In many practical situations when analyzing a dependence of one or more explanatory variables on a response variable it is essential to assume that the relationship of interest obeys certain shape constraints, such as monotonicity or monotonicity and convexity/concavity. In this thesis a new approach to shape preserving smoothing within generalized additive models has been developed. In contrast with previous quadratic programming based methods, the project develops intermediate rank penalized smoothers with shape constrained restrictions based on re-parameterized B-splines and penalties based on the P-spline ideas of Eilers and Marx (1996). Smoothing under monotonicity constraints and monotonicity together with convexity/concavity for univariate smooths; and smoothing of bivariate functions with monotonicity restrictions on both covariates and on only one of them are considered. The proposed shape constrained smoothing has been incorporated into generalized additive models with a mixture of unconstrained and shape restricted smooth terms (mono-GAM). A fitting procedure for mono-GAM is developed. Since a major challenge of any flexible regression method is its implementation in a computationally efficient and stable manner, issues such as convergence, rank deficiency of the working model matrix, initialization, and others have been thoroughly dealt with. A question about the limiting posterior distribution of the model parameters is solved, which allows us to construct Bayesian confidence intervals of the mono-GAM smooth terms by means of the delta method. The performance of these confidence intervals is examined by assessing realized coverage probabilities using simulation studies. The proposed modelling approach has been implemented in an R package monogam. The model setup is the same as in mgcv(gam) with the addition of shape constrained smooths. In order to be consistent with the unconstrained GAM, the package provides key functions similar to those associated with mgcv(gam). Performance and timing comparisons of mono-GAM with other alternative methods has been undertaken. The simulation studies show that the new method has practical advantages over the alternatives considered. Applications of mono-GAM to various data sets are presented which demonstrate its ability to model many practical situations.

Empirically-based models of landslide distribution and susceptibility are currently the most commonly used approach for mapping probabilities of landslide initiation and analyzing their association with natural and anthropogenic environmental factors. In general, these models statistically estimate susceptibility based on the predisposition of an area to experience a landslide given a range of environmental factors, which may include land use, topography, hydrology and other spatial attributes. Novel statistical approaches include the generalized additive model (GAM), a non-parametric regression technique, which is used in this study to explore the relationship of landslide initiation to topography, rainfall and forest land cover and logging roads on Vancouver Island, British Columbia. The analysis is centered on an inventory of 639 landslides of winter 2006/07. Data sources representing potentially relevant environmental conditions of landslide initiation are based on: terrain analysis derived from a 20-m CDED digital elevation model; forest land cover classified from Landsat TM scenes for the summer before the 2006 rainy season; geostatistically interpolated antecedent rainfall patterns representing different temporal scales of rainfall (a major storm, winter and annual rainfall); and the main lithological units of surface geology. In order to assess the incremental effect of these data sources to predict landslide susceptibility, predictive performances of models based on GAMs are compared using spatial cross-validation estimates of the area under the ROC curve (AUROC), and variable selection frequencies are used to determine the prevalence of non-parametric associations to landslides. In addition to topographic variables, forest land cover (e.g., deforestation), and logging roads showed a strong association with landslide initiation, followed by rainfall patterns and the very general lithological classification as less important controls of landscape-scale landslide activity in this area. Annual rainfall patterns are found not to contribute significantly to model prediction improvement and may lead to model overfitting. Comparisons to generalized linear models (i.e., logistic regression) indicate that GAMs are significantly better for modeling landslide susceptibility. Overall, based on the model predictions, the most susceptible 4% of the study area had 29 times higher density of landslide initiation points than the least susceptible 73% of the study area (0.156 versus 0.005 landslides/km2).

