The personnel classification problem is identified mathematically with other problems in the social and biological sciences. This mathematical problem is shown to be a special case of the general mathematical problem of linear programming. It is proposed here that the personnel classification problem may be solved directly by methods particularly appropriate to it as well as by the simplex method, which is a standard method for solving the general linear programming problem. The method of optimal regions is derived and illustrated in this paper.

The monotone regression function of Kruskal and the rank image function of Guttman and Lingoes were fitted to bivariate normal samples and their statistical properties contrasted.

This article examines how the “arbitrary content of culture” (Bourdieu 1977) comes to be inscribed onto patterns of sociolinguistic variation. Specifically, we consider the role of iconicity in this process. Studies of iconicity and variation to date have tended to focus on the iconic properties of the speech signal itself (e.g., an association between higher-frequency sounds and smallness). We bring these ideas about sound symbolism into dialogue with research on embodied behavioral codes, which link particular forms of bodily comportment and their associated qualia with specific social categories and positions. We suggest that certain claims about sound symbolic meanings may be better interpreted as derived effects of socially meaningful bodily hexis. Our arguments are illustrated through a consideration of two variables, both of which have received widespread attention in the literature on variation in English: the backing and lowering of the short front vowels and the fronting/backing of /s/. We discuss how treating these variables from the perspective of socially inculcated bodies can provide a unified account of their observed sociolinguistic patterning and help to shed light on how variables accrue social meaning more generally.

A new solution to the additive constant problem in metric multidimensional scaling is developed. This solution determines, for a given dimensionality, the additive constant and the resulting stimulus projections on the dimensions of a Euclidean space which minimize the sum of squares of discrepancies between the formal model for metric multidimensional scaling and the original data. A modification of Fletcher-Powell style functional iteration is used to compute solutions. A scale free index of the goodness of fit is developed to aid in selecting solutions of adequate dimensionality from multiple candidates.

One of the major concerns of reliability theory has been the estimation of the reliability of a composite measure from the degree of agreement among its component parts. In the classical theory, formulas were developed under the assumption that the parts are strictly equivalent. It was later shown that the same formulas follow from various sets of weaker assumptions which require the composites to be strictly equivalent and require the parts to have a certain homogeneity of statistical properties, but not necessarily to be equivalent. An alternative model which has received increasing attention in recent years regards a given measure as a random sample from a universe of measures whose homogeneity or equivalence is not specified a priori, and a composite test as a random sample of items from a universe of not-necessarily-equivalent items. This too permits an internal-consistency estimate of reliability. Both the equivalent-composites model and the randomsampling model appear to be unduly restrictive and unrealistic; we propose here to develop the implications of a third model in which a test is considered to have been formed by stratified sampling of items.

This note uses the EM-algorithm in an item response model as an illustration of a general method of parameter estimation, which geometrically can be described as an alternating projection method.

Behavioral science researchers have shown strong interest in disaggregating within-person relations from between-person differences (stable traits) using longitudinal data. In this paper, we propose a method of within-person variability score-based causal inference for estimating joint effects of time-varying continuous treatments by controlling for stable traits of persons. After explaining the assumed data-generating process and providing formal definitions of stable trait factors, within-person variability scores, and joint effects of time-varying treatments at the within-person level, we introduce the proposed method, which consists of a two-step analysis. Within-person variability scores for each person, which are disaggregated from stable traits of that person, are first calculated using weights based on a best linear correlation preserving predictor through structural equation modeling (SEM). Causal parameters are then estimated via a potential outcome approach, either marginal structural models (MSMs) or structural nested mean models (SNMMs), using calculated within-person variability scores. Unlike the approach that relies entirely on SEM, the present method does not assume linearity for observed time-varying confounders at the within-person level. We emphasize the use of SNMMs with G-estimation because of its property of being doubly robust to model misspecifications in how observed time-varying confounders are functionally related to treatments/predictors and outcomes at the within-person level. Through simulation, we show that the proposed method can recover causal parameters well and that causal estimates might be severely biased if one does not properly account for stable traits. An empirical application using data regarding sleep habits and mental health status from the Tokyo Teen Cohort study is also provided.

Formulas for computing the exact signed and unsigned areas between two item characteristic curves (ICCs) are presented. It is further shown that when thec parameters are unequal, the area between two ICCs is infinite. The significance of the exact area measures for item bias research is discussed.

Factorial results are affected by selection of subjects and by selection of tests. It is shown that the addition of one or more tests which are linear combinations of tests already in a battery causes the addition of one or more incidental factors. If the given test battery reveals a simple structure, the addition of tests which are linear combinations of the given tests leaves the structure unaffected unless the number of incidental factors is so large that the common factors become indeterminate.

Beginning with sets of arbitrary elements, concepts of distance and betweenness of sets are defined. Since betweenness as defined is not transitive, an investigation is made of the conditions which ensure desirable regularity. It is found that a straight line or linear array of sets is a generalization of nested sets (Guttman scales). Close relationships among the notions of distance, betweenness, and linear arrays are demonstrated. Parallel and perpendicular arrays, dimensions, and multidimensional spaces are characterized.

The present paper contains a lemma which implies that varimax rotation can be interpreted as a special case of diagonalizing symmetric matrices as discussed in multidimensional scaling. It is shown that the solution by De Leeuw and Pruzansky is essentially equivalent to the solution by Kaiser. Necessary and sufficient conditions for maxima and minima are derived from first and second order partial derivatives. A counter-example by Gebhardt is reformulated and examined in terms of these conditions. It is concluded that Kaiser's method or, equivalently, the method by De Leeuw and Pruzansky is the most attractive method currently available for the problem at hand.

We report results from a replication of Solnick (Econ Inq 39(2):189, 2001), which finds using an ultimatum game that, in relation to males, more is demanded from female proposers and less is offered to female responders. We conduct Solnick’s (2001) game using participants from a large US university and a large Chinese university. We find little evidence of gender differences across proposer and responder decisions in both locations.

When a new reference vector is chosen graphically from the plane of two old ones, its direction cosines as well as the projections of the tests on it are most easily computed by applying certain multipliers d and Sd to quantities which are already known. The nomogram quickly supplies d, after S has been read from the graph.