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The article focuses on prediction logic and quasi-independence in empirical evaluation of formal theory. In the paper by researchers D.K. Hildebrand, J.D. Laing and H.L. Rosenthal, a paradigm for the statement and empirical evaluation of a class of propositions predicting specific relations between qualitative variables was proposed. The approach represents a substantial departure from traditional modes of analysis. Consequently, it is not surprising that one encounters resistance and misunderstanding in those who work in different traditions. The lengthy critique of the paper by researchers L.A. Goodman and W.H. Kruskal, henceforth G&K, illustrates the inappropriateness of evaluating the paradigm using traditional perspectives. G&K operate in two contexts: measures of association and multiplicative models for probabilities in cross-classifications. The primary objective in the paper discussed by G&K was to design a general model that provides a distinct and operationally interpretable measure of the prediction success attained in a population by any logically distinct proposition stated, a priori, in the prediction logic.

This paper develops a model, with assumptions similar to those of the linear model, for use when the observed dependent variable is ordinal. This model is an extension of the dichotomous prohibit model, and assumes that the ordinal nature of the observed dependent variable is due to methodological limitations in collecting the data, which force the researcher to lump together and identify various portions of an (otherwise) interval level variable. The model assumes a linear effect of each independent variable as well as a series of break points between categories for the dependent variable. Maximum likelihood estimators are found for these parameters, along with their asymptotic sampling distributions, and an analogue of R[SUP2] (the coefficient of determination in regression analysis) is defined to measure goodness of fit. The use of the model is illustrated with an analysis of Congressional voting on the 1965 Medicare Bill. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to data analysis that assists the investigator in discriminating among specific relations corresponding to alternative scientific predictions about qualitative variates. [ABSTRACT FROM AUTHOR]

The article focuses on empirical evaluation of formal theory. In the paper by researchers D.K. Hildebrand, J.D. Laing and H.L. Rosenthal, henceforth HLR, proposed an index to measure the adequacy of a particular kind of theory when confronted with harsh facts. The authors L.A. Goodman and W.H. Kruskal, henceforth GK, presented a critical analysis, together with constructive proposals towards partial mitigation of the flaws and gaps they found in HLR. The authors do not agree with the rationales given in HLR for the independence like denominator of the proposed index. One can, however, take the index as given and ask how it performs. It was noted in GK that the HLR index compares the theoretically empty cells with the multiplicative yardstick probabilities for those cells, and no adequate justification for this comparison was found. This is so for both the unweighted and weighted forms of the index. In GK, some modest ways around this problem was suggested without claiming necessarily wide applicability for the suggestions.

Most current implementations of multiple imputation (MI) assume that data are missing at random (MAR), but this assumption is generally untestable. We performed analyses to test the effects of auxiliary variables on MI when the data are missing not at random (MNAR) using simulated data and real data. In the analyses we varied (a) the correlation, (b) the level of missing data, (c) the pattern of missing data, and (d) sample size. Results showed that MI performed adequately without auxiliary variables but they also had a modest impact on bias in the real data and improved efficiency in both data sets. The results of this study suggest that, counter to the concern about the violation of the MAR assumption, MI appears to be quite robust to missing data that are MNAR in analytic situations such as the ones presented here. Further, results can be made even better via the use of auxiliary variables, particularly when efficiency is a primary concern. [ABSTRACT FROM PUBLISHER]

How do individuals shape societies? How do societies shape individuals? This article develops a framework for studying the connections between micro and macro phenomena. The framework builds on two ingredients widely used in social science—population and variable. Starting with the simplest case of one population and one variable, additional variables and additional populations are systematically introduced. This approach enables simple and natural introduction and exposition of such operations as pooling, matching, regression, hierarchical and multilevel modeling, calculating summary measures, finding the distribution of a function of random variables, and choosing between two or more distributions. To illustrate the procedures we draw on problems from a variety of topical domains in social science, including an extended illustration focused on residential racial segregation. Three useful features of the framework are: First, similarities in the mathematical structure underlying distinct substantive questions, spanning different levels of aggregation and different substantive domains, become apparent. Second, links between distinct methodological procedures and operations become apparent. Third, the framework has a potential for growth, as new models and operations become incorporated into the framework. [ABSTRACT FROM AUTHOR]

This article analyzes, based on Boolean approach by C. C. Ragin, how the subjective internal structure of social roles conditions the possibility of discrimination of role performance (role discrimination). I postulate, in an actor's image, a role consists of some role elements, which make up the internal hierarchical structure (role image) according to each element's importance for the role After introducing a set of definitions and assumptions, the role discrimination is formulated as a Boolean equation, taking the role elements as independent variables and the role discrimination itself as a dependent variable. Suppose role X, and suppose a performer and an observer interact each other on role performing, each having his/her own image. In general, between such two given actors, the performance of X by the performer can be discriminated by the observer under the condition that the pattern of practicing role elements included in each image ("practical profile") coincides with each other, at least partially, Taking up a simple case of two elements and introducing the judgment rule, I examine the possibility of role discrimination for all possible combinations of the images, After that, some general propositions as to the possibility of role discrimination, that hold regardless of the number of role elements, are discussed. [ABSTRACT FROM AUTHOR]

The purpose of this article is to examine the effects of five univariate scoring techniques for rank order categorical data and the results of analyses using each of the techniques for five- and ten-point bi-polar adjective scales. The effect of scoring method and scale length is assessed for the resultant distance to multivariate normality, inter-item reliability, discriminant analysis, least squares regression and logistic regression. For these data, the strongest effect of scoring was on distance to multivariate normality and determination of significant variables. [ABSTRACT FROM AUTHOR]