FROM AUTHOR]

The article presents comments of the author on two mathematical formulations developed by sociologists Norman P. Hummon and Marshall W. Meyer in their papers respectively, published in one of the previous issues of the journal "American Sociological Review." According to the author, Hummon develops a dynamic theory designed to explain his first generalization by postulating some axioms that make size a function of the demand for the organization's services and technology. Hummon postulates are themselves in need of explication. Conceptual analysis and clarification must precede the construction of mathematical models. Furthermore, Meyer presents an intriguing reformulation of the theory of organizational differentiation, putting it on its head by using one of the derived propositions as the fundamental axiom. But his discussion is vitiated by the misleading assumption on which it rests. He starts with a model of a perfectly symmetrical organization, with the same number of levels in all branches and the same span of control of all managers and supervisors, regardless of rank in the hierarchy and duties of subordinates.

The article comments on the paper "Moderator Subgroups for the Estimation of Educational Performance: A Comparison of Prediction Models," by R.W. Lissitz and L.F. Schoenfeldt, which appear in the January 1974 issue of the "American Educational Research Journal." The paper discusses the effectiveness of moderator subgroup models, including two least square procedures, two probability weighting (semi-Bayesian) methods, and the Bayesian m-group regression method, in predicting college grade point average. Schoenfeldt and Lissitz have taken the authors' general comment that moderator variable methods are typically unsuccessful when "subgrouping follows from a blind fishing expedition or data dredging as applying to their study. They then clearly demonstrate that their subgroupings had a solid theoretical basis. The fact that these subgroupings did not prove useful is thus even more noteworthy. The purpose of the authors' paper was to demonstrate the usefulness of Bayesian m-group regression when within-group sample sizes are small.

This paper provides information on theoretical sociology. By theoretical is meant "theory-using." Any type of statistical technique uses a model of nature, that is, a certain technique makes assumptions about reality and here the approach to theory construction is through the use of models. This is the orientation which regards each theoretical construction in levels, from the most abstract to the most empirical—and each theory construction should contain some of these levels. In this paper the concern will be with the use of an orientation involving the reduction of linear models of techniques which makes a first step towards this. The author also discusses rather more techniques. By following this course, the logic underpinning stochastic analytical techniques, and causal modeling techniques can be revealed. Also it is hoped to reveal how theoretical sociology can be synthesized with a branch of statistics.

This paper looks at an area, which has proved very attractive to the stochastic modeler, that of social mobility. The author wants to survey it, not so much from the point of view of the mathematician striving to achieve the best fit he can to the data available, but more from the point of view of the sociologist who needs models which provide him with a theoretic framework which is readily translated into sociological concepts, and which contain assumptions to which the subject matter of the process, the individual actors, may reasonably be expected to adhere. This paper surveys a number of approaches to the finding of an appropriate mathematical model of social mobility. The author compares them with respect to the sociological theory of mobility, and concludes that the last model discussed is by far the most satisfactory from this point of view. One can anticipate a considerable gain in knowledge of social mobility when empirical research puts such a model to the test.

The article presents a study on how an axiom system works. This paper develops further concepts and theoretical considerations about the structure of role systems. The author tried to clarify the general concept structure of a group and to define role structure in particular. With this, the solution proposed was to define three heterogeneous variables which include persons, positions, and tasks and to examine the interrelations between them. This paper begins on the empirical problems and its detailed quantitative analyses.

This paper reviews die use of "hazard "formulas for allocating police patrol personnel and indicates the need for new quantitative methods to assist decision makers. Mathematical models of patrol activity can be structured to provide insight to such planning and management problems as optimal design of patrol sectors, formulation of preventive patrol strategies, evaluation of technological and administrative in nova- dons, and precinct-by-precinct allocation of personnel. Several illustrative models are discussed, with emphasis placed on the diversity of modeling applications in patrol operations and on the insights provided by use of the models. [ABSTRACT FROM AUTHOR]

