Browsing by Author "Davison, Mark L."
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Item Ability factor differentiation, Grades 5 through 11(1977) Atkin, Robert; Bray, Robert; Davison, Mark L.; Herzberger, Sharon; Humphreys, Lloyd G.; Selzer, UziFactor analyses have been computed in samples of white male and female and black male and female students for the same 16 cognitive variables at grade levels 5, 7, 9, and 11. Samples for each of the four independent groups remained constant at the four grade levels. The latent roots as analyzed in three ways show a clear but small increase in the number of common factors during this time period, particularly for the white groups. Rotated factor loadings also support the differentiation hypothesis. For the white males, who showed the clearest evidence for differentiation of abilities, rotated loadings provide descriptions of the emerging factors. Although the evidence for differentiation is less clear in white females, the emerging factors appear to become identical by the 11th grade. Data for black males and females, which are based on smaller Ns, are more ambiguous.Item Acquiescence in components analysis and multidimensional scaling of self-rating items(1988) Davison, Mark L.; Srichantra, NiyadaEarlier work has shown that when multidimensional scaling (MDS) is applied to item intercorrelations, metric MDS implicitly subtracts the standardized person mean (SPM) from responses. As a result, when a metric or nonmetric MDS solution is compared to a components solution, the components solution often contains one component with no counterpart among the scaling dimensions. If self-report items form a balanced scale and negatively worded items are not reverse scored, the SPM is closely related to several concepts of acquiescence and disacquiescence. In this paper, MDS and components solutions are compared using two balanced self-report item sets. In the Likert self-report attitude item set, the MDS and components solutions were essentially the same. In a set of affective well-being items, the components solution contained a general component with no counterpart among the scaling dimensions. Scores along the general component were substantially correlated with measures of acquiescence and disacquiescence. Results in the second dataset suggest that when the self-report items are balanced and the negatively worded items have not been reverse scored, MDS and components solutions can differ largely with respect to a component closely associated with certain measures of acquiescence. Index terms: acquiescence, attitude measurement, factor analysis, multidimensional scaling, personality measurement, response bias, self-report items.Item Fitting unidimensional choice models with nonmetric multidimensional scaling(1983) Davison, Mark L.; Wood, Phillip K.A class of unidimensional choice models is described. Thurstone’s paired comparisons model, Case 5, and the Bradley-Terry-Luce model both fall into the class. A simple nonmetric method is presented for estimating scale values from choice data which satisfy any model in the class. In two examples, nonmetric scale values are compared to Thurstone estimates. The scaling method is extended to permit estimation of scale values in a class of unidimensional ordered-category models, a class which includes the law of categorical judgment.Item Introduction to multidimensional scaling and its applications(1983) Davison, Mark L.Although Richardson (1938) and Young and Householder (1938) may have officially initiated the multidimensional scaling (MDS) literature in psychology, frequent applications did not begin to appear until the seminal papers on nonmetric MDS by Shepard (1962) and Kruskal (1964). Twenty years later, it is time to critically examine the MDS literature and its contribution to psychology. The first two papers in this special issue review statistical developments in MDS with an emphasis on the design of MDS studies. The last four papers scrutinize the MDS research in four areas of common application: consumer, social, cognitive, and vocational psychology. Carroll and Arabie (1980) have described two ways to define MDS. According to the broader of the two definitions, MDS means a set of techniques for estimating parameters in geometric models so as to yield a representation of data structure. Such a broad definition would encompass cluster, discriminant, and factor analysis. These techniques are treated here as alternatives to MDS, rather than as methods included within it. In this special issue, the MDS literature refers to a body of knowledge involving (1) a set of statistical techniques for estimating the parameters in and assessing the fit of various spatial distance models for proximity or preference data and (2) the coordinate representations of stimulus structure that result from such statistical techniques. This introduction first briefly reviews the past 50 years of developments in MDS, developments covered more extensively by Coxon (1982), Davison (1993), Kruskal and Wish (1978), and Schiffman, Reynolds, and Young (1981). Then it summarizes the six papers that follow.Item Minneapolis Public Schools Start Time Study Executive Summary 2001(University of Minnesota, Center for Applied Research and Educational Improvement, 2001-08) Wahlstrom, Kyla; Davison, Mark L.; Center for Applied Research and Educational ImprovementEffective with the 1997-98 school year, the Minneapolis School District changed the starting time of its seven comprehensive high schools to 8:40 AM and the dismissal time to 3:20 PM. Prior to the change, classes began at the high schools at 7:15 AM and dismissed at 1:45 PM. In the fall of the 2000-01 school year, CAREI was asked by the school district