David V. Budescu

Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression.

Whenever multiple regression is used to test and compare theoretically motivated models, it is of interest to determine the relative importance of the predictors. Specifically, researchers seek to rank order and scale variables in terms of their importance and to express global statistics of the model as a function of these measures. This article reviews the many meanings of importance of predictors in multiple regression, highlights their weaknesses, and proposes a new method for comparing variables: dominance analysis. Dominance is a qualitative relation defined in a pairwise fashion: One variable is said to dominate another if it is more useful than its competitor in all subset regressions. Properties of the newly proposed method are described and illustrated

The dominance analysis approach for comparing predictors in multiple regression.

A general method is presented for comparing the relative importance of predictors in multiple regression. Dominance analysis (D. V. Budescu, 1993), a procedure that is based on an examination of the R2 values for all possible subset models, is refined and extended by introducing several quantitative measures of dominance that differ in the strictness of the dominance definition. These are shown to be intuitive, meaningful, and informative measures that can address a variety of research questions pertaining to predictor importance. The bootstrap is used to assess the stability of dominance results across repeated sampling, and it is shown that these methods provide the researcher with more insights into the pattern of importance in a set of predictors than were previously available.

Measuring the vague meanings of probability terms.

Can the vague meanings of probability terms such as doubtful, probable, or likely be expressed as membership functions over the [0, 1] probability interval? A function for a given term would assign a membership value of /ero to probabilities not at all in the vague concept represented by the term, a membership value of one to probabilities definitely in the concept, and intermediate membership values to probabilities represented by the term to some degree. A modified pair-comparison procedure was used in two experiments to empirically establish and assess membership functions for several probability terms. Subjects performed two tasks in both experiments: They judged (a) to what degree one probability rather than another was better described by a given probability term, and (b) to what degree one term rather than another better described a specified probability. Probabilities were displayed as relative areas on spinners. Task a data were analyzed from the perspective of conjoint-measurement theory, and membership function values were obtained for each term according to various scaling models. The conjoint-measurement axioms were well satisfied and goodness-of-fit measures for the scaling procedures were high. Individual differences were large but stable. Furthermore, the derived membership function values satisfactorily predicted the judgments independently obtained in task b. The results support the claim that the scaled values represented the vague meanings of the terms to the individual subjects in the present experimental context. Methodological implications are discussed, as are substantive issues raised by the data regarding the vague meanings of probability terms.

Consistency in interpretation of probabilistic phrases

Abstract It is occasionally claimed in both applied decision analysis and in basic research that people can better use and understand probabilistic opinions expressed by nonnumerical phrases, such as “unlikely” or “probably,” than by numbers. It is important for practical and theoretical reasons to evaluate this claim. The available literature indicates that there is large variability in the mapping of phrases to numbers, but provides no indication as to its cause. This study asks (a) whether the variability can be attributed to how people interpret the phrases per se, rather than to how they use the number scale and (b) whether the variability is due primarily to between-subject or to within-subject factors. In order to answer these questions, 32 subjects ranked and compared 19 probability phrases on each of three occasions. The results show that individuals have a relatively stable rank ordering of the phrases over time, but that different individuals have different rank orderings. Practical and methodological implications of these data are discussed.

Preferences and reasons for communicating probabilistic information in verbal or numerical terms.

Despite much disagreement regarding how probabilistic information is best communicated, virtually no research has been done to determine what communication modes people prefer or what factors affect their communication preferences. To address these issues, we did a survey of 442 graduate and undergraduate students in several specialties and universities. Some group differences emerged, but overall, 34% expressed preference for both conveying and receiving information about uncertainty in numerical rather than verbal form, 30% expressed the opposite preferences, and 35% indicated that they preferred to receive such information numerically but to convey it verbally. Generally, respondents who endorsed the use of verbal information said that it is easier to use, as well as more natural and personal. Those preferring numerical information said that it is more precise. Virtually all respondents, however, evidenced a willingness to use the opposite of their initially preferred mode if the situation should warrant it. The willingness to switch from one mode to another was said to depend on the level of precision implied by the data and the importance of the issue, as was suggested by Budescu and Wallsten (1987). These results may be helpful in structuring risk communication strategies.