Relatively few of the many theories developed by sociologists have been stated in other than verbal symbols. Although the supposed advantages of mote rigorous formalizations have been discussed at length, many sociologists maintain that the assertion by mathematical model-builders that their approach will actually advance thinking in substantive areas of sociology still remains to be demonstrated. The present paper is an attempt to show some of the ways in which this approach can yield new insights into old theories. First, Sutherland's widely used formulation in criminology is translated into set theory statements. Then, the value of this translation is shown by developing a set of underlying postulates from which the nine major prepositions of the theory can be formally derived. Finally, additional propositions are shown to follow as logical consequences of the re formulated theory in such a way that a strategy for its empirical verification is obtained. [ABSTRACT FROM AUTHOR]

A range of hypotheses of varying specificity is examined in this paper in an attempt to account for the location of racial disorders during the 1960's. The initial sections consider what general assumptions must be met by any satisfactory explanation of the distribution of the disorders. Mathematical models are constructed which embody the most prevalent assumptions as to the determinants of community disorder-proneness, and their predictions are compared with empirical data. The specific assumptions considered are: (1) all cities have an identical probability of experiencing a disorder; (2) communities are heterogeneous in their underlying disorder propensities; (3) a Process of reinforcement characterizes the occurrence of disorders; (4) contagion among communities contributes to the distribution of racial disturbances. Only the heterogeneity assumption is supported by the data. The concluding sections consider the explanatory abilities of several additional theories, each of which assumes the importance of particular community characteristics. All are rejected in favor of an explanation which argues that the racial disorders of the 1960's were responses to frustrations which are uniformly felt by Negroes, irrespective of their community situations. [ABSTRACT FROM AUTHOR]

The article presents a reply to a paper titled "Predicting Passenger Miles Flown," by sociologist Hornell Hart's, published in the February 1, 1949 issue of the journal "American Sociological Review." The article states that the discussion in the paper by Hart falls into two parts, the fitting of curve to existing data and the extrapolation of those curves for prediction purposes. The author of the article is not as enthusiastic about the goodness of fitting curves to existing time series, as Hart appears to be. According to him, a curve can be fitted so well to a time series that it passes through every point. The fit is perfect and the correlation is 1. But the predictive value of such a perfect fit through extrapolation would be worse in general than a line with a poorer fit. In the analysis of time series for prediction purposes, the procedure should be to separate the trend from the cyclical or other fluctuation around the trend. Two series may have the same identical trend but in one case fluctuations around it may be twice as great as in the other and hence the fit twice as bad. The trend, though, is not unrelated to the fit, for if the trend is a curve and a straight line is used to measure the trend, the fit will be bad.

The article discusses the effectiveness of moderator subgroup models, including two least square procedures, two probability weighting (semi-Bayesian) methods, and the Bayesian m-group regression method, in predicting college grade point average. It was found that the semi-Bayesian, the Bayesian, and within group least squares procedures offered no improvement over the simpler total group least squares method. The subgroups utilized by the authors were formed on the basis of carefully selected developmental-interest dimensions found to differentiate individuals with respect to a wide spectrum of criteria, particularly those associated with progress in higher education. The groups were formed to maximize between-group variation, minimize within-group variation, and insure psychological meaningfulness. With respect to a comparison of moderator subgroup procedures and the Bayesian m-group regression, the similarities are far more notable than any distinctions. Both procedures attempt to incorporate collateral information in ways that would result in improved prediction.

The article presents a discussion between authors William H. Starbuck and P. G. Herbst concerning the latter's article "Measurement of Behavior Structures by Means of Input-Output Data." Starbuck stresses that Herbst's notion is intriguing, but he argues that his article is hardly convincing. He contends that the quantitative model presented by Herbst contains deductive reasoning and a mathematical error. Herbst defends his side and explains that the primary aim of his paper is to demonstrate the possibility of using changes of discontinuities in the input-output relationships to distinguish between different types of organizational structures.

