A probability model for errors of classification. II. Particular cases

General features of a probability model for errors of classification are recapitulated as an introduction to particular cases and applications. Several models for dichotomous and nondichotomous systems are examined in sufficient detail to elaborate a procedure for dealing with any particular case. The systemO =f(T,E) has empirical reference where, as statistic or parameter, probability of occasional subclass membership is given by observation, and one seeks to recoverT andE values fromO. A procedure for relating models and data is described. Applications of the concepts and methods are illustrated for several areas of psychological research.With grateful acknowledgment to the Rockefeller Foundation; and to the United States Department of Health, Education, and Welfare, Public Health Service, for N. I. M. H. Grant M-3950.     

A generalized solution of the orthogonal procrustes problem

A solutionT of the least-squares problemAT=B +E, givenA andB so that trace (EE)= minimum andTT=I is presented. It is compared with a less general solution of the same problem which was given by Green [5]. The present solution, in contrast to Green's, is applicable to matricesA andB which are of less than full column rank. Some technical suggestions for the numerical computation ofT and an illustrative example are given.This paper is based on parts of a thesis submitted to the Graduate College of the University of Illinois in partial fulfillment of the requirements for a Ph.D. degree in Psychology.The work reported here was carried out while the author was employed by the Statistical Service Unit Research, U. of Illinois. It is a pleasure to express my appreciation to Prof. K. W. Dickman, director of this unit, for his continuous support and encouragement in this and other work. I also gratefully acknowledge my debt to Prof. L. Humphreys for suggesting the problem and to Prof. L. R. Tucker, who derived (1.7) and (1.8) in summation notation, suggested an iterative solution (not reported here) and who provided generous help and direction at all stages of the project.     

Failure of interpolation in relevant logics

Craig's interpolation theorem fails for the prepositional logicsE of entailment,R of relevant implication andT of ticket entailment, as well as in a large class of related logics. This result is proved by a geometrical construction, using the fact that a non-Arguesian projective plane cannot be imbedded in a three-dimensional projective space. The same construction shows failure of the amalgamation property in many varieties of distributive lattice-ordered monoids.     

Children's Classification Skills as Predictors of Their Referential Communicative Encodings

Younger and older children's classification skills were assessed, and their classificatory performance was used as a predictor variable in a multiple-linear-regression analysis to determine whether their classificatory skills accounted for a significant proportion of the variance in their performance on referential communication tasks. We tested 10 boys and 10 girls at each of six age levels between 5 and 10 years individually on a vocabulary test, four classification tasks, and six referential communication tasks. Order of task presentations was counterbalanced; reliabilities for all tasks were high. A series of related multiple-regression analyses showed that grade and vocabulary accounted for a significant proportion of the variance on the referential communication tasks; the series also showed a large decrease in the F value for grade and vocabulary when the contribution of the classification variables was partialled out. No evidence for an independent contribution of the classification variables was found.     

Social predictivism

Predictivism holds that, where evidence E confirms theory T, E confirms T more strongly when E is predicted on the basis of T and subsequently confirmed than when E is known in advance of T's formulation and used, in some sense, in the formulation of T. Predictivism has lately enjoyed some strong supporting arguments from Maher (1988, 1990, 1993) and Kahn, Landsberg, and Stockman (1992). Despite the many virtues of the analyses these authors provide it is my view that they (along with all other authors on this subject) have failed to understand a fundamental truth about predictivism: the existence of a scientist who predicted T prior to the establishment that E is true has epistemic import for T (once E is established) only in connection with information regarding the social milieu in which the T-predictor is located and information regarding how the T-predictor was located. The aim of this paper is to show that predictivism is ultimately a social phenomenon that requires a social level of analysis, a thesis I deem social predictivism.For comments and criticisms I am indebted to Doug Ehring, Mark Heller, Jean Kazez, Patrick Maher, and Alastair Noreross. Special thanks are due to Wayne Woodword for help with the proof in Section 7.     

Coordination dynamics of rhythmical and discrete prehension movements: Implications of the scanning procedure and individual differences

The aim of this study was to compare the coordination dynamics of discrete and rhythmical reaching and grasping movements from a dynamical systems perspective. Previous research from this theoretical perspective had focused on rhythmical actions and it is unclear to what extent discrete movements are amenable to a similar dynamical systems analysis. Six adult subjects performed prehension in two conditions: a discrete, non-continuous mode and a rhythmical, continuous mode. A `scanning procedure' was implemented between pre- and post-tests in which the required time of final relative hand closure (T_rfc) was systematically varied. It was shown that the error in the reaching and grasping pattern was least at an attractor region and systematically increased with deviation from the attractor. Results also indicated that there were no differences between condition or trial block for the group. However, there were several within-subject effects of interest. The validity of the scanning procedure was found to be questionable in the discrete condition, where four subjects showed differences in T_rfc between pre- or post-test and the predicted T_rfc of the scanning procedure. Four out of six subjects also had different preferred T_rfc values for discrete and rhythmical movement, indicating that individual specific models might need to be constructed for future dynamical modelling of discrete movement.PsycINFO classification: 2330     