Empirically-based models of landslide distribution and susceptibility are currently the most commonly used approach for mapping probabilities of landslide initiation and analyzing their association with natural and anthropogenic environmental factors. In general, these models statistically estimate susceptibility based on the predisposition of an area to experience a landslide given a range of environmental factors, which may include land use, topography, hydrology and other spatial attributes. Novel statistical approaches include the generalized additive model (GAM), a non-parametric regression technique, which is used in this study to explore the relationship of landslide initiation to topography, rainfall and forest land cover and logging roads on Vancouver Island, British Columbia. The analysis is centered on an inventory of 639 landslides of winter 2006/07. Data sources representing potentially relevant environmental conditions of landslide initiation are based on: terrain analysis derived from a 20-m CDED digital elevation model; forest land cover classified from Landsat TM scenes for the summer before the 2006 rainy season; geostatistically interpolated antecedent rainfall patterns representing different temporal scales of rainfall (a major storm, winter and annual rainfall); and the main lithological units of surface geology. In order to assess the incremental effect of these data sources to predict landslide susceptibility, predictive performances of models based on GAMs are compared using spatial cross-validation estimates of the area under the ROC curve (AUROC), and variable selection frequencies are used to determine the prevalence of non-parametric associations to landslides. In addition to topographic variables, forest land cover (e.g., deforestation), and logging roads showed a strong association with landslide initiation, followed by rainfall patterns and the very general lithological classification as less important controls of landscape-scale landslide activity in this area. Annual rainfall patterns are found not to contribute significantly to model prediction improvement and may lead to model overfitting. Comparisons to generalized linear models (i.e., logistic regression) indicate that GAMs are significantly better for modeling landslide susceptibility. Overall, based on the model predictions, the most susceptible 4% of the study area had 29 times higher density of landslide initiation points than the least susceptible 73% of the study area (0.156 versus 0.005 landslides/km2).

This thesis is concerned, loosely, with time series analysis. It is also, loosely, concerned with smoothers and Generalized Additive Models. And, finally, it is also concerned with the estimation of health risk due to air pollution. In the field of time series analysis, we develop two data-driven interpolation algorithms for interpolation of mixed time series data; that is, data which has a stationary or “almost” stationary background with embedded deterministic trend and sinusoidal components. These interpolators are developed to deal with the problem of estimating power spectra under the condition that some observations of the series are unavailable. We examine the structure of time-based cubic regression spline smoothers in Generalized Additive Models and demonstrate several interpretation problems with the resultant models. We propose, implement, and test a replacement smoother and show dramatic improvement. We further demonstrate a new, spectrally motivated way of examining residuals in Generalized Additive Models which drives many of the findings of this thesis. Finally, we create and analyze a large-scale Canadian air pollution and mortality database. In the course of analyzing the data we rebuild the standard risk estimation model and demonstrate several improvements. We conclude with a comparison of the original model and the updated model and show that the new model gives consistently more positive risk estimates. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-10-26 14:32:00.678

The acidification of soils has been a continuous process since at least the beginning of the 20th century. Therefore, an inquiry of how and when the soil pH levels have changed is relevant to gain better understanding of this process. The aim of this thesis is to study the average national soil pH level over time in Sweden and the local spatial differences within Sweden over time. With data from the Swedish National Forest Inventory, soil pH surfaces are estimated for each surveyed year together with the national average soil pH using a generalized additive modeling approach with one model for each pair of consecutive years. A decreasing trend in average national level soil pH was found together with some very weak evidence of year-to-year differences in the spatial structure of soil pH.

People at risk for blood clots are often treated with anticoagulants, warfarin is such an anticoagulant. The dose's effect is measured by comparing the time for blood to clot to a control time called an INR value. Previous anticoagulant studies have addressed agreement between fingerstick (POC) devices and the standard laboratory, however these studies rely on mathematical formulas as criteria for clinical evaluations, i.e. clinical evaluation vs. precision and bias. Fourteen such criteria were found in the literature. There exists little consistency among these criteria for assessing clinical agreement, furthermore whether these methods of assessing agreement are reasonable estimates of clinical decision-making is unknown and has yet to be validated. One previous study compared actual clinical agreement by having two physicians indicate a dosing decision based on patient history and INR values. This analysis attempts to justify previously used mathematical criteria for clinical agreement. Generalized additive models with smoothing spline estimates were calculated for each of the 14 criteria and compared to the smoothing spline estimate for the method using actual physician decisions (considered the "gold standard"). The area between the criteria method spline and the gold standard method spline served as the comparison, using bootstrapping for statistical inference. Although some of the criteria methods performed better than others, none of them matched the gold standard. This stresses the need for clinical assessment of devices.

