Medical research currently involves the collection of large and complex data. One such type of data is functional data where the unit of measurement is a curve measured over a grid. Functional data comes in a variety of forms depending on the nature of the research. Novel methodologies are required to accommodate this growing volume of functional data alongside new testing procedures to provide valid inferences. In this dissertation, I propose three novel methods to accommodate a variety of questions involving functional data of multiple forms. I consider three novel methods: (1) a function-on-function regression for Gaussian data; (2) a historical functional linear models for repeated measures; and (3) a generalized functional outcome regression for ordinal data. For each method, I discuss the existing shortcomings of the literature and demonstrate how my method fills those gaps. The abilities of each method are demonstrated via simulation and data application.

The purpose of this study was to investigate the relationship between cigarette smoking and socio-demographic variables based on the empirical literature and the primitive theories in the field. Two regression approaches, logistic regression and linear multiple regression, were conducted on the two most recent Arizona Adult Tobacco Surveys to test the hypothesized models. The results showed that cigarette smokers in Arizona are mainly residents who have not completed a four-year college degree, who are unemployed, White, non-Hispanic, or young to middle-aged adults. Among the socio-demographic predictors of interest, education is the most important variable in identifying cigarette smokers, even though the predictive power of these socio-demographic variables is small. Practical and methodological implications of these findings are discussed.

To significantly improve the early detection of cervical precancers and cancers, LightTouch™ is under development by SpectRx Inc.. LightTouch™ identifies cancers and precancers quickly by using a spectrometer to analyze light reflected from the cervix. Data from the spectrometer is then used to create an image of the cervix that highlights the location and severity of disease. Our research is conducted to find the appropriate models that can be used to generate map-like image showing disease tissue from normal and further diagnose the cervical cancerous conditions. Through large work of explanatory variable search and reduction, logistic regression and Partial Least Square Regression successfully applied to our modeling process. These models were validated by 60/40 cross validation and 10 folder cross validation. Further examination of model performance, such as AUC, sensitivity and specificity, threshold had been conducted.

Substance abuse is the overindulgence in and dependence on a drug or chemical leading to detrimental effects on the individual’s health and the welfare of those surrounding him or her. Logistic regression analysis is an important tool used in the analysis of the relationship between various explanatory variables and nominal response variables. The objective of this study is to use this statistical method to determine the factors which are considered to be significant contributors to the use or abuse of substances in school-aged children and also determine what measures can be implemented to minimize their effect. The logistic regression model was used to build models for the three main types of substances used in this study; Tobacco, Alcohol and Drugs and this facilitated the identification of the significant factors which seem to influence their use in children.

Most American universities and colleges require students to provide faculty evaluation at end of each academic term, as a way of measuring faculty teaching performance. Although some analysts think that this kind of evaluation does not necessarily provide a good measurement of teaching effectiveness, there is a growing agreement in the academic world about its reliability. This study attempts to find any strong statistical evidence supporting faculty evaluation by students as a measure of faculty teaching effectiveness. Emphasis will be on analyzing relationships between instructor ratings by students and corresponding students’ grades. Various statistical methods are applied to analyze a sample of real data and derive conclusions. Methods considered include multivariate statistical analysis, principal component analysis, Pearson's correlation coefficient, Spearman's and Kendall’s rank correlation coefficients, linear and logistic regression analysis.

An experiment was conducted to obtain a hepatic gene expression dataset from postpubertal dairy heifers that could be fit to a computational model capable of predicting future lactation performance values. The initial animal experiment was conducted to characterize the hepatic transcriptional response to 24-hour total feed withdrawal in one-hundred and two postpubertal Holstein dairy heifers using an 8329-gene oligonucleotide microarray in a randomized block design. Plasma concentration of non-esterified fatty acids was significantly higher, while levels of beta-hydroxybutyrate, triacylglycerol, and glucose were significantly lower with the 24-hour total feed withdrawal. In total, 505 differentially expressed genes were identified and microarray results were confirmed by real-time PCR. Upregulation of key gluconeogenic genes occurred despite diminished dietary substrate and lower hepatic glucose synthesis. Downregulation of ketogenic genes was contrary to the non-ruminant response to feed withdrawal, but was consistent with a lower ruminal supply of short-chain fatty acids as precursors. Following the microarray experiment, the first series of regression analyses was employed to identify relationships between gene expression signal and lactation performance measurements taken over the first lactation of 81 of the subjects from the original study. Regression models were evaluated using mean square prediction error (MSPE) and concordance correlation coefficient (CCC) analysis. The strongest validated stepwise regression models were constructed for milk protein percentage (r = 0.04) and lactation persistency (r = 0.09). To determine if another type of regression analysis would better predict lactation performance, partial least squares (PLS) regression analysis was then applied. Selection of gene expression data was based on an assessment of the linear dependence of all genes in normalized datasets for 81 subjects against 18 dairy herd index (DHI) variables using Pearson correlation analysis. Results were distributed into two lists based on correlation coefficient. Each gene expression dataset was used to construct PLS models for the purpose of predicting lactation performance. The strongest predictive models were generated for protein percentage (r = 0.46), 305-d milk yield (r = 0.44), and 305-d protein yield (r = 0.47). These results demonstrate the suitability of using hepatic gene expression in young animals to quantitatively predict future lactation performance. / Ontario Centre for Agricultural Genomics, NSERC Canada, and the Ontario Ministry of Agriculture, Food and Rural Affairs (OMAFRA)

Substance abuse is the overindulgence in and dependence on a drug or chemical leading to detrimental effects on the individual’s health and the welfare of those surrounding him or her. Logistic regression analysis is an important tool used in the analysis of the relationship between various explanatory variables and nominal response variables. The objective of this study is to use this statistical method to determine the factors which are considered to be significant contributors to the use or abuse of substances in school-aged children and also determine what measures can be implemented to minimize their effect. The logistic regression model was used to build models for the three main types of substances used in this study; Tobacco, Alcohol and Drugs and this facilitated the identification of the significant factors which seem to influence their use in children.

Bostadsmarknaden är en av de största tillgångsmarknaderna i ett land varpå förändringar i bostadspriserna får långt gångna konsekvenser för det enskilda hushållet, det finansiella systemet och samhällsekonomin i stort. Flertalet tidigare studier har analyserat den svenska bostadsmarknaden utifrån ett storstadsperspektiv alternativt jämfört Sveriges bostadsmarknad mot andra länder. Vi har identifierat att studiet kring vad som bestämmer prisnivån på regionala bostadsmarknader i Sverige är tämligen oexploaterat varför avsikten med den här studien är att analysera bestämningsfaktorer till de svenska bostadspriserna på länsnivå. Sålunda är ett bidragande mål med denna studie att tillföra en bättre förståelse för dynamiken på den svenska bostadsmarknaden. I studien använder vi multipel regression där vi bearbetar paneldata med en Fixed Effect Model. Ett flertal förtester har gjorts för att få fram den mest tillförlitliga modellen i vilken vi skattat bostadspriserna utifrån teoretiskt belagda förklaringsvariabler. De slutsatser vi har dragit är att disponibel inkomst, befolkningstäthet och sysselsättningsgrad kan förklara bostadspriserna på länsnivå med en procents signifikansnivå. Skillnaden i bostadspriserna mellan länen har relativt sett ökat över tidsperioden för studien. Avslutningsvis diskuteras uppvisade avvikelser mellan de verkliga bostadspriserna och de skattade bostadspriserna vilka kan förklaras av att bostadsmarknaden är känslostyrd med inslag av spekulationer. / The housing market is one of the greatest assets markets in a given country. Therefore, changes in housing prices have a big impact on the single household, the financial system and the economic system as a whole. Due to the housing markets vital role in the society, many scientific studies have been done with the purpose of enlighten and discover the dynamics of the Swedish housing market. The focuses in these earlier studies have more than often taken a metropolitan perspective or compared the Swedish housing market with other countries. However, this study divides the Swedish housing market into regional county level with the purpose of analyzing determinants of housing prices due to county specific variables. By analyzing the housing prices due to county specific factors a contributing goal with this study is to deepen the understanding about the dynamics in the Swedish housing market. In this study we have used multiple regressions in order to work with panel data. The Fixed Effect Model fitted our purpose well which is why that kind of model was used in order to estimate the housing prices for every single Swedish county. The conclusions drawn in this study are that disposable income, people density and employment rate are all statistically significant on one percent level in order to explain the housing price at state level. We have also discovered that, during the observed period, the relative differences in housing prices between the different states have increased. Finally, the differences found between the real housing prices and the estimated housing prices, can be explained by the assumption that the housing market is driven by emotions and speculations.

Good quality management decisions often rely on the evaluation and interpretation of data. One of the most popular ways to investigate possible relationships in a given data set is to follow a process of fitting models to the data. Regression models are often employed to assist with decision making. In addition to decision making, regression models can also be used for the optimization and prediction of data. The success of a regression model, however, relies heavily on assumptions made by the model builder. In addition, the model may also be influenced by the presence of outliers; a more robust model, which is not as easily affected by outliers, is necessary in making more accurate interpretations about the data. In this research study robust techniques for regression models with minimal assumptions are explored. Mathematical programming techniques such as linear programming, mixed integer linear programming, and piecewise linear regression are used to formulate a nonlinear regression model. Outlier detection and smoothing techniques are included to address the robustness of the model and to improve predictive accuracy. The performance of the model is tested by applying it to a variety of data sets and comparing the results to those of other models. The results of the empirical experiments are also presented in this study. / Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2011.

Good quality management decisions often rely on the evaluation and interpretation of data. One of the most popular ways to investigate possible relationships in a given data set is to follow a process of fitting models to the data. Regression models are often employed to assist with decision making. In addition to decision making, regression models can also be used for the optimization and prediction of data. The success of a regression model, however, relies heavily on assumptions made by the model builder. In addition, the model may also be influenced by the presence of outliers; a more robust model, which is not as easily affected by outliers, is necessary in making more accurate interpretations about the data. In this research study robust techniques for regression models with minimal assumptions are explored. Mathematical programming techniques such as linear programming, mixed integer linear programming, and piecewise linear regression are used to formulate a nonlinear regression model. Outlier detection and smoothing techniques are included to address the robustness of the model and to improve predictive accuracy. The performance of the model is tested by applying it to a variety of data sets and comparing the results to those of other models. The results of the empirical experiments are also presented in this study. / Thesis (M.Sc. (Computer Science))--North-West University, Potchefstroom Campus, 2011.