This paper reviews theoretical models which try to account for cooperation and conflict between two organized decision‐making entities. Although most existing models focus on either “negotiation” or “influence” actions, both may be seen as part of a single process of interaction. Some recent theories have tried to take account of both types of action and there is a need for further work in this direction. Suggestions are made about explaining both types within a motivational framework. Three major types of theoretical models dealing with influence actions are (1) cognitive, (2) learning, and (3) reaction process. Integration is needed between the first two. One direction for such an integration is to treat both the present situation (cognitive) and previous learning as sets of variables which affect current incentives, motives, and expectancies. Although reaction process models view each side's actions as more mechanical than seems appropriate for most situations, the emphasis of such models (and of learning models) on the interaction between the parties needs to be retained in more general models. Journal Abstract [ABSTRACT FROM AUTHOR]

The article presents comments on Norman Hummon's mathematical formulation of Peter M. Blau's axioms concerning the effect of size on differentiation in organizations. Hummon's model assumes that the size of an organization can be taken as the main independent variable influencing the extent of differentiation within the organization. In addition to this sociological assumption Hummon makes a tacit mathematical assumption that leads him to his new proposition. The article elaborates on Hummon's new proposition that states with increasing organizational size, the rate of increase in the size of the average component itself increases. Hummon claims that this proposition follows from his mathematical model of Blau's axioms, and Blau uses a numerical example to show that the axiom implies the very opposite of his new proposition. To illuminate Hummon's error, the article briefly sketches his model of Blau's first axioms. It shows that Hummon neglects to mention the mathematical hypothesis in his verbal translation.

The article presents comments of the author on the method of linear casual analysis developed by Raymond Boudon. Boudon's procedure is dominated by one which is not only simpler from the computational point of view, but also preferable according to standard criteria of statistical inference. The preferable estimation procedure is just linear regression. The classes of models under discussion are recursive with independent errors. In such models, the causal ordering of the variables is unambiguous, and in any structural equation there is just one variable, which is the dependent variable for that equation. The other variables in that equation are uncorrelated with the error in that equation and may be considered as predetermined variables. Multiplying through the structural equation by each of these predetermined variables in turn, summing over the sample observations, and discarding the error terms, produces a set of estimating equations. These are the familiar normal equations of linear regression, which can be solved for estimates of the structural parameters. What Boudon does is to call attention to the fact that there may be other variables in the model, which can be used as multipliers in the same fashion. A variable, which, while causally prior to the dependent variable, does not explicitly appear in a structural equation, is also predetermined because it is uncorrelated with the error term in a equation.

Even a casual reader of current research literature gets the impression that the word "model" is one of the latest in scientific language. Linked with the equally fashionable concept of system, model has become a powerful and prestigious tool. This article proposes the prosaic task of underwriting, if possible, the rather elementary generalizations which are as follows. One tends to think in terms of systems, system is itself a model, the primordial model in fact, the history of science indicates a succession of models by which systems have been explored and explained, the dominant model of system analysis today is the organic image, and any model-patterned analysis, organic or otherwise, involves valuable possibilities as well as serious but often overlooked limitations. The formulation of a model consists in conceptually marking off a perceptual complex. It involves, moreover, replacing part or parts of a perceptual complex by some representation, or symbol. Every model is a pattern of symbols, rules, and processes regarded as matching, in part or in totality, an existing perceptual complex.

In this article a mathematical model is constructed that appears to translate with tolerable accuracy certain propositions to hold for behavior in human groups. Assumptions the model requires and further propositions that can be deduced from it are examined. In particular, it is seen that it offers an explanation for some of the commonly observed phenomena relating to the stability and dissolution of groups. In the last section it is shown that models of this general class can be applied to a rather wide range of behavioral phenomena beyond those originally examined. It is not implied from this that the psychological mechanisms involved in all these situations are identical. The underlying similarity appears to be of a rather different character. In all of these situations there are present, an external motivational force toward some activity and a secondary "internal" motivational force induced by the activity itself. It is the combined effect of two such motivational forces that produces in each case phenomena of the sort observed in this article. And especially when the relations are not linear and the non-linear must be supposed to be the general case, "persistent" and "gregarious" patterns of behavior can result.

