Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

A method of optimal scaling for multivariate ordinal data and its extensions

This paper develops a method of optimal scaling for multivariate ordinal data, in the framework of a generalized principal component analysis. This method yields a multidimensional configuration of items, a unidimensional scale of category weights for each item and, optionally, a multidimensional configuration of subjects. The computation is performed by alternately solving an eigenvalue problem and executing a quasi-Newton projection method. The algorithm is extended for analysis of data with mixed measurement levels or for analysis with a combined weighting of items. Numerical examples and simulations are provided. The algorithm is discussed and compared with some related methods.Earlier results of this research appeared in Saito and Otsu (1983). The authors would like to acknowledge the helpful comments and encouragement of the editor.     

Functional measurement approach to self-estimation in multiattribute evaluation

Multiattribute analysis depends on measurement of values and weights. Unless these measures reflect the decision maker's true values and weights, the multiattribute formula may put a less-preferred alternative in first place. To avoid such disordinality requires stringent measurement conditions: First, the values and weights must be on linear (equal interval) or ratio (known zero) scales. Second, these scales must satisfy a condition of common unit across disparate attribute dimensions. Most methods of range adjustment beg both of these measurement questions. Functional measurement theory can solve both problems and so can be useful in multiattribute analysis. Past work has established the operation of a general cognitive algebra as an empirical reality. The averaging model, in particular, makes possible the definition and estimation of weights and values as distinct psychological parameters. It can also solve the problem of common unit. Cognitive algebra thus provides a grounded theoretical foundation on which to develop self-estimation methodology, in which decision makers provide direct estimates of their values and weights. The logic is straightforward. Functional measurement can analyze global judgments to obtain validated psychological scales. These scales may then be used as validational criteria for the self-estimates. Procedures to eliminate biases in the self-estimates can thus be tested and refined in well-learned multiattribute tasks, such as judgments of meals, in which global judgments are trustworthy. Once developed, such self-estimation procedures may be used with some confidence for general multiattribute analysis. A number of studies from 20-odd years of work on the theory of information integration are summarized to show good, although not unmixed promise for self-estimation.     

Factor invariance of the Millon Clinical Multiaxial Inventory

Several factor analyses of the Millon Clinical Multiaxial Inventory (MCMI) have resulted in very similar solutions. Interpretation of this consistency is hampered by the fact that the 20 scales of the inventory share items. Overlapping items cause the scales to be linearly dependent and may create structure in the interscale correlation matrix which is separate from the subject response patterns. A factor analysis was performed on the matrix of item-overlap coefficients which describes the underlying artifactual structure of the instrument. Data from two new subject samples were factor analyzed and compared to previously published studies. Similarity coefficients among factors across studies were calculated.     

PROMOTING LAW ENFORCEMENT FOR CHILD PROTECTION: A COMMUNITY ANALYSIS

The Colorado Occupant Protection Project (COPP) intervention provided police with brief instruction concerning the importance of citations for drivers' failure to use child safety seats and special coupons to accompany citations. Coupons were exchangeable by drivers for a safety seat and brief training in its use, plus a waiver of the $50 citation fine. Over 4.5 years of archival records were employed, using an ABA design and a comparison community to evaluate the program. Few tickets were issued for nonuse of safety seats during the 3-year baseline in either community. Citations for nonuse of safety seats increased to over 50 per month during the intervention period at the test site, whereas rates remained essentially zero at the comparison site. After the COPP intervention was removed at the intervention site, citation rates for nonuse of safety seats decreased to about 15 per month. Differences between intervention conditions and settings were statistically significant. During the intervention, officers were 44 times more likely to write citations than were controls. Results suggested that a behavioral program can increase police citation writing for child protection purposes.     

COVARIATION WITHIN FUNCTIONAL RESPONSE CLASSES: IMPLICATIONS FOR TREATMENT OF SEVERE PROBLEM BEHAVIOR

Two studies examined the effects of a reductive treatment versus instruction-based treatments on the generalized reduction of problem behaviors. Each study involved a detailed analysis of multiple problem behaviors performed by school-aged youth with severe intellectual disabilities. The analysis examined the contrasting effects of one of two different positive intervention procedures (teaching a positive alternative behavior or providing additional teacher assistance during instruction) versus blocking and/or verbally reprimanding a problem behavior. The focus of each analysis was on the covariation of multiple problem behaviors within functional response classes. Results of the investigation indicated that when only one member of the response class was blocked, a collateral increase was observed in one or more different problem behaviors from the same response class. Alternatively, when 1 participant was taught a functionally equivalent mand response, all problem behaviors in the response class were reduced. Problem behaviors also were reduced for the remaining participant by presenting antecedent teacher assistance. Implications of the research extend to analysis of covariation within response classes and to procedures that result in generalized reduction of problem behaviors within a response class.     

AN ANALYSIS OF MAINTENANCE FOLLOWING FUNCTIONAL COMMUNICATION TRAINING

The multiple and long-term effects of functional communication training relative to a common reductive procedure (time-out from positive reinforcement) were evaluated. Twelve children participated in a functional analysis of their challenging behaviors (Study 1), which implicated adult attention as a maintaining variable. The children were then matched for chronological age, mental age, and language age and assigned to two groups. One group received functional communication training as an intervention for their challenging behavior, and the second group received time-out as a contrast. Both interventions were initially successful (Study 2), but durable results were achieved only with the group that received functional communication training across different stimulus conditions (Study 3). Students whose challenging behaviors were previously reduced with time-out resumed these behaviors in the presence of naive teachers unaware of the children's intervention history. The value of teaching communicative responses to promote maintenance is discussed as it relates to the concept of functional equivalence.     

Beyond principal component analysis: A trilinear decomposition model and least squares estimation

The paper derives sufficient conditions for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis.     

谈谈个人对智力落后儿童早期干预的看法

本文作者根据从事智力落后儿童的早期干预教学研究的实践经验对当今在我国开展早期干预的必要性以及早期干预的目的、设置的理由、内容、方式、对象、教师的条件、效果的评价以及开展的步骤等9个问题,提出了自己的看法。     

PARADIGMS OF BELIEF, THEORY AND METATHEORY

Abstract. My account of the recent turnabout in the treatment of mental states in science and its basis in a modified concept of causal determinism and my claim that this opens the way for beliefs and values consistent with science are here reaffirmed in response to perceived weaknesses and "inherent incompleteness." Contested issues are reviewed to better clarify the main thesis. An inherent weakness in respect to deep spiritual needs is recognized and tentative remedial measures explored.