published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability. Monte Carlo simulation methodology was used to fulfill the purpose of this study. Initially, data populations with various manipulated conditions were generated (N = 100,000). Subsequently, 500 random samples were drawn with replacement from each population, and data was subjected to canonical correlation analyses. The canonical correlation results were then analyzed using descriptive statistics and an ANOVA design to determine under which condition(s) the squared canonical correlation coefficient was most attenuated when compared to population Rc2 values. This information was analyzed and used to determine what effect, if any, the different conditions considered in this study had on Rc2. The results from this Monte Carlo investigation clearly illustrated the importance of score reliability when interpreting study results. As evidenced by the outcomes presented, the more measurement error (lower reliability) present in the variables included in an analysis, the more attenuation experienced by the effect size(s) produced in the analysis, in this case Rc2. These results also demonstrated the role between and within set correlation, variable set size, and sample size played in the attenuation levels of the squared canonical correlation coefficient.

This dissertation: (a) investigated the degree to which the squared canonical correlation coefficient is biased in multivariate nonnormal distributions and (b) identified formulae that adjust the squared canonical correlation coefficient (Rc2) such that it most closely approximates the true population effect under normal and nonnormal data conditions. Five conditions were manipulated in a fully-crossed design to determine the degree of bias associated with Rc2: distribution shape, variable sets, sample size to variable ratios, and within- and between-set correlations. Very few of the condition combinations produced acceptable amounts of bias in Rc2, but those that did were all found with first function results. The sample size to variable ratio (n:v)was determined to have the greatest impact on the bias associated with the Rc2 for the first, second, and third functions. The variable set condition also affected the accuracy of Rc2, but for the second and third functions only. The kurtosis levels of the marginal distributions (b2), and the between- and within-set correlations demonstrated little or no impact on the bias associated with Rc2. Therefore, it is recommended that researchers use n:v ratios of at least 10:1 in canonical analyses, although greater n:v ratios have the potential to produce even less bias. Furthermore,because it was determined that b2 did not impact the accuracy of Rc2, one can be somewhat confident that, with marginal distributions possessing homogenous kurtosis levels ranging anywhere from -1 to 8, Rc2 will likely be as accurate as that resulting from a normal distribution. Because the majority of Rc2 estimates were extremely biased, it is recommended that all Rc2 effects, regardless of which function from which they result, be adjusted using an appropriate adjustment formula. If no rationale exists for the use of another formula, the Rozeboom-2 would likely be a safe choice given that it produced the greatest number of unbiased Rc2 estimates for the greatest number of condition combinations in this study.

Thesis (Ph. D.)--University of Hawaii at Manoa, 1990. / Includes bibliographical references (leaves 94-95) / Microfiche. / vii, 95 leaves, bound 29 cm

Determining protein structure and function experimentally is both costly and time consuming. Transferring function-related protein annotations based on homology-based methods is relatively straightforward for proteins that have sequence identity of more than 40%. However, there are many proteins in the "twilight zone" where sequence similarity with any other protein is very weak, while being structurally similar to several. Such cases require methods that are capable of using and exploiting both sequence and structural similarity. To understand ways of how such methods can and should be designed is the focus of this study. In this thesis, models that use both sequence and structure features are applied on two protein prediction problems that are particularly challenging when relying on sequence alone. Enzyme classification benefits from both kinds of features because on one hand, enzymes can have identical function with limited sequence similarity while on the other hand, proteins with similar fold may have disparate enzyme class annotation. This thesis shows that the full integration of protein sequence and structure-related features (via the use of kernels) automatically places proteins with similar biological properties closer together, leading to superior classification accuracy using Support Vector Machines. Disulfide-bonds link residues in a protein structure, but may appear distant in sequence. Sequence similarity reflecting such structural properties is thus very hard to detect. It is sufficient for the structure to be similar for accurate prediction of disulfide-bonds, but such information is very scarce and predictors that rely on protein structure are not nearly as useful as those operating on sequence alone. This thesis proposes a novel approach based on Kernel Canonical Correlation Analysis that uses structural features during training only. It does so by finding sequence representations that correlate with structural features that are essential for a disulfide bond. The resulting representations enable high prediction accuracy for a range of disulfide-bond problems. The proposed model thus taps the advantage of structural features without requiring protein structure to be available in the prediction process. The merits of this approach should apply to a number of open protein structure prediction problems.

The purpose of the current study was to explore the relationships between Attention-Deficit/Hyperactivity Disorder, depression, and memory impairment in children. It was hypothesized that level of inattention would negatively correlated with performance on measures of visual-spatial short-term memory and verbal memory. Children with greater levels of depressive symptoms were predicted to perform more poorly than less depressed peers on effortful measures of verbal and visual short-term memory, measures of verbal working memory, and measures of verbal long-term memory recall. Results indicated that impaired performance on one measure of visual-spatial short-term memory was related to increased levels of inattention and depression. Impairments were found on measures of verbal long-term memory recall and recognition related to greater attention problems, hyperactivity, and depressive symptoms. These deficits remained significantly related to inattention and hyperactivity beyond a deficit in encoding verbal material.

abstract: Estimating cointegrating relationships requires specific techniques. Canonical correlations are used to determine the rank and space of the cointegrating matrix. The vectors used to transform the data into canonical variables have an eigenvector representation, and the associated canonical correlations have an eigenvalue representation. The number of cointegrating relations is chosen based upon a theoretical difference in the convergence rates of the eignevalues. The number of cointegrating relations is consistently estimated using a threshold function which places a lower bound on the eigenvalues associated with cointegrating relations and an upper bound on the eigenvalues on the eigenvalues not associated with cointegrating relations. The proposed estimator performs better with a large number of cross-sectional observations and moderate time series length. / Dissertation/Thesis / Ph.D. Economics 2012

This article reports the results and managerial implications of a Turkish study which investigated relationships between service quality, background characteristics and, customer satisfaction and selected behavioral outcomes.

High dimensional, low sample, data have singular sample covariance matrices,rendering them impossible to analyse by regular canonical correlation (CC). Byusing random subspace method (RSM) calculation of canonical correlation be-comes possible, and a Monte Carlo analysis shows resulting maximal CC canreliably distinguish between data with true correlation (above 0.5) and with-out. Statistics gathered from RSMCCA can be used to model true populationcorrelation by beta regression, given certain characteristic of data set. RSM-CCA applied on real biological data however show that the method can besensitive to deviation from normality and high degrees of multi-collinearity.