The article focuses on the problems associated with the game theory of international negotiation. The theory of games is a branch of mathematics that aims to analyze various problems of conflict by abstracting common strategic features for study in theoretical models. The problems of game theory as applied to international negotiation seems to stem from misunderstanding of what it comprises. It lacks several elements including an extensive form adequate to describe the temporal sequence of negotiations. It fails to encompass the objectives of the participants and their estimation and modification through negotiation. It does not provide concepts of solutions which incorporate the dynamic nature of the negotiations and the lack of information concerning objectives.

The article focuses on two-person, non-zero-sum games. The method employed is to have members of pairs of subjects seated on opposite sides of a partition. In front of each subject was a panel containing a red button and a black button. When subjects pressed their buttons, the combination of buttons that had been pressed was registered by a light on the experimenter's panel, and the subjects were paid off after each trial with pennies. The subjects in pairs were not permitted to communicate with each other, but the game contained no hidden information. Each subject, at the end of each trial, could determine which button the other had pressed by consulting the payoff matrix. The authors conclude that performance in these games is determined by a maximization-of-difference principle.

This article presents information on the relationship between mathematical models and empirical data. It is informed that Larry Schroeder has offered some empirical evidence regarding the relationship between the length of time spent in an occupation and the probabilities of observing subsequent moves from that occupation. It is opined that an important point often overlooked is that not all mathematical models are intended to fit empirical data; not infrequently mathematical models are developed to work out the implications of postulates their authors themselves regard as counterfactual or at least dubious. It is concluded that the task for future empirical studies is not, as Schroeder seems to believe, to provide a clear-cut choice among competing models designed to explain observed associations between mobility and duration, but to determine the relative importance in various circumstances of the variables suggested by the different models. S. Spilerman has carried out such a study for the case of geographic mobility. But these variables must be directly measured if one is to determine empirically which of them are how important under what conditions.

This article presents an analysis of variance techniques for unbalanced data. Some of the more important issues encountered in the analysis of unbalanced data is examined here within a single framework. These issues are broadly defined as solutions to the normal equations for linear models where the incidence or design matrix is not of full column rank, estimable functions of the parameters and tests of hypotheses, and reductions in sums of squares and interpretation of results.

This article examines mathematical models that are developed with a view to help in educational planning. Mathematical models can be used to predict the implications of policy decisions on an educational system. These models are classified as micro and macro models. Micro educational models describe, explain and predict behavior in the learning process. Macro educational models deal with the problems outside the classroom. Four distinct mathematical models, including deterministic models, Markov chain models, regression models and mathematical programming models, have been described.

This article presents information on non-random exogenous variables. It is informed that D.L. Klemmack's study on the above mentioned subject allows one to ignore the specification error of omitting relevant variables; and make misleading assertions about alleged bias and inconsistency in standardized path coefficients in such situations. Klemmack and his colleagues note that for the estimates of effect parameters generated from path analysis to be consistent the exogenous variables must not be correlated with the disturbance terms incorporated in the model. It is opined that the solution presented by Klemmack and his colleagues to the problem of correlation between disturbances and exogenous variables is indeed not a solution and is dangerously misleading. They appear to have arrived at the solution through a misunderstanding of the assumptions of the general linear model (GLM). Path analysis as both a mathematical and statistical technique depends fully on the successful realization of the assumptions of the GLM for its validity.

The article discusses the models made of equilateral triangles constructed by the students as part of his invention class . The author asked his students to picture the model in their minds first before putting it into paper and before constructing it in the cardboard. However, a twelve year old girl was allowed to experiment with the forms of equilateral triangles with even numbers between ten and twenty. The author presents some of the diagrams in this article.

This article focuses on the larger research endeavor which is designed to develop a mathematical model to predict spelling difficulty. A common method used to study spelling difficulty was to compile and examine lists of demon spelling words. These lists of consistently difficult words were first compiled at the turn of the century. Two different sources of demon words were commonly used. Spelling demon lists were also used to analyze the elements of words that seemed to contribute to their difficulty.

