In the last decade, genome-wide association studies have helped to advance our understanding of the genetic architecture of many important traits, including diseases. However, the statistical analysis of genotype-phenotype associations remains challenging due to multiple factors. First, many traits have polygenic architectures, which means that they are controlled by a large number of variants with small individual effects. Second, as increasingly deep phenotype data are being generated there is a need for multivariate analysis approaches to leverage multiple related phenotypes while retaining computational efficiency. Additionally, genetic analyses are confronted by strong confounding factors that can create spurious associations when not properly accounted for in the statistical model. We here derive more flexible methods that allow integrating genetic effects across variants and multiple quantitative traits. To do so, we build on the classical linear mixed model (LMM), a widely adopted framework for genetic studies. The first contribution of this thesis is mtSet, an efficient mixed-model approach that enables genome-wide association testing between sets of genetic variants and multiple traits while accounting for confounding factors. In both simulations and real-data applications we demonstrate that mtSet effectively combines the advantages of variant-set and multi-trait analyses. Next, we present a new model for gene-context interactions that builds on mtSet. The proposed interaction set test (iSet) yields increased statistical power for detecting polygenic interactions. Additionally, iSet enables the identification of genetic loci that are associated with different configurations of causal variants across contexts. After benchmarking the proposed method using simulated data, we consider two applications to real datasets, where we investigate genetic effects on gene expression across different cellular contexts and sex-specific genetic effects on lipid levels. Finally, we describe LIMIX, a software framework for the flexible implementation of different LMMs. Most of the models considered in this thesis, including mtSet and iSet, are implemented and available in LIMIX. A unique aspect of the software is an inference framework that allows a large class of genetic models to be defined and, in many cases, to be efficiently fitted by exploiting specific algebraic properties. We demonstrate the utility of this software suite in two applied collaboration projects. Taken together, this thesis demonstrates the value of flexible and integrative modelling in genetics and contributes new statistical methods for genetic analysis. These approaches generalise previous models, yet retain the computational efficiency that is needed to tackle large genetic datasets.

We collected the data for decomposition of spruce litter to determine the limit values of mass loss and to find both chemical and climate factors that influence limit values. Our data contained 28 sequences of spruce which mainly in Sweden and a small part in other places. We choose mean annual temperature (MAT) and mean annual precipitation (MAP) as climate factors and water solubles, lignin, N, P, K, Ca, Mg and Mn as chemical factors. Then we got the estimated limit values by performing a nonlinear model with mass loss and time spots, and found out the influential factors by using another linear mixed model. At the end we knew that linear mixed model is a proper and efficient approach for determining the factors, P and MAP are the significant factors and Species is a good random effect to explain the variance within groups.

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In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch project, a computer-based initiative designed to improve the mathematical skills of children from grades 5-8 in the Southwest. A sample of 86 students (26 ELs and 60 EPs), clustered in four different classes, was used for this project. A Generalized Linear Mixed Model (GLMM) approach with the GLIMMIX procedure in SAS 9.3 showed that students from the classes that had a higher percentage of EL students performed better than those in the classes where the EL concentration was lower. Classes with more EL males were better at learning mathematics than classes with more EP females. The results also indicated: (a) a positive correlation between the students' ability to solve algebra word problems on their first attempt and their success ratio in solving all problems, and (b) a negative correlation between the percentage of problems solved correctly and those considered too hard from the very beginning. I conclude my dissertation by making specific recommendations for further research.

Master of Science / Department of Statistics / Christopher Vahl / In animal health research, it is quite common for a clinical trial to be designed to demonstrate the efficacy of a new drug where a binary response variable is measured on an individual experimental animal (i.e., the observational unit). However, the investigational treatments are applied to groups of animals instead of an individual animal. This means the experimental unit is the group of animals and the response variable could be modeled with the binomial distribution. Also, the responses of animals within the same experimental unit may then be statistically dependent on each other. The usual logit model for a binary response assumes that all observations are independent. In this report, a logit model with a random error term representing the group of animals is considered. This is model belongs to a class of models referred to as generalized linear mixed models and is commonly fit using the SAS System procedure PROC GLIMMIX. Furthermore, practitioners often adjust the denominator degrees of freedom of the test statistic produced by PROC GLIMMIX using one of several different methods. In this report, a simulation study was performed over a variety of different parameter settings to compare the effects on the type I error rate and power of two methods for adjusting the denominator degrees of freedom, namely “DDFM = KENWARDROGER” and “DDFM = NONE”. Despite