Hormonal,anthropometrical, and behavioral correlates of physical aggression in !Kung San men of Namibia

Differences in physical aggression among 114 male !Kung San (bushmen) from Namibia were investigated with regard to sex hormone levels, body dimensions, consumption of alcohol, and degree of acculturation. Subjects were classified from injuries resulting from prior conflicts with mutual physical aggression between the opponents as either violent or nonviolent. The comparison of mean sex hormone values (total serum testosterone, T_ser; serum 5α-dihydrotestosterone, DHT; serum estradiol 17β, E₂; “free,” non-SHBG-bound salivary testosterone, T_sal) and hormone ratios (T_sal/T_ser; DHT/T_ser) did not yield any significant differences between the violent and nonviolent group. However, correlation coefficients of sex hormone levels with the frequency of violent behavior within the group of physically aggressive San men were significantly positive for DHT, T_sal, and T_sal/T_ser (P < .05) while T_ser, E₂, and DHT/T_ser showed only weak positive correlations. Moreover, the violent men exhibit higher mean values in certain measures of physical robustness which may point to a possible pathway of indirect androgen action on human aggression. When the probands were classified according to their drinking habits, usually abstinent men had shown significantly less violent behavior in the past than men who habitually consume alcohol.     

Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A search procedure to locate the greatest lower bound

Finding the greatest lower bound for the reliability of the total score on a test comprisingn non-homogenous items with dispersion matrix Σ _x is equivalent to maximizing the trace of a diagonal matrix Σ _E with elements θ _I , subject to Σ _E and Σ _T =Σ _x − Σ _E being non-negative definite. The casesn=2 andn=3 are solved explicity. A computer search in the space of the θ _i is developed for the general case. When Guttman's λ₄ (maximum split-half coefficient alpha) is not the g.l.b., the maximizing set of θ _i makes the rank of Σ _T less thann − 1. Numerical examples of various bounds are given. Present affiliation of the first author: St. Hild's College of Education, Durham City, England.     

On the misuse of manifest variables in the detection of measurement bias

Measurement invariance (lack of bias) of a manifest variableY with respect to a latent variableW is defined as invariance of the conditional distribution ofY givenW over selected subpopulations. Invariance is commonly assessed by studying subpopulation differences in the conditional distribution ofY given a manifest variableZ, chosen to substitute forW. A unified treatment of conditions that may allow the detection of measurement bias using statistical procedures involving only observed or manifest variables is presented. Theorems are provided that give conditions for measurement invariance, and for invariance of the conditional distribution ofY givenZ. Additional theorems and examples explore the Bayes sufficiency ofZ, stochastic ordering inW, local independence ofY andZ, exponential families, and the reliability ofZ. It is shown that when Bayes sufficiency ofZ fails, the two forms of invariance will often not be equivalent in practice. Bayes sufficiency holds under Rasch model assumptions, and in long tests under certain conditions. It is concluded that bias detection procedures that rely strictly on observed variables are not in general diagnostic of measurement bias, or the lack of bias.Preparation of this article was supported in part by PSC-CUNY grant #661282 to Roger E. Millsap.     

Counselor Values: A National Survey

A national sample (n = 479) of counselors representative of the 1993 American Counseling Association membership was surveyed regarding their value orientations in four domains: universal values, mental health values, individualistic-collectivistic values, and religious-spiritual values. Results yielded a multifaceted, generally concordant (although by no means unanimous) value profile for professional counselors across these value domains, presenting an overall content pattern that might be globally summarized as a strong core valuing of holistic-humanistic empowerment related to personal development and interpersonal and social concern. Implications for counseling practice, limitations, and suggestions for future research are discussed.     

Valuation Semantics for First-Order Logics of Evidence and Truth

This paper introduces the logic QLET_F, a quantified extension of the logic of evidence and truth LET_F, together with a corresponding sound and complete first-order non-deterministic valuation semantics. LET_F is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (FDE) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘A entails that A behaves classically, ∙A follows from A’s violating some classically valid inferences. The semantics of QLET_F combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of FDE, K3, and LP, we show how these tools, which we call here the method of anti-extensions + valuations, can be naturally applied to a number of non-classical logics.