This article discusses about factor analysis in educational research. The purpose of the researcher is to present a basis for the evaluation of factor analysis as a research technique, with proper concern for results and application. Factor analysis can be described as an extension of the correctional method. The various factor method differ fundamentally only in the criteria which they set for determining factor weights. The data ordinarily subjected to factor analysis consist of the correlations between a set of variables. In all cases, however, caution must be exercised to see that application of factor analysis realistically conforms to the mathematical model it assumes.

The article presents information on recent developments in the field of statistical theory. A conceptual model was formed to deal with statistical data which is based on the theory of probability. The primary purpose of the theory of the design of experiments is to obtain maximum information from the data. The problem of estimation is the basis of statistical theory. The variance technique provides the appropriate method of evaluating the experimental error and carrying out the tests of significance with precision. According to modern research workers, inferences drawn from experimental results must be based on the knowledge of experimental principles at all stages of an experiment.

Hernes' mathematical model for the process of entry into first marriage is applied to U.S. women, cohorts 1891-1945. Selected cohorts with incomplete data proportions on age- specific first marriage were estimated following a modification of a technique suggested by Ryder. Hernes' model was found applicable across successive cohorts and estimated parameters of his model depicted historical shifts in the nuptial tempo. [ABSTRACT FROM AUTHOR]

The extent to which mate selection is limited by residential propinquity is greater than has been apparent in the usual presentation of a mere frequency distribution, but less than it should be according to the usual theoretical interpretation. In a sample of Seattle marriages, the usual propinquity pattern holds, but the data are better fitted by Zipf's P1,P2/D model than by Stouffer's intervening opportunities model or the model implied by the Katz-Hill "norm interaction" theory. Distance gradients in marriage rates thus seem to reflect an economy of time and energy, rather than competition between near and remote courtship opportunities, or operation of normative factors. It may therefore be more accurate to say that norms are enforceable because departures from them are rare for other reasons, rather than to explain homogamy or other conforming behavior as a result of norms. [ABSTRACT FROM AUTHOR]

This report confines itself to aspect of interstate migration differentials. Its objective is to explain the variations in the annual interstate migration rates in the U.S. during the 13 year period 1947-1948 through 1959-1960. The underlying hypothesis is that age, sex, and year exert a selective influence upon annual interstate migration rates. The report analyzes annual Current Population Survey (CPS) data obtained in nationwide samples by the Bureau of the Census. It computes an analysis of variance for the selected sources of variation, employing conventional techniques. Specifically, it lays out the 13 annual CPS interstate migration rates for 1947-1948 through 1959-1960 in a randomized block design and analyzes them by the a mathematical model. Males have slightly higher interstate migration rates than females, even though the differences are insignificant. Females tend to move at younger ages than males and their peak movement comes at an earlier age. Whereas females 18 and 19 years of age tend to be more mobile than males, men 20-34 years of age generally have much higher interstate migration rates than females of the same ages. Dips in migration rates in 1954-1955, 1956-1957, and 1958-1959 signify minor contractions in business conditions and in opportunities.

Scientists who seek a general theory of community are handicapped by lack of comparability of community studies and by the great complexity of their subject matter. This study attempts to deal with the first problem by applying a single mathematical model to quantitative variables operationally defined and to data gathered at one period of time from 88 community systems. It seeks to reduce complexity by a search for a few factors or fundamental unities in terms of which variations between community systems can be explained. Factor analysis extracted, from the great complexity presented by 82 variables, seven orthogonal factors that account for most of the variations in the systems analyzed. [ABSTRACT FROM AUTHOR]

The concepts of model, methodology, and measurement have assumed importance in the behavioral sciences concurrently with the refinement of research technique, the adaptation of statistics, and the increase of rigor and precision in the statement of theoretical schemes. These three concepts may be used to examine the emerging research process. In particular, they may highlight the interdependence among theoretical assumptions, methods of data collection, methods of data analysis, and types of data, thereby facilitating the construction of research design. Sociologist C.H. Coombs and others have attacked these problems using mathematical models and non-metric measurement theory to deal with psychological data. In one discussion they have brought out some of the general relationships between model building and research. Mathematical models are constructed by abstracting the properties of some data by measurement, and by expressing these properties in a set of symbolic statements that include the logical relationships that hold for the entire set of statements. The point of view in this article is similar to that of Coombs, but directed more to the attention of the general sociologist.

