Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Development of a new student evaluation instrument of instructor effectiveness in online courses

The purpose of this study was to (a) develop an evaluation instrument capable of rating students' perceptions of the instructional quality of an online course and the instructor’s performance, and (b) validate the proposed instrument with a study conducted at a major public university. The instrument was based upon the Seven Principles of Good Practice for Undergraduate Education (Chickering & Gamson, 1987). The study examined four specific questions. 1. Is the underlying factor structure of the new instrument consistent with Chickering and Gamson's Seven Principles? 2. Is the factor structure of the new instrument invariant for male and female students? 3. Are the scores on the new instrument related students’ expected grades? 4. Are the scores on the new instrument related to the students' perceived course workload? ^ The instrument was designed to measure students’ levels of satisfaction with their instruction, and also gathered information concerning the students’ sex, the expected grade in the course, and the students’ perceptions of the amount of work required by the course. A cluster sample consisting of an array of online courses across the disciplines yielded a total 297 students who responded to the online survey. The students for each course selected were asked to rate their instructors with the newly developed instrument. ^ Question 1 was answered using exploratory factor analysis, and yielded a factor structure similar to the Seven Principles.^ Question 2 was answered by separately factor-analyzing the responses of male and female students and comparing the factor structures. The resulting factor structures for men and women were different. However, 14 items could be realigned under five factors that paralleled some of the Seven Principles. When the scores of only those 14 items were entered in two principal components factor analyses using only men and only women, respectively and restricting the factor structure to five factors, the factor structures were the same for men and women.^ A weak positive relationship between students’ expected grades and their scores on the instrument was found (Question 3). There was no relationship between students’ perceived workloads for the course and their scores on the instrument (Question 4).^

A Q factor analysis of college undergraduate students' study behaviors

The purpose of this study was to better understand the study behaviors and habits of university undergraduate students. It was designed to determine whether undergraduate students could be grouped based on their self-reported study behaviors and if any grouping system could be determined, whether group membership was related to students’ academic achievement. A total of 152 undergraduate students voluntarily participated in the current study by completing the Study Behavior Inventory instrument. All participants were enrolled in fall semester of 2010 at Florida International University. The Q factor analysis technique using principal components extraction and a varimax rotation was used in order to examine the participants in relation to each other and to detect a pattern of intercorrelations among participants based on their self-reported study behaviors. The Q factor analysis yielded a two factor structure representing two distinct student types among participants regarding their study behaviors. The first student type (i.e., Factor 1) describes proactive learners who organize both their study materials and study time well. Type 1 students are labeled “Proactive Learners with Well-Organized Study Behaviors”. The second type (i.e., Factor 2) represents students who are poorly organized as well as being very likely to procrastinate. Type 2 students are labeled Disorganized Procrastinators. Hierarchical linear regression was employed to examine the relationship between student type and academic achievement as measured by current grade point averages (GPAs). The results showed significant differences in GPAs between Type 1 and Type 2 students at the .05 significance level. Furthermore, student type was found to be a significant predictor of academic achievement beyond and above students’ attribute variables including sex, age, major, and enrollment status. The study has several implications for educational researchers, practitioners, and policy makers in terms of improving college students' learning behaviors and outcomes.

Forecasting Responses of Seagrass Distributions to Changing Water Quality Using Monitoring Data

Extensive data sets on water quality and seagrass distributions in Florida Bay have been assembled under complementary, but independent, monitoring programs. This paper presents the landscape-scale results from these monitoring programs and outlines a method for exploring the relationships between two such data sets. Seagrass species occurrence and abundance data were used to define eight benthic habitat classes from 677 sampling locations in Florida Bay. Water quality data from 28 monitoring stations spread across the Bay were used to construct a discriminant function model that assigned a probability of a given benthic habitat class occurring for a given combination of water quality variables. Mean salinity, salinity variability, the amount of light reaching the benthos, sediment depth, and mean nutrient concentrations were important predictor variables in the discriminant function model. Using a cross-validated classification scheme, this discriminant function identified the most likely benthic habitat type as the actual habitat type in most cases. The model predicted that the distribution of benthic habitat types in Florida Bay would likely change if water quality and water delivery were changed by human engineering of freshwater discharge from the Everglades. Specifically, an increase in the seasonal delivery of freshwater to Florida Bay should cause an expansion of seagrass beds dominated by Ruppia maritima and Halodule wrightii at the expense of the Thalassia testudinum-dominated community that now occurs in northeast Florida Bay. These statistical techniques should prove useful for predicting landscape-scale changes in community composition in diverse systems where communities are in quasi-equilibrium with environmental drivers.