     

Correcting Too Much or Too Little? The Performance of Three Chi-Square Corrections

This simulation study investigates the performance of three test statistics, T₁, T₂, and T₃, used to evaluate structural equation model fit under non normal data conditions. T₁ is the well-known mean-adjusted statistic of Satorra and Bentler. T₂ is the mean-and-variance adjusted statistic of Sattertwaithe type where the degrees of freedom is manipulated. T₃ is a recently proposed version of T₂ that does not manipulate degrees of freedom. Discrepancies between these statistics and their nominal chi-square distribution in terms of errors of Type I and Type II are investigated. All statistics are shown to be sensitive to increasing kurtosis in the data, with Type I error rates often far off the nominal level. Under excess kurtosis true models are generally over-rejected by T₁ and under-rejected by T₂ and T₃, which have similar performance in all conditions. Under misspecification there is a loss of power with increasing kurtosis, especially for T₂ and T₃. The coefficient of variation of the nonzero eigenvalues of a certain matrix is shown to be a reliable indicator for the adequacy of these statistics.     

A Five‐dimensional Model of Attributes: Some precursors of executive coach selection

The purpose of this study was to specify a set of attributes, identified as important precursors to coach selection. Executive coaching has grown exponentially, but there have been few studies as to the efficacy of coaching, including the factors that influence a manager's choice of coach. This study sought to identify these factors. The 45‐item, online survey produced 267 useable responses. Results of the principal component analysis suggested a five‐factor solution, with women showing a statistically significant preference over men for coaches who have the Ability to Develop Critical Thinking and Action, the Ability to Forge the Coaching Partnership and Coach Experience and Qualifications. The impact of coachee age was not significant in selecting executive coaches. The findings show a statistically significant relationship between coach attributes and the intention to continue with coaching. The implications of these findings for the selection of coaches, and for the coaching profession are discussed.     

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model sayM ₀ implies on a less restricted oneM ₁. IfT ₀ andT ₁ denote the goodness-of-fit test statistics associated toM ₀ andM ₁, respectively, then typically the differenceT _d =T ₀−T ₁ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the modelsM ₀ andM ₁. As in the case of the goodness-of-fit test, it is of interest to scale the statisticT _d in order to improve its chi-square approximation in realistic, that is, nonasymptotic and nonormal, applications. In a recent paper, Satorra (2000) shows that the difference between two SB scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are not available in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of modelsM ₀ andM ₁. A Monte Carlo study is provided to illustrate the performance of the competing statistics. This research was supported by the Spanish grants PB96-0300 and BEC2000-0983, and USPHS grants DA00017 and DA01070.     

Two Empirical Inquiries Into the Role of The Personnel and Guidance Journal As a Professional Publication

A survey of the APGA membership was undertaken in the fall of 1977 to determine interest and content-process priorities of readers of the Personnel and Guidance Journal. The survey was sent to a stratified random sample of members reflecting appropriate distribution by division membership and geographic area of residence. The list of members was obtained from the APGA central office. The result of the data analyses suggests that the Personnel and Guidance Journal has generally served the diverse interests of the membership well. Some differences in emphasis and content preferences were identified between divisions.     

On the Concept of Comparison in Mentally Retarded and Nonretarded Children

Two adjective pairs in comparative form, more-less and taller-shorter, were tested with moderately mentally retarded (MR) and nonretarded children (NR) matched on verbal mental age (MA) and socioeconomic status (SES) in a show and an act-out experimental condition. The data indicated that all the main effects, the group, the experimental condition, and the unmarked-marked relational terms were significant and so were the interactions of the Group × Experimental Conditions, Group × Unmarked Versus Marked Relational Terms, and Group × Experimental Conditions and Unmarked Versus Marked Relational Terms. A logistic regression analysis (LRA) showed that the relational term shorter in the act-out condition best predicted classification membership for the subjects in either group, suggesting that the MR children were less able to self-regulate behavior. The error types, however, mainly observed in the act-out experimental condition were the same from a semantic point of view in either group. The effect of the unmarked versus marked distinction cannot be considered independent of the experimental conditions applied.     

Creative idea generation: harmony versus stimulation

The literature on maintaining versus changing membership of groups has generally favored stable membership, not only for more cohesion and morale but for better performance via comfort and shared experiences. On the other hand, research on the stimulating properties of dissent, debate and diversity would argue for a change in membership in that it would provide access to differing views and stimulate more divergent and creative thought. The present study investigated idea generation when membership was maintained versus completely changed. We predicted and found that maintaining membership increases comfort and also the perception of creativity but not actual creative behavior whereas changing membership results in a less comfortable experience but also an increase in the number and creativity of the ideas generated. Copyright © 2006 John Wiley & Sons, Ltd.