The argument of this article is that the use of mathematical models for predicting social phenomena requires matching the social and mathematical conditions and that all-or-none elements often help this matching as illustrated in the particular cases of the normal probability distribution and the logistic growth curve. It is assumed that sociologists, being scientists, are trying to predict social phenomena better. It is noted that they are using mathematical models increasingly for such predicting. For a mathematical model to be used as a rational social hypothesis requires both that the model fit the data closely and reliably and that the mathematical conditions match the social conditions. Thus, in the case of the normal curve and the logistic S-shaped growth curve, the mathematical derivation from all-or-none elements can be matched by suitable combining of present-or-absent social variables. Knowing this structure of binary elements enables the social engineer, for example, to convert normally distributed phenomena into logistically distributed phenomena. This suggests that binary elements may become useful tools for changing some social distributions.

The article examines the design of game theoretic models used in the discussion and study of international threats and deterrence policies. It states that the mathematical thinking exemplified in the theory of games provides a useful methodology for the construction of models of many person decision-making processes. It proposes the use of a self-policing system in the study of political or diplomatic threats and international deterrence policies. It also explores the fundamental differences between the individual, team and institutional decision-makers in the models of conflict.

The article presents information on social mobility models for heterogeneous populations. The article presents a unified framework to view models as well as more intricate social mobility models. The essence of conceptual apparatus involves a formal distinction between individual-level or microscopic process, which is usually unobserved and the population level or macroscopic process. An individual is identified by a collection of rates that describe average times he stays in particular states before moving or by a stochastic matrix whose entries can be interpreted as propensities to favor transitions to certain states. It is also conceivable that an individual can be classified by specifying both a matrix of rates of movement and a stochastic matrix listing probabilities of making particular transitions when a move occurs. From a description of individual-level behavior and a specification of the form that heterogeneity takes, it has been shown, how the population-level process can be constituted. The article describes a class of Markov and semi-Markov processes which serve as models for the evolution of individual behavior. In addition the ideas involved in identification of indirectly observable parameters are illustrated by examples with the simplest Markov chain models. Another section cites examples to show how the above mentioned population processes can be described mathematically. The basic mathematical structures characterizing the observable macroscopic-level processes are mixtures of Markov and semi-Markov models. Finally an inverse problem where gross macroscopic-level information is used to obtain partial and in a few instances complete, information about the mechanics of the individual-level process.

The article presents information on ratios and difference scores that are often used in sociology. There are correlations involving such measures that frequently have a component in common in the independent and the dependent variable. The purpose of this research article is to review several aspects of such statistical associations and from this review to make some recommendations regarding appropriate procedures. First, an argument can be made that spurious correlation is not an issue in correlating ratios or differences having common terms, provided that one's interest is exclusively in the composite variables rather than the component. Second, in considering the component variables we can identify two special types of ratios and difference correlations. Third, if one's basic interest is not in the specific association of components one may wish to examine the functional relation between ratio and difference correlations and their component correlations along with coefficients of variation or variance.

The article presents alternative approaches for the analysis of variance (AOV) tables. This article has a dual objective: to elucidate the statistical equivalence between conceptually different ways of doing an AOV and to assess criteria for selecting between these procedures in sociological research. In analyzing measures in an AOV table, it makes no difference statistically whether sums of squares are expressed in terms of fitted constants, regression coefficients, or path coefficients. However, these terms answer to somewhat different purposes, they are liable to different abuses, they carry somewhat different connotations and imagery, and since they differ in nuance, one may be mistakenly used when another is called for. This tendency towards imprecise and misleading expression may be especially marked in sociology whose methodology is so heavily borrowed from other fields. Fitted constants answer to the question of whether two or more populations differ in their characteristics, regression coefficients answer to the predicted change in one variable per unit change in another and path coefficients answer to the question of causal effects. Accordingly, fitted constants might be chosen when emphasis is on differences among population characteristics, regression coefficients when the emphasis is on prediction and path coefficients when the emphasis is on direct and indirect causal influences.