Adult Curiosity Dimensionality

The need to discern the dimensions of curiosity is compelling as researchers strive to understand better the developmental implications of learning. Six hundred and two participants completed 10 curiosity scales. Scores were factored using Principal Components Analysis and a varimax solution. A threefactor interpretation of the curiosity construct was supported.

Relationships Between Hydrology and Soils Describe Vegetation Patterns in Seasonally Flooded Tree Islands of the Southern Everglades, Florida

Tree island ecosystems are important and distinct features of Florida Everglades wetlands. We described the inter-relationships among abiotic factors describing seasonally flooded tree islands and characterized plant–soil relationships in tree islands occurring in a relatively unimpacted area of the Everglades. We used Principal Components Analysis (PCA) to reduce our multi-factor dataset, quantified forest structure and vegetation nutrient dynamics, and related these vegetation parameters to PCA summary variables using linear regression analyses. We found that, of the 21 abiotic parameters used to characterize the ecosystem structure of seasonally flooded tree islands, 13 parameters were significantly correlated with four principal components, and they described 78% of the variance among the study islands. Most variation was described by factors related to soil oxidation and hydrology, exemplifying the sensitivity of tree island structure to hydrologic conditions. PCA summary variables describing tree island structure were related to variability in Chrysobalanus icaco (L.) canopy cover, Ilex cassine (L.) and Salix caroliniana (Michx.) canopy cover, Myrica cerifera (L.) plot frequency, litter turnover, % phosphorus resorption of co-dominant species, and nitrogen nutrient-use efficiency. This study supported findings that vegetation characteristics can be sensitive indicators of variability in tree island ecosystem structure. This study produced valuable, information which was used to recommend ecological targets (i.e. restoration performance measures) for seasonally flooded tree islands in more impacted regions of the Everglades landscape.

The Five Essentials of Private Club Leadership

The authors examine underlying dimensions of private club leadership using principal components analysis. The data were collected between 1996 and 2003 from 702 club managers or club chief operating officers who are members of the Club Managers Association of America (CMAA). Five factors - innovation, vision, inner values, stewardship, and communication - were identified as essentials of private club leadership.

Occupational therapists' attitudes toward family -centered care

The purpose of this study was to examine pediatric occupational therapists attitudes towards family-centered care. Specific attributes identified by the literature (professional characteristics, educational experiences and organizational culture) were investigated to determine their influence on these attitudes. Study participants were 250 pediatric occupational therapists who were randomly selected from the American Occupational Therapy Association special interest sections. ^ Participants received a mail packet with three instruments to complete and mail back within 2 weeks. The instruments were (a) the Professional Attitude Scale, (b) the Professional Characteristics Questionnaire, and (c) the Family-Centered Program Rating Scale. There was a 50% return rate. Data analysis was conducted in SPSS using descriptive statistics, correlations and regression analysis. ^ The analysis showed that pediatric occupational therapists working in various practice settings demonstrate favorable attitudes toward family-centered care as measured by the Professional Attitude Scale. There was no correlation between professional characteristics and educational experiences to therapists' attitudes. A moderate correlation (r = .368, p < .05) was found between the occupational therapists attitudes and the organizational culture of their workplaces. A factor analysis was conducted on the organizational culture instrument (FamPRS) as this sample was exclusively pediatric occupational therapists and the original sample was interdisciplinary professionals. Two factors were extracted using a principal components extraction and varimax rotation, in addition to examination of the scree plot. These two factors accounted for 50% of the total variance of the scores on the instrument. Factor 1, called empowerment accounted for 45.6% of the variance, and Factor 2, responsiveness accounted for 4.3% of the variance of the entire instrument. Stepwise regression analysis demonstrated that these two factors accounted for 16% of the variance toward attitudes clinicians hold toward family-centered care. These factors support the tenets of family-centered care; empowering parents to be leaders in their child's health care and helping organizations become more responsive to family needs. ^ These study findings suggest that organizational culture has some influence on occupational therapists attitudes toward family-centered care (R 2 = .16). These findings suggest educators should consider families as valuable resources when considering program planning in family-centered care at preservice and workplace settings. ^

Elemental analysis and forensic comparison of soils by laser-induced breakdown spectroscopy (LIBS) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS)

