The effectiveness of multidimensional scaling (MDS) techniques in recovering the underlying dimensionality of dichotomously-scored data was examined for unidimensional and multidimensional data. Thirty-three data sets of varying numbers of dimensions with differing patterns of item discrimination were generated using a multidimensional latent trait model in a Monte Carlo simulation study. Margin-sensitive measures (agreement, phi, and kappa) and margin-free measures (Φ/ Φ(max), Yule's Q, and the tetrachoric correlation) were used as measures of similarity and the resulting matrices were scaled in one through five dimensions. Values of the stress coefficient, S₁, S₁ by dimensionality plots, and plot configurations were examined to determine the dimensionality of the item set. Principal components analyses (PCAs) of phi and tetrachoric matrices were carried out as a basis for comparison. In addition, MDS and PCA were used to examine a data set comprised of items obtained from the routing tests of the Head Start Measures Battery. Two effects of item discrimination on MDS results were especially noteworthy. First, factors tended to be located equally distant from each other in the MDS space. Items were located closest to the factor for which the primary factor loading occurred. Second, as item discrimination decreased, items tended to be more widely dispersed from their appropriate locations in space. Extra dimensions in the MDS representational space were required for margin-sensitive coefficients to accommodate difficulty effects. Margin-free coefficients generally eliminated difficulty-related dimensions, although occasional problems were noted with the tetrachoric correlation. Analysis of the HSMB revealed that the data were primarily unidimensional, although specific effects due to each subtest were clearly present in the analysis. MDS was found to be a useful technique and its use in conjunction with PCA or factor analysis is recommended.

This thesis argues that a multidimensional profile incorporating mastery goals, performance goals, social goals and extrinsic goals, as well as factors relating to self-perceptions, would provide a better understanding of achievement motivation in adolescents than a univariate or dichotomous framework. Additionally this thesis also explores whether the use of lower-order dimensions provides information that offers a more detailed analysis of achievement goals over and above that found by the higher-order factors alone. A newly developed multidimensional measure, the SMOSA (Self Motivational Orientation Scale for Adolescents) of achievement motivation was used to examine changes of different motivational pursuits and perceptions of self across grades and sex in an adolescent population. The information found provides a more detailed analysis than previous research, which relied on an evaluation of means to explain differences between samples. Therefore, educators will be provided with a comprehensive understanding of the patterns of change in achievement motivation during adolescence and such knowledge may equip them with a way of measuring students’ approaches to facilitative learning and the ability to explore students’ paths for optimal engagement. / Doctor of Philosophy (PhD)

This thesis argues that a multidimensional profile incorporating mastery goals, performance goals, social goals and extrinsic goals, as well as factors relating to self-perceptions, would provide a better understanding of achievement motivation in adolescents than a univariate or dichotomous framework. Additionally this thesis also explores whether the use of lower-order dimensions provides information that offers a more detailed analysis of achievement goals over and above that found by the higher-order factors alone. A newly developed multidimensional measure, the SMOSA (Self Motivational Orientation Scale for Adolescents) of achievement motivation was used to examine changes of different motivational pursuits and perceptions of self across grades and sex in an adolescent population. The information found provides a more detailed analysis than previous research, which relied on an evaluation of means to explain differences between samples. Therefore, educators will be provided with a comprehensive understanding of the patterns of change in achievement motivation during adolescence and such knowledge may equip them with a way of measuring students’ approaches to facilitative learning and the ability to explore students’ paths for optimal engagement. / Doctor of Philosophy (PhD)

Thesis (Ph. D.)--University of Toronto, 2004. / Adviser: Shizuhiko Nishisato.

Thesis (Ph. D.)--Brigham Young University. Dept. of Instructional Psychology and Technology, 2004. / Includes bibliographical references (p. 103-106).

published_or_final_version / Psychology / Master / Master of Philosophy

In this article we explore the semantic space spanned by self-reported statements of Republican voters. Our semantic structure analysis uses multidimensional scaling and social network analysis to extract, explore, and visualize word patterns and word associations in response to the stimulus statement "I'm a Republican, because ..." which were collected from the official website of the Republican Party. With psychological value theory as our backdrop, we examine the association of specific keywords within and across the statements, compute clusters of statements based on these associations, and explore common word sequences Republican voters use to characterize their political association with the Party. (authors' abstract)

Li Chi Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 78-80). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multidimensional Scaling (MDS) --- p.1 / Chapter 1.2 --- Unidimensional Scaling (UDS) --- p.15 / Chapter 1.3 --- Circular Unidimensional Scaling (CDS) --- p.17 / Chapter 1.4 --- The Goodness of fit of models --- p.24 / Chapter 1.5 --- The admissible transformations of the MDS configuration --- p.26 / Chapter 2 --- "Computational Methods on MDS, UDS and CDS" --- p.29 / Chapter 2.1 --- Classical Scaling --- p.29 / Chapter 2.2 --- Guttman's updating algorithm and Pliner's smoothing algorithm --- p.36 / Chapter 2.3 --- Circular Unidimensional Scaling/Circumplex Model --- p.43 / Chapter 3 --- A new algorithm for CDS --- p.45 / Chapter 3.1 --- Method of choosing a good starting value in Guttman's updating algorithm and Pliner's smoothing algorithm --- p.46 / Chapter 3.2 --- A new approach for circular unidimensional scaling --- p.54 / Chapter 3.3 --- Examples --- p.62 / Chapter 3.3.1 --- Comparison of the new approach to existing method --- p.62 / Chapter 3.3.2 --- Illustrations of application to political data --- p.64 / Chapter 4 --- Conclusion and Extensions --- p.67 / Chapter A --- Figures and Tables --- p.70 / Chapter B --- References --- p.78

Public street surveillance, a domain of Closed Circuit Television (CCTV), has grown enormously and is becoming common place with increasing utilization in society as an all-purpose security tool. Previous authors (Ditton, 1999; Davies, 1998; Horne, 1998; Tomkins, 1998) have raised concern over social, civil and privacy issues, but there has been limited research to quantify these concerns. There are a number of core aspects that could relocate the risk perception and therefore, social support of public street surveillance. This study utilized the psychometric paradigm to quantitatively measure the social risk perception of public street surveillance. The psychometric paradigm is a method that presents risk perception in a two factor representation, being dread risk and familiarity to risk. Four additional control activities and technologies were tested, being radioactive waste, drinking water chlorination, coal mining disease and home swimming pools. Analysis included spatial representation, and multidimensional scaling (MDS) Euclidean and INDSCAL methods. The study utilized a seven point Likert scale, pre and post methodology, and had a target population of N=2106, with a sample of N=135 (alpha=0.7).

A Monte Carlo study was performed to investigate the ability of MSCAL to recover by Euclidean metric multi-dimensional scaling (MDS) the true structure for dissimilarity data with different underlying error distributions. Error models for three typical error distributions: normal, lognormal, and squared normal are implemented in MSCAL through data transformations incorporated into the criterion function. Recovery of the true configuration and true distances for (i) single replication data with low error levels and (ii) matrix conditional data with high error levels was studied as a function of the type of error distribution, fitting criterion, and dimensionality. Results indicated that if the data conform to the error distribution hypotheses, then the corresponding fitting criteria provide improved recovery, but only for data with low error levels when the true dimensionality is known.