Processing Linguistic Probabilities: General Principles and Empirical Evidence

Publisher Summary This chapter discusses that practical issues arise because weighty decisions often depend on forecasts and opinions communicated from one person or set of individuals to another. The standard wisdom has been that numerical communication is better than linguistic, and therefore, especially in important contexts, it is to be preferred. A good deal of evidence suggests that this advice is not uniformly correct and is inconsistent with strongly held preferences. A theoretical understanding of the preceding questions is an important step toward the development of means for improving communication, judgment, and decision making under uncertainty. The theoretical issues concern how individuals interpret imprecise linguistic terms, what factors affect their interpretations, and how they combine those terms with other information for the purpose of taking action. The chapter reviews the relevant literature in order to develop a theory of how linguistic information about imprecise continuous quantities is processed in the service of decision making, judgment, and communication. It provides current view, which has evolved inductively, to substantiate it where the data allow, and to suggest where additional research is needed. It also summarizes the research on meanings of qualitative probability expressions and compares judgments and decisions made on the basis of vague and precise probabilities.

Evaluating and Combining Subjective Probability Estimates

This paper concerns the evaluation and combination of subjective probability estimates for categorical events. We argue that the appropriate criterion for evaluating individual and combined estimates depends on the type of uncertainty the decision maker seeks to represent, which in turn depends on his or her model of the event space. Decision makers require accurate estimates in the presence of aleatory uncertainty about exchangeable events, diagnostic estimates given epistemic uncertainty about unique events, and some combination of the two when the events are not necessarily unique, but the best equivalence class definition for exchangeable events is not apparent. Following a brief reveiw of the mathematical and empirical literature on combining judgments, we present an approach to the topic that derives from (1) a weak cognitive model of the individual that assumes subjective estimates are a function of underlying judgment perturbed by random error and (2) a classification of judgment contexts in terms of the underlying information structure. In support of our developments, we present new analyses of two sets of subjective probability estimates, one of exchangeable and the other of unique events. As predicted, mean estimates were more accurate than the individual values in the first case and more diagnostic in the second. #1997 by John Wiley & Sons, Ltd.

A review of human linguistic probability processing: General principles and empirical evidence

This article reviews research on how people use and understand linguistic expressions of uncertainty, with a view toward the needs of researchers and others interested in artificial intelligence systems. We discuss and present empirical results within an inductively developed theoretical framework consisting of two background assumptions and six principles describing the underlying cognitive processes.

Effective communication of uncertainty in the IPCC reports

The Intergovernmental Panel on Climate Change (IPCC) publishes periodical assessment reports informing policymakers and the public on issues relevant to the understanding of human induced climate change. The IPCC uses a set of 7 verbal descriptions of uncertainty, such as unlikely and very likely to convey the underlying imprecision of its forecasts and conclusions. We report results of an experiment comparing the effectiveness of communication using these words and their numerical counterparts. We show that the public consistently misinterprets the probabilistic statements in the IPCC report in a regressive fashion, and that there are large individual differences in the interpretation of these statements, which are associated with the respondents’ ideology and their views and beliefs about climate change issues. Most importantly our results suggest that using a dual (verbal—numerical) scale would be superior to the current mode of communication as it (a) increases the level of differentiation between the various terms, (b) increases the consistency of interpretation of these terms, and (c) increases the level of consistency with the IPCC guidelines. Most importantly, these positive effects are independent of the respondents’ ideological and environmental views.

The elusive wishful thinking effect

Abstract We define a desirability effect as the inflation of the judged probability of desirable events or the diminution of the judged probability of undersirable events. A series of studies of this effect are reported. In the first four experiments, subjects were presented with visual stimuli (a grid matrix in two colours, or a jar containing beads in two colours), and asked to estimate the probability of drawing at random one of the colours), and asked to estimate the probability of drawing at random one of the colours. The estimated probabilities for a defined draw were not higher when the draw entailed a gain than when it entailed a loss. In the fifth and sixth experiments, subjects read short stories each describing two contestants competing for some desirable outcome (e.g. parents fighting for child custody, or firms bidding for a contract). Some judged the probability that A would win, others judged the Desirability that A would win. Story elements that enhanced a contestants desirability did not...