The elemental analysis of soil is useful in forensic and environmental sciences. Methods were developed and optimized for two laser-based multi-element analysis techniques: laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and laser-induced breakdown spectroscopy (LIBS). This work represents the first use of a 266 nm laser for forensic soil analysis by LIBS. Sample preparation methods were developed and optimized for a variety of sample types, including pellets for large bulk soil specimens (470 mg) and sediment-laden filters (47 mg), and tape-mounting for small transfer evidence specimens (10 mg). Analytical performance for sediment filter pellets and tape-mounted soils was similar to that achieved with bulk pellets. An inter-laboratory comparison exercise was designed to evaluate the performance of the LA-ICP-MS and LIBS methods, as well as for micro X-ray fluorescence (μXRF), across multiple laboratories. Limits of detection (LODs) were 0.01-23 ppm for LA-ICP-MS, 0.25-574 ppm for LIBS, 16-4400 ppm for μXRF, and well below the levels normally seen in soils. Good intra-laboratory precision (≤ 6 % relative standard deviation (RSD) for LA-ICP-MS; ≤ 8 % for μXRF; ≤ 17 % for LIBS) and inter-laboratory precision (≤ 19 % for LA-ICP-MS; ≤ 25 % for μXRF) were achieved for most elements, which is encouraging for a first inter-laboratory exercise. While LIBS generally has higher LODs and RSDs than LA-ICP-MS, both were capable of generating good quality multi-element data sufficient for discrimination purposes. Multivariate methods using principal components analysis (PCA) and linear discriminant analysis (LDA) were developed for discriminations of soils from different sources. Specimens from different sites that were indistinguishable by color alone were discriminated by elemental analysis. Correct classification rates of 94.5 % or better were achieved in a simulated forensic discrimination of three similar sites for both LIBS and LA-ICP-MS. Results for tape-mounted specimens were nearly identical to those achieved with pellets. Methods were tested on soils from USA, Canada and Tanzania. Within-site heterogeneity was site-specific. Elemental differences were greatest for specimens separated by large distances, even within the same lithology. Elemental profiles can be used to discriminate soils from different locations and narrow down locations even when mineralogy is similar.

A model of school managerial control : the systematic analysis of managerial behaviors, processes, and indicators

The theoretical construct of control has been defined as necessary (Etzioni, 1965), ubiquitous (Vickers, 1967), and on-going (E. Langer, 1983). Empirical measures, however, have not adequately given meaning to this potent construct, especially within complex organizations such as schools. Four stages of theory-development and empirical testing of school building managerial control using principals and teachers working within the nation's fourth largest district are presented in this dissertation as follows: (1) a review and synthesis of social science theories of control across the literatures of organizational theory, political science, sociology, psychology, and philosophy; (2) a systematic analysis of school managerial activities performed at the building level within the context of curricular and instructional tasks; (3) the development of a survey questionnaire to measure school building managerial control; and (4) initial tests of construct validity including inter-item reliability statistics, principal components analyses, and multivariate tests of significance. The social science synthesis provided support of four managerial control processes: standards, information, assessment, and incentives. The systematic analysis of school managerial activities led to further categorization between structural frequency of behaviors and discretionary qualities of behaviors across each of the control processes and the curricular and instructional tasks. Teacher survey responses (N=486) reported a significant difference between these two dimensions of control, structural frequency and discretionary qualities, for standards, information, and assessments, but not for incentives. The descriptive model of school managerial control suggests that (1) teachers perceive structural and discretionary managerial behaviors under information and incentives more clearly than activities representing standards or assessments, (2) standards are primarily structural while assessments are primarily qualitative, (3) teacher satisfaction is most closely related to the equitable distribution of incentives, (4) each of the structural managerial behaviors has a qualitative effect on teachers, and that (5) certain qualities of managerial behaviors are perceived by teachers as distinctly discretionary, apart from school structure. The variables of teacher tenure and school effectiveness reported significant effects on school managerial control processes, while instructional levels (elementary, junior, and senior) and individual school differences were not found to be significant for the construct of school managerial control.

Composition date of the synoptic gospels

The purpose of this research paper is to follow a line of ongoing investigations that discuss dates for the origin of the synoptic gospels and evaluate the arguments for early, late, and intermediate dating and their susceptibility to critique from opposing arguments. There are three principal components in dating theories: (1) data from the Greek in the earliest texts (2) data concerning the provenance of the earliest texts (3) and data from the historical context of the first century. The study is significant because, contrary to what might be expected, the starting and key point in deciding on a composition date is the Book of Acts of the Apostles. This study compiled and integrated information, in an unbiased fashion, based on reading and researching large numbers of texts by scholars, such as Hengel, who support an earlier dating, as well as those, such as Fitzmyer, who support a later dating. Furthermore, this study also required knowledge of those scholars who propose dates that do not fall into these main categories. The research demonstrated that by looking at the Book of Acts of the Apostles as the key starting point, the synoptic gospels were most likely composed before 70 CE, therefore, supporting scholars who argue for an earlier date.

The use of computer technology to compare and analyze community college dissertations

A purpose of this research study was to demonstrate the practical linguistic study and evaluation of dissertations by using two examples of the latest technology, the microcomputer and optical scanner. That involved developing efficient methods for data entry plus creating computer algorithms appropriate for personal, linguistic studies. The goal was to develop a prototype investigation which demonstrated practical solutions for maximizing the linguistic potential of the dissertation data base. The mode of text entry was from a Dest PC Scan 1000 Optical Scanner. The function of the optical scanner was to copy the complete stack of educational dissertations from the Florida Atlantic University Library into an I.B.M. XT microcomputer. The optical scanner demonstrated its practical value by copying 15,900 pages of dissertation text directly into the microcomputer. A total of 199 dissertations or 72% of the entire stack of education dissertations (277) were successfully copied into the microcomputer's word processor where each dissertation was analyzed for a variety of syntax frequencies. The results of the study demonstrated the practical use of the optical scanner for data entry, the microcomputer for data and statistical analysis, and the availability of the college library as a natural setting for text studies. A supplemental benefit was the establishment of a computerized dissertation corpus which could be used for future research and study. The final step was to build a linguistic model of the differences in dissertation writing styles by creating 7 factors from 55 dependent variables through principal components factor analysis. The 7 factors (textual components) were then named and described on a hypothetical construct defined as a continuum from a conversational, interactional style to a formal, academic writing style. The 7 factors were then grouped through discriminant analysis to create discriminant functions for each of the 7 independent variables. The results indicated that a conversational, interactional writing style was associated with more recent dissertations (1972-1987), an increase in author's age, females, and the department of Curriculum and Instruction. A formal, academic writing style was associated with older dissertations (1972-1987), younger authors, males, and the department of Administration and Supervision. It was concluded that there were no significant differences in writing style due to subject matter (community college studies) compared to other subject matter. It was also concluded that there were no significant differences in writing style due to the location of dissertation origin (Florida Atlantic University, University of Central Florida, Florida International University).

Elemental Analysis and Forensic Comparison of Soils by Laser-Induced Breakdown Spectroscopy (LIBS) and Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS)

The elemental analysis of soil is useful in forensic and environmental sciences. Methods were developed and optimized for two laser-based multi-element analysis techniques: laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and laser-induced breakdown spectroscopy (LIBS). This work represents the first use of a 266 nm laser for forensic soil analysis by LIBS. Sample preparation methods were developed and optimized for a variety of sample types, including pellets for large bulk soil specimens (470 mg) and sediment-laden filters (47 mg), and tape-mounting for small transfer evidence specimens (10 mg). Analytical performance for sediment filter pellets and tape-mounted soils was similar to that achieved with bulk pellets. An inter-laboratory comparison exercise was designed to evaluate the performance of the LA-ICP-MS and LIBS methods, as well as for micro X-ray fluorescence (μXRF), across multiple laboratories. Limits of detection (LODs) were 0.01-23 ppm for LA-ICP-MS, 0.25-574 ppm for LIBS, 16-4400 ppm for µXRF, and well below the levels normally seen in soils. Good intra-laboratory precision (≤ 6 % relative standard deviation (RSD) for LA-ICP-MS; ≤ 8 % for µXRF; ≤ 17 % for LIBS) and inter-laboratory precision (≤ 19 % for LA-ICP-MS; ≤ 25 % for µXRF) were achieved for most elements, which is encouraging for a first inter-laboratory exercise. While LIBS generally has higher LODs and RSDs than LA-ICP-MS, both were capable of generating good quality multi-element data sufficient for discrimination purposes. Multivariate methods using principal components analysis (PCA) and linear discriminant analysis (LDA) were developed for discriminations of soils from different sources. Specimens from different sites that were indistinguishable by color alone were discriminated by elemental analysis. Correct classification rates of 94.5 % or better were achieved in a simulated forensic discrimination of three similar sites for both LIBS and LA-ICP-MS. Results for tape-mounted specimens were nearly identical to those achieved with pellets. Methods were tested on soils from USA, Canada and Tanzania. Within-site heterogeneity was site-specific. Elemental differences were greatest for specimens separated by large distances, even within the same lithology. Elemental profiles can be used to discriminate soils from different locations and narrow down locations even when mineralogy is similar.