Some relationships between factors and components

The asymptotic correlations between the estimates of factor and component loadings are obtained for the exploratory factor analysis model with the assumption of a multivariate normal distribution for manifest variables. The asymptotic correlations are derived for the cases of unstandardized and standardized manifest variables with orthogonal and oblique rotations. Based on the above results, the asymptotic standard errors for estimated correlations between factors and components are derived. Further, the asymptotic standard error of the mean squared canonical correlation for factors and components, which is an overall index for the closeness of factors and components, is derived. The results of a Monte Carlo simulation are presented to show the usefulness of the asymptotic results in the data with a finite sample size.The author is indebted to anonymous referees for their comments, corrections and suggestions which have led to the improvement of this article.     

Improving an optimization‐based framework for sensitivity analysis in multi‐criteria decision‐making

The framework for sensitivity analysis in discrete multi‐criteria decision analysis developed by Rios Insua and French allows simultaneous variation of all parameters and applies to many paradigms for decision analysis. However, its computational load may inhibit use, particularly in the context of a decision conference where results are required in near real time. In order to improve on the current algorithm and its implementation, we investigate, on the one hand, an opportunistic approach aimed at reducing the number of optimization problems solved in the original framework and, on the other, an alternative framework based on distance analysis. Computational results on linear and bilinear models are reported. Copyright © 2001 John Wiley & Sons, Ltd.     

Assessing risky public investments with MUSTARD

This paper presents a practical implementation of multicriteria methodologies based on the UTA model by Jacquet‐Lagrèze and Siskos and Quasi‐UTA model by Beuthe and Scannella, which are specified with a non‐linear, but piecewise linear, additive utility function. In contrast with the general UTA model, the Quasi‐UTA specification structures the partial utilities as recursive exponential functions of only one curvature parameter. This allows for a reduction of the quantity of information necessary to build the utility function. The software MUSTARD implements different variants of these models. Firstly, it offers the basic deterministic UTA model of disaggregation, but also its first programmed stochastic version. In both cases, the software proceeds stepwise and interactively helping the decision maker to formulate the problem and state preferences between projects; in the stochastic case, the decision maker is even helped to build the criteria distributions. The Quasi‐UTA specification can be introduced in this disaggregation model. Secondly, the software offers an aggregation model whereby the Quasi‐UTA partial utility functions are built separately through specific questioning processes. The questions relating to deterministic criteria are of the ‘direct rating type’, while those of the stochastic criteria are either of the ‘variable probability’ or the ‘variable outcome’ type. The criteria weights can be assessed by the ‘swing weight’ method or by a UTA‐II side‐program. As an example as well as a test of the Quasi‐UTA aggregation approach, the paper presents its application to a real problem of selecting road investment projects in Belgium. Several experts and civil servants were interviewed, and their individual utility functions derived. The projects are ranked according to their rate of return, which is computed on the basis of the projects certain equivalent money value. Copyright © 2002 John Wiley & Sons, Ltd.     

An evaluation of multi‐criteria methods in integrated assessment of climate policy

Those who conduct integrated assessments (IAs) are aware of the need to explicitly consider multiple criteria and uncertainties when evaluating policies for preventing global warming. MCDM methods are potentially useful for understanding tradeoffs and evaluating risks associated with climate policy alternatives. A difficulty facing potential MCDM users is the wide range of different techniques that have been proposed, each with distinct advantages. Methods differ in terms of validity, ease of use, and appropriateness to the problem. Alternative methods also can yield strikingly different rankings of alternatives. A workshop was held in which climate change experts and policy makers evaluated the usefulness of MCDM for IA. Participants applied several methods in the context of a hypothetical greenhouse gas policy decision. Methods compared include value and utility functions, goal programming, ELECTRE, fuzzy sets, stochastic dominance, min max regret, and several weight selection methods. Ranges, rather than point estimates, were provided for some questions to incorporate imprecision regarding weights. Additionally, several visualization methods for both deterministic and uncertain cases were used and evaluated. Analysis of method results and participant feedback through questionnaires and discussion provide the basis for conclusions regarding the use of MCDM methods for climate change policy and IA analyses. Hypotheses are examined concerning predictive and convergent validity of methods, existence of splitting bias among experts, perceived ability of methods to aid decision‐making, and whether expressing imprecision can change ranking results. Because participants gained from viewing a problem from several perspectives and results from different methods often significantly differed, it appears worthwhile to apply several MCDM methods to increase user confidence and insight. The participants themselves recommended such multimethod approaches for policymaking. Yet they preferred the freedom of unaided decision‐making most of all, challenging the MCDM community to create transparent methods that permit maximum user control. Copyright © 2002 John Wiley & Sons, Ltd.     

5·12汶川地震后灾区教师主观幸福感的变化趋势及中介效应分析

·12汶川地震发生两个月后,对508名灾区的幼儿园、中小学教师进行测量,结合他们对地震前状况的回忆,考察其地震后主观幸福感的变化情况及其影响因素。结果表明：（1）与回忆得到的地震前感受相比,地震后灾区教师体验到主观幸福感水平显著降低。（2）极重灾区教师体验到的主观幸福感降低程度大于重灾区和轻灾区教师。（3）教师遭受的客观损失严重程度能显著预测其体验到的主观幸福感降低;而创伤后身心症状在其中起完全中介的作用,即创伤事件引发教师创伤后身心症状,而这些症状日趋严重,使其体验到的消极情感增加、主观幸福感降低。     

Similarity and reluctance to trade

Previous research has shown that after decision makers are endowed with an object, they are reluctant to trade it for an alternative item. This endowment effect can be explained by loss aversion, the tendency to weight losses more heavily than gains. Consequently, there is no reluctance to trade when no true loss is involved. Four studies investigated whether reluctance to trade declines when the trade involves less of a loss—specifically, when one item is traded for another very similar item. Three experiments did not reveal a relation between willingness to trade and the similarity between the two items being traded. A fourth experiment, however, indicated that subjects were quite willing to trade for an identical item, less willing to trade for a similar item, and even less willing to trade for a dissimilar item. Thus, reluctance to trade decreased as the similarity between the endowment and the alternative increased. This result suggests that loss aversion is a function not only of the item being lost but also of the trade itself—that is, of the relation between the two items being traded. © 1998 John Wiley & Sons, Ltd.     

Attribute‐based differentiation of alternatives

An intermediate step is introduced to the dialogue decision process for decision analysis. Alternatives are refined after they have been generated within a strategy table but before they are subject to more detailed evaluation. Two or more judges create a subjective mapping from alternatives to attributes that will later be mapped to criteria. In strategy tables, each of the alternative strategies consists of a coherent set of choices made across several decisions that are to be coordinated. These strategic alternatives are modified so as to increase their differentiation in the attribute space, rather than in the decision space alone. When criteria weights are unknown, the best alternative from the modified set may be superior to the best alternative from the original set. Furthermore, analysis of the resulting alternatives may yield a better mapping of the value response surface for the action space, in the sense that this mapping leads to eventual construction of a higher value alternative. Results are reported for a consulting engagement incorporating the proposed step. Copyright © 2003 John Wiley & Sons, Ltd.