Techniques are derived for the estimation and testing of the effects on an intervention into a time-series. The time-series process postulated is a more general form of the integrated moving average model than for which estimation and testing procedures were formerly available. Application of the techniques to the analysis of data from a time-series experiment is illustrated. [ABSTRACT FROM AUTHOR]

Presents the author's opinions on partitioning variance in multiple regression analysis as a tool for developing learning models. Discussion on orthogonal and non-orthogonal methods for partitioning regression variance; Information on the concept of "independent contributions" in regression analysis; Views on orthogonality in regression analysis; Information on mathematical models related to regression analysis.

Comments on the use of the squared beta weight for partitioning variance in school effects studies. Exploration of the relationship between the models used to analyze the data; Interpretation of the beta squared statistics; Focus on structural equation or path analytic approaches.

The present study investigated the efficacy of prediction of Horst's Absolute and Differential Prediction Methods when applied to within-groups correlation matrices. Two treatments of missing data, employing increases of total group intercorrelation matrices and subgroup intercorrelation matrices were incorporated in both the Absolute and Differential Prediction Methods. The synthesis of these methods generated four composite weighting systems, thus permitting a comparison of the accuracy of predictions resulting from the four systems on the basis of weight validities (cross-validation correlation coefficients). [ABSTRACT FROM AUTHOR]

The article presents information on an analysis of researcher Ledyard R. Tucker's central-prediction-system model and an empirical comparison of it with two competing models. One of these competing models is a modification of Tucker's model developed by researcher Wilbur L.A. Bashaw. The other is the standard linear-regression model. For a given college system, a central-prediction system is characterized by the inclusion of information from all schools and all colleges. Greater accuracy of prediction is possible because differences among institutional grading practices can be taken into account. Flexible utilization is possible as predictions can be made for alternative courses of action open to students in the school system. Central-prediction models have been developed because the linear-regression model that is traditionally used is insensitive to the supposed differences among schools with regard to the validity of the grades received in them. The central-prediction model, modified to include the grade main effect, resulted in multiple-correlation coefficients as high as, or higher than, those obtained from standard multiple-regression analyses.

Dissolution rates and apparent solubilities for synthetic hydroxyapatite in acetate buffers containing phosphate and strontium ions in the range of 10-3 to 10-2 M were determined under various pH and buffer conditions. Critical examination of the role of strontium with a physical model suggests that a calcium-strontium apatite surface complex may govern the driving force of the dissolution reaction. [ABSTRACT FROM AUTHOR]

Multiple regression techniques were used to determine the impact of several demographic, socioeconomic, and environmental characteristics of the population on the supply and distribution of dental services among 342 large and small metropolitan areas. The variables selected explained about 48% of the variance in the supply of dental services. [ABSTRACT FROM AUTHOR]

Output of three commercially available electric pulp testers were compared. Clinical threshold settings of the instruments could not be correlated to peak voltage, root mean square voltage, or power outputs determined by use of a simulated load impedance. A mathematical expression to establish a relation between threshold settings and output information is suggested. [ABSTRACT FROM AUTHOR]

The toxicity of a series of esters of acrylic and methacrylic acids was determined in groups of mice, and the resultant LD50 values were analyzed with the use of the mathematical models of Free and Wilson and of Hansch to relate structure of the compounds to toxicity. Both models proved valuable in relating structures to toxicity parameters, but the more useful method for predicting toxicity was the Hansch model. [ABSTRACT FROM AUTHOR]

The article focuses on producing genetically-uniform stocks of laboratory animals that are susceptible or resistant to dental caries. Topics include: intense inbreeding and breeding within a closed population; phenotypic selection of the animals for caries susceptibility or resistance and progeny testing for the parents; and mathematical models for the inbreeding coefficients and the estimated percentages of heterozygosis in one gene pair.