Ecosystem-level changes have taken place in the Mediterranean Sea over the last decades due to both anthropogenic interferences and natural perturbations. Compared to the western Mediterranean Sea, influences of these factors especially on flora and fauna characteristics are much more dramatic and intense in the eastern part, particularly in the northeastern Levant Sea where the study area is located. In this study, life history traits of some core species (both native and immigrant) occupying the continental shelf of the northeastern Levant Sea were studied in this changing ecosystem to improve limited ecological understanding of the demersal fish assemblages of the northeastern Levant Sea. For this purpose, the annual patterns in allocation and utilization of energy in demersal fish species, temporal and bathymetrical trends in fish distribution with respect to biological requirements of the species and strategies adapted by the species in growth, reproduction and energy storage were investigated by examining growth parameters, biological indices and abundance and biomass variations. Influences of environmental variables on spatiotemporal distribution and biological characteristic of Mullus barbatus were also explored by generalized additive models. Biological data were collected at monthly intervals between May 2007 and May 2010 by trawl sampling while sample collection of environmental variables (temperature and salinity) was performed from December 2008 to May 2010. Results of this study reveal that the components of the demersal fish assemblage in the region fulfill their biological activities within a short period of time when the highest productivity is reached in the area. Moreover, results indicate that within this short period of time, some native components of the demersal fish assemblages studied (Mullus barbatus and Pagellus erythrinus) exhibit strategies such as fast growth, early maturation, short reproduction season, secondary spawners to cope with the environmental peculiarities. On the other hand, the successful exotic colonizers develop strategies as well but these successful immigrants also use time (Lagocephalus suezensis) and space (depth) (Upeneus pori) slot that the native species avoid. In some of the species examined (Mullus barbatus and Lagocephalus suezensis), growth is fast, sexual maturity is early, reproduction period is short, and reproduction potential is high. With the peculiar environmental condition, these life history traits are attributed to the &ldquo / r-strategy&rdquo / of the species. In this study, generalized additive models of Mullus barbatus explain 81.5 % variations in Gonadosomatic Index (GSI), 55.2 % in Hepatosomatic Index (HSI) and 43.9 % in Condition Factor (K). The time component in the GAM model captures the same cyclic pattern observed in GSI of Mullus barbatus. Besides, The GAM results suggest that the highest GSI values associated with the bottom water temperature are between 18 &ndash / 19 &deg / C while the partial effect of bottom salinity is at 38.7 psu. A positive effect of depth on GSI of the species starts after 60 meters depth and increasing trend continues until 125 meters depth and then decreases. The HSI results are almost identical to GSI outputs indicating that the effects of the parameters concerned act in a similar manner. The results of the GAM models failed to explain influence of environmental parameters on vertical and seasonal distribution of adult Mullus barbatus. However 83.5 % variances were explained in distribution of juveniles. The salinity and temperature have the highest impact on the distribution of juveniles among the parameters evaluated. The results indicate that the occurrence of Atlantic Water in the area has a positive influence on M. barbatus, particularly on the recruits through either by its low salinity or by another factor associated with this water mass. The vertical distribution range are set by the high temperatures (&gt / 27 &deg / C) at the shallow depths during summer and the low temperatures on the shelf break zone (&lt / 16 &deg / C). A comparison of vertical abundance distribution of Mullus barbatus and the vertical temperature variations indicate that the species may tolerate up to 27 &deg / C and then individuals move to the deeper depths so that to the cooler waters when the temperature exceeds their tolerance limit. As well as the life history traits adopted by the species, there are some other factors providing advantages to the species. The fisheries regulations, particularly the time limits applied in the area are in favor of the species especially of pre-recruits. In the study area the pre-recruitment phase and summer YOY aggregations in shallow waters of most species studied in this thesis take place during a time when the fishing season is closed.

Artificial reefs have been deployed throughout the world’s oceans to act as habitat and fishing enhancement tools. To expand current research on the role of artificial reefs in the marine community, ordination and multivariate regression methods were used here to analyze survey data of natural and artificial reefs. The reefs, located in the Northern Gulf of Mexico (NGOM) and on the West Florida Shelf (WFS), had been previously surveyed from 2004 to 2015 using remote operated vehicle and stationary video techniques. This study tested the hypothesis that similar functional roles are accounted for at both natural and artificial reef sites even if species composition varies. Secondly, it examines the role of environment and fisheries in determining the assemblages. Artificial reefs tended to host communities that were as biodiverse as natural reefs, although not necessarily composed of the same species. Results of an ordination confirmed that as the classification was broadened from the level of species, to family, to functional group, the assemblages on each reef type (natural vs. artificial and NGOM vs WFS) appeared more similar. Dominant groups were present at all levels of classification and included the families Lutjanidae and Carangidae, as well as functional groups Red Snapper and Small Reef Fish. Both natural and artificial reefs tended to be dominated by one of the following: Lutjanidae, Carangidae, or Small Reef Fish, although a continuous gradient was found across the extremes of natural versus artificial reefs. Generalized Additive Models were developed to examine the influence of reef type, location, environment and fishing intensity covariates. Results indicated that for both natural and artificial reefs, the abundance of families and functional groups can be influenced by environmental factors. In both cases, there is strong spatial autocorrelation suggesting connectivity with neighboring reefs.