to examine the data about student grades and attendance and to repeat the administration of the School Sleep Habits Survey. The district was interested in knowing if the positive outcomes that had been present during the first year of the change were persisting over the long term. This report is the result of that follow-up study.Item The reliability and validity of objective indices of moral development(1978) Davison, Mark L.; Robbins, StephenThe present paper addresses three issues surrounding Rest’s Defining Issues Test, an objective test of moral development based on Kohlberg’s six-stage theory of moral development. Those issues are (1) the stability of test scores over time; (2) correlation of scores with Kohlberg’s interview measure of moral development; and (3) the insensitivity of its scoring procedure, which ignores responses to all items keyed to lower stages. In two age heterogeneous samples, total score test-retest reliabilities were generally in the high .70’s or low .80’s, regardless of which of several scoring schemes was used. In another age heterogeneous sample, the correlation with scores on Kohlberg’s test was .70; but in two age homogeneous samples, the correlations were about .35 and .20. These validity coefficients suggest that (1) the common variance shared by Rest’s and Kohlberg’s tests in age heterogeneous samples can be attributed to the fact that scores on both tests increase with age and (2) the two tests cannot be considered equivalent measures of the same construct differing only in format. Results also indicated that an empirically weighted scoring scheme is more sensitive to longitudinal change than is Rest’s P score. This sensitivity to longitudinal trends is an important property for tests such as Rest’s which claim to be developmental and are frequently used to assess educational change. The empirically weighted sum had a significantly higher test-retest reliability (p < .05) than did a simple sum of item responses, and it had a significantly higher correlation with Kohlberg’s measure than did a theoretically weighted sum.Item Testing the equality of scale values and discriminal dispersions in paired comparisons(1995) Davison, Mark L.; McGuire, Dennis P.; Chen, Tsuey-Hwa; Anderson, Ronald O.General normal ogive and logistic multiple-group models for paired comparisons data are described. In these models, scale value and discriminal dispersion parameters are allowed to vary across stimuli and respondent populations. Submodels can be fit to choice proportions by nonlinearly regressing sample estimates of choice proportions onto a complex design matrix. By fitting various submodels and by appropriate coding of parameter effects, selected hypotheses about the equality of scale value and dispersion parameters across groups can be tested. Model fitting and hypothesis testing are illustrated using health care coverage data collected in two age groups. Index terms: Bradley- Terry-Luce Model, choice models, logistic regression, paired comparisons, probit regression, Thurstone’s Law of Comparative,General normal ogive and logistic multiple-group models for paired comparisons data are described. In these models, scale value and discriminal dispersion parameters are allowed to vary across stimuli and respondent populations. Submodels can be fit to choice proportions by nonlinearly regressing sample estimates of choice proportions onto a complex design matrix. By fitting various submodels and by appropriate coding of parameter effects, selected hypotheses about the equality of scale value and dispersion parameters across groups can be tested. Model fitting and hypothesis testing are illustrated using health care coverage data collected in two age groups. Index terms: Bradley- Terry-Luce Model, choice models, logistic regression, paired comparisons, probit regression, Thurstone’s Law of ComparativeGeneral normal ogive and logistic multiple-group models for paired comparisons data are described. In these models, scale value and discriminal dispersion parameters are allowed to vary across stimuli and respondent populations. Submodels can be fit to choice proportions by nonlinearly regressing sample estimates of choice proportions onto a complex design matrix. By fitting various submodels and by appropriate coding of parameter effects, selected hypotheses about the equality of scale value and dispersion parameters across groups can be tested. Model fitting and hypothesis testing are illustrated using health care coverage data collected in two age groups. Index terms: Bradley-Terry-Luce Model, choice models, logistic regression, paired comparisons, probit regression, Thurstone’s Law of Comparative Judgment.Item Two-dimensional configurations on unidimensional stimulus sets in nonmetric multidimensional scaling(1989) Davison, Mark L.; Hearn, MarshaWhen unidimensional stimulus sets are subjected to a nonmetric scaling in two dimensions, the stimuli frequently form a C- or S-shaped configuration. In simulated unidimensional data scaled in two dimensions, stimuli formed a C-shaped configuration when the monotone function relating distances to dissimilarity data was negatively accelerating. They formed an S-shaped configuration when the monotone function was positively accelerating. Results suggest that when unidimensional stimulus sets are scaled in two dimensions using a rational starting configuration, the nature of the two-dimensional configuration can indicate the general form of the function mapping psychological dissimilarity, represented as distance in the scaling model, onto the observed response scale. Index terms: data transformations, multidimensional scaling, paired comparisons, proximity data, unidimensional scaling, unidimensionality.