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Journal ArticleDOI

Multidimensional Data Analysis

01 Sep 1989-Biometrics-Vol. 45, Iss: 3, pp 1034
About: This article is published in Biometrics.The article was published on 1989-09-01. It has received 90 citations till now. The article focuses on the topics: Multidimensional analysis.
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Journal ArticleDOI
TL;DR: In this article, the authors examined the conceptualization and measurement of the political skill construct and provided validation evidence for the Political Skill Inventory (PSI) and found that political skill was positively related to self-monitoring, political savvy, and emotional intelligence; negatively related to trait anxiety; and not correlated with general mental ability.

1,102 citations

Journal ArticleDOI
TL;DR: The smoothing approximation of the cross-validation criterion (SACV) and the GCV criterion is defined and the method is assessed with simulations and gives promising results.

197 citations


Cites background from "Multidimensional Data Analysis"

  • ...It is also possible to define a generalized cross-validation (GCV) criterion (Craven and Wahba, 1979) which consists in substituting each element Pik,ik by its average value, i....

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  • ...As explained in the introduction, in a linear smoothing framework, the prediction error for an individual i can be written explicitly from the adjustment error and the smoothing matrix (Craven and Wahba, 1979) as (3). Consequently, there is no need to perform cross-validation to compute the mean square error of prediction. It is sufficient to compute the adjusted vector and the smoothing matrix. A linear smoother means that the fit at a point can be expressed as a linear combination of the response vector and that the coefficients in the linear combination do not depend on the response vector. In other words, ŷ = Py with P independent of y. The smoother involved in PCA (9) is nonlinear since it depends on the data. In the framework of nonlinear smoothers, only approximations of the prediction error can be derived as shown in O’Sullivan and Wahba (1985), Ke and Wang (2004) and Sima (2006, p....

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  • ...It is also possible to define a generalized cross-validation (GCV) criterion (Craven and Wahba, 1979) which consists in substituting each element Pik,ik by its average value, i.e. tr(P)/(IK)....

    [...]

  • ...As explained in the introduction, in a linear smoothing framework, the prediction error for an individual i can be written explicitly from the adjustment error and the smoothing matrix (Craven and Wahba, 1979) as (3)....

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Journal ArticleDOI
TL;DR: The GRT identification model accurately predicted the similarity judgments under the assumption that Ss allocated attention to the 2 stimulus dimensions differently in the 2 tasks, and the categorization data were predicted successfully without appealing to the notion of selective attention.
Abstract: In this article, the relation between the identification, similarity judgment, and categorization of multidimensional perceptual stimuli is studied. The theoretical analysis focused on general recognition theory (CRT), which is a multidimensional generalization of signal detection theory. In one application, 2 Ss first identified a set of confusable stimuli and then made judgments of their painvise similarity. The second application was to Nosofsky's (1985b, 1986) identificationcategorization experiment. In both applications, a GRT model accounted for the identification data better than Luce's (1963) biased-choice model. The identification results were then used to predict performance in the similarity judgment and categorization conditions. The GRT identification model accurately predicted the similarity judgments under the assumption that Ss allocated attention to the 2 stimulus dimensions differently in the 2 tasks. The categorization data were predicted successfully without appealing to the notion of selective attention. Instead, a simpler GRT model that emphasized the different decision rules used in identificatio n and categorization was adequate. The perceptual processes involved when subjects identify, categorize, or judge the pairwise similarity of multidimensional perceptual stimuli are closely related (e.g., Ashby & Perrin, 1988; Getty, Swets, Swets, & Green, 1979; Nosofsky, 1986; Shepard & Chang, 1963; Shepard, Hovland, & Jenkins, 1961). Roughly speaking, as the similarity between a pair of stimuli increases, so too does the probability that one will be misidentified as the other and the probability that they will be assigned to the same category. This observation suggests a possible close relationship between these three tasks. During the past several years, a number of theories have been developed that attempt to simultaneousl y account for data from all three of these tasks. Such theories are important because they represent attempts to integrate a broad spectrum of psychological data within one theoretical framework. In this article, we (a) explore the empirical relation between identification, categorization, and similarity judgment and (b) examine the ability of the more powerful of these theories to predict categorization performance and judgments of perceived similarity from the confusions that subjects make in an identification task. The models that we focus most heavily on are derived from general recognition theory (GRT; Ashby & Gott, 1988; Ashby & Perrin, 1988; Ashby & Townsend, 1986). They assume that the perceptual effect associated with each presentation of a stimulus can be represented as a point in a multidimensional space but that perceptual noise causes the percept to vary over trials. Thus, GRT assumes that a distribution of percepts is the appropriate perceptual representation of a stimulus. During identification or categorization, the subject is assumed to

194 citations

01 Jul 2002
TL;DR: In this article, a method is developed to determine how crash characteristics are related to traffic flow conditions at the time of occurrence, and crashes are described in terms of the type and location of the collision, the number of vehicles involved, movements of these vehicles prior to collision and severity.
Abstract: A method is developed to determine how crash characteristics are related to traffic flow conditions at the time of occurrence. Crashes are described in terms of the type and location of the collision, the number of vehicles involved, movements of these vehicles prior to collision, and severity. Traffic flow is characterized by central tendencies and variations of traffic flow and speed for three different lanes at the time and place of the crash. The method involves nonlinear canonical correlation applied together with cluster analyses to identify traffic flow regimes with distinctly different crash taxonomies. A case study using data for more than 1,000 crashes in Southern California identified twenty-one traffic flow regimes for three different ambient conditions: dry roads during daylight (eight regimes), dry roads at night (six regimes), and wet conditions (seven regimes). Each of these regimes has a unique profile in terms of the type of crashes that are most likely to occur. A matching of traffic flow parameters and crash characteristics reveals ways in which congestion affects highway safety.

164 citations

Journal ArticleDOI
TL;DR: In this article, a method is developed to determine how crash characteristics are related to traffic flow conditions at the time of occurrence, and crashes are described in terms of the type and location of the collision, the number of vehicles involved, movements of these vehicles prior to collision and severity.
Abstract: A method is developed to determine how crash characteristics are related to traffic flow conditions at the time of occurrence. Crashes are described in terms of the type and location of the collision, the number of vehicles involved, movements of these vehicles prior to collision, and severity. Traffic flow is characterized by central tendencies and variations of traffic flow and flow/occupancy for three different lanes at the time and place of the crash. The method involves nonlinear canonical correlation applied together with cluster analyses to identify traffic flow regimes with distinctly different crash taxonomies. A case study using data for more than 1000 crashes in Southern California identified twenty-one traffic flow regimes for three different ambient conditions: dry roads during daylight (eight regimes), dry roads at night (six regimes), and wet conditions (seven regimes). Each of these regimes has a unique profile in terms of the type of crashes that are most likely to occur, and a matching of traffic flow parameters and crash characteristics reveals ways in which congestion affects highway safety.

162 citations