Machine learning has revolutionized recommendation systems by employing ranking models for personalized item suggestions. However, the complexity of learning-to-rank (LTR) models poses challenges in understanding the underlying reasons contributing to the ranking outcomes. This lack of transparency raises concerns about potential errors, biases, and ethical implications. To address these issues, interpretable LTR models have emerged as a solution. Currently, the state-of-the-art for interpretable LTR models is led by generalized additive models (GAMs). However, ranking GAMs face limitations in terms of computational intensity and handling high-dimensional data. To overcome these drawbacks, post-hoc methods, including local interpretable modelagnostic explanations (LIME), have been proposed as potential alternatives. Nevertheless, a quantitative evaluation comparing post-hoc methods efficacy to state-of-the-art ranking GAMs remains largely unexplored. This study aims to investigate the capabilities and limitations of LIME in an attempt to approximate a complex ranking model using a surrogate model. The proposed methodology for this study is an experimental approach. The neural ranking GAM, trained on two benchmark information retrieval datasets, serves as the ground truth for evaluating LIME’s performance. The study adapts LIME in the context of ranking by translating the problem into a classification task and asses three different sampling strategies against the prevalence of imbalanced data and their influence on the correctness of LIME’s explanations. The findings of this study contribute to understanding the limitations of LIME in the context of ranking. It analyzes the low similarity between the explanations of LIME and those generated by the ranking model, highlighting the need to develop more robust sampling strategies specific to ranking. Additionally, the study emphasizes the importance of developing appropriate evaluation metrics for assessing the quality of explanations in ranking tasks.

O objetivo deste trabalho foi descrever as associações entre os percentuais de gravidez na adolescência e indicadores socioeconômicos e de responsabilidade social dos municípios do estado de Minas Gerais, sudeste do Brasil, no ano de 2000 a 2010. Trata-se de um estudo ecológico, utilizando dados do Sistema de Informações sobre Nascidos Vivos (SINASC). O percentual de nascidos vivos de mães adolescentes para cada município foi calculado segundo o quociente entre o número de nascidos vivos de mães com idade entre 10 e 19 anos e o número total de nascidos vivos registrados no ano de 2000 a 2010. Modelos bayesianos e modelos aditivos generalizados foram utilizados para a obtenção de percentuais de gravidez adolescente ajustados por efeitos espaciais e para avaliar as possíveis associações com os indicadores socioeconômicos e de responsabilidade social. Os percentuais brutos de gravidez adolescente em relação ao total de nascidos vivos nos municípios de Minas Gerais no ano de 2010 variaram de 0 a 46,4%, com uma mediana de 19,6%. O primeiro e o terceiro quartis são, respectivemente, 15,6% e 23,1%. O estudo evidenciou uma estreita relação entre a gravidez na adolescência e indicadores econômicos e sociais. Os percentuais de gravidez adolescente se mostraram maiores nos municípios com menor tamanho populacional, menores valores do Índice de Desenvolvimento Humano e menores valores de outros indicadores de desenvolvimento. A forte relação entre os percentuais de gravidez adolescente e os indicadores sociais e econômicos sugerem que a gravidez adolescente é muito mais um problema social que biológico. Os programas e as ações devem ir muito além de educação sexual e informações sobre métodos preventivos de saúde. / The objective of this study was to describe associations between pregnancy rates in adolescence and socio-economic and social responsibility indicators in the municipalities of the State of Minas Gerais, Southeast of Brazil, in the year of 2010- 2010. This is an ecological study using data from the Brazilian Live Birth Information System (SINASC). The percentage of live births to adolescent mothers for each municipality was calculated based on the quotient between number of born alive infants of mothers aged 10-19 years old and total number of live births in the year of 2000-2010. Bayesian models and generalized additive model were used to obtain the percentages of adolescence pregnancy adjusted for spatial effects and to assess possible associations with socio-economic and social responsibility indicators. The crude percentage of adolescence pregnancy for the total number of live births in the municipalities of Minas Gerais in 2010 ranged from 0 to 46.4%, with median percentage being 19.6% and the first and third quartiles being 15.6% and 23.1%, respectively. This study has demonstrated a close relationship between adolescent pregnancy and socio-economic indicators. Live births to adolescent mothers percentages were found to be higher in municipalities with low population density, low human development index, and other low development indicators. The strong relationship between adolescence pregnancy percentages and socio-economic indicators suggests that adolescent pregnancy is more a social than a biological problem. Therefore, programs and actions should go beyond sexual education and information on preventive health methods.