Exposure to community violence and social support as predictors of anxiety and social and emotional behavior among African American children

We examined the effects of exposure to violence and social support on self-reported state and trait anxiety and parental rated problem behaviors among school-aged African-American children in low and high violence areas. Ninety-seven (97) fourth through sixth graders and their parents were interviewed about exposure to community violence, social support, and state and trait anxiety. Results indicate that trait anxiety was correlated positively with exposure to violence and negatively with social support. State anxiety was correlated negatively with family social support. Problem behaviors were correlated negatively with family support and income. Hierarchial multiple regression analyses indicated that children's reports of their exposure to community violence continued to explain significant variability in trait anxiety, and problem behavior after controlling for both income and social support measures. Social support from peers, family and teachers played differential roles in predicting problem behaviors among children from high and lower violence areas. These findings suggest that in planning intervention programs for children exposed to violence, greater attention to empowering parents to support their children, to fostering peer group support, and to bolstering teacher support may be useful, but attention to the underlying socio-political causes of violence exposure is essential.     

An alternative two stage least squares (2SLS) estimator for latent variable equations

The Maximum-likelihood estimator dominates the estimation of general structural equation models. Noniterative, equation-by-equation estimators for factor analysis have received some attention, but little has been done on such estimators for latent variable equations. I propose an alternative 2SLS estimator of the parameters in LISREL type models and contrast it with the existing ones. The new 2SLS estimator allows observed and latent variables to originate from nonnormal distributions, is consistent, has a known asymptotic covariance matrix, and is estimable with standard statistical software. Diagnostics for evaluating instrumental variables are described. An empirical example illustrates the estimator. I gratefully acknowledge support for this research from the Sociology Program of the National Science Foundation (SES-9121564) and the Center for Advanced Study in the Behavioral Sciences, Stanford, California. This paper was presented at the Interdisciplinary Consortium for Statistical Applications at Indiana University at Bloomington (March 2, 1994) and at the RMD Conference on Causal Modeling at Purdue University, West Lafayette, Indiana (March 3-5, 1994).     

Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

Acceleration model in the heterogeneous case of the general graded response model

A new model, called acceleration model, is proposed in the framework of the heterogenous case of the graded response model, based on processing functions defined for a finite or enumerable number of steps. The model is expected to be useful in cognitive assessment, as well as in more traditional areas of application of latent trait models. Criteria for evaluating models are proposed, and soundness and robustness of the acceleration model are discussed. Graded response models based on individual choice behavior are also discussed, and criticisms on model selection in terms of fitnesses of models to the data are also given.This research was supported by the Office of Naval Research (N00014-90-J-1456).     

Models for measurement,precision, and the nondichotomization of graded responses

It is common in educational, psychological, and social measurement in general, to collect data in the form of graded responses and then to combine adjacent categories. It has been argued that because the division of the continuum into categories is arbitrary, any model used for analyzing graded responses should accommodate such action. Specifically, Jansen and Roskam (1986) enunciate ajoining assumption which specifies that if two categoriesj andk are combined to form categoryh, then the probability of a response inh should equal the sum of the probabilities of responses inj andk. As a result, they question the use of the Rasch model for graded responses which explicitly prohibits the combining of categories after the data are collected except in more or less degenerate cases. However, the Rasch model is derived from requirements of invariance of comparisons of entities with respect to different instruments, which might include different partitions of the continuum, and is consistent with fundamental measurement. Therefore, there is a strong case that the mathematical implication of the Rasch model should be studied further in order to understand how and why it conflicts with the joining assumption. This paper pursues the mathematics of the Rasch model and establishes, through a special case when the sizes of the categories are equal and when the model is expressed in the multiplicative metric, that its probability distribution reflects the precision with which the data are collected, and that if a pair of categories is collapsed after the data are collected, it no longer reflects the original precision. As a consequence, and not because of a qualitative change in the variable, the joining assumption is destroyed when categories are combined. Implications of the choice between a model which satisfies the joining assumption or one which reflects on the precision of the data collection considered are discussed.     

Perceptual unit formation in simple motion patterns

The present study investigated the proximal constraints that determine perceptual unit formation under minimal stimulus conditions. Projections of three moving dots, which could form two possible two-dot configurations, were presented to naive observers. In a forced-choice situation, their task was to report which two-dot configuration was perceived as a distinct perceptual unit. The results showed that common motions (arbitrary translations and rigid rotations in the frontoparallel plane) have stronger grouping power as compared to different relative motions (expansions/contractions, or simultaneous expansions/contractions and deformations in the frontoparallel plane). It was found that proximal changes of distances between elements in two-dot structures reduce grouping power. Changes of proximal directions, however, did not affect unit formation in two-dot structures at all. The effect of vector algebraic combinations on grouping power in three-dot strutures was also investigated. Evidently, visual vector analysis splits up motion combinations into their constituents, and in come cases this contributes to additive effects.     

Resilience in siblings of children with sickle cell disease

This pilot study was conducted to identify factors responsible for promoting resilience in siblings of children with sickle cell disease. Twenty siblings (10–17 years of age) of children (5–13 years) with sickle cell disease were selected from the Pediatric Clinic of Howard University Center for Sickle Cell Disease. The siblings responded to questionnaires, and the data obtained was analyzed by chi-square for association. The results indicated that age, birth order, and gender had no effect on resilience in the siblings. However, family size, number of parents in the home, sibling's knowledge of the illness, degree of morbidity of the illness, socioeconomic status of the family, and parents' attitudes and childrearing practices were all found to affect resilience. These findings provide additional insight into the psychosocial aspects of, and genetic counseling for sickle cell disease, as well as for other chronic genetic disorders.     

教师解决结构不良问题策略的发展研究

以成人期个体解决结构不良问题的有关认知加工理论为框架,运用多因素设计的方法,对９０名不同年龄的教师在解决教育和教学实践中常见的三种冲突情景下使用策略的情况进行了探讨。结果发现,教师在解决结构不良问题时,从总体上说不存在年龄差异,但在处理教师与教师、教师与家长等较为复杂的冲突问题时,随着年龄的增长,更趋向于使用元认知和认识论认知策略。该研究对教师培训中如何根据不同年龄特点来进行教育机智训练有一定的理论意义和应用价值。     

Three-mode orthomax rotation

Factor analysis and principal components analysis (PCA) are often followed by an orthomax rotation to rotate a loading matrix to simple structure. The simple structure is usually defined in terms of the simplicity of the columns of the loading matrix. In Three-mode PCA, rotational freedom of the so called core (a three-way array relating components for the three different modes) can be used similarly to find a simple structure of the core. Simple structure of the core can be defined with respect to all three modes simultaneously, possibly with different emphases on the different modes. The present paper provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally, this approach relies on repeated (two-way) orthomax applied to supermatrices containing the frontal, lateral or horizontal slabs, respectively. The procedure is illustrated by means of a number of exemplary analyses. As a by-product, application of the Three-mode Orthomax procedures to two-way arrays is shown to reveal interesting relations with and interpretations of existing two-way simple structure rotation techniques.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge and two anonymous reviewers for useful comments on an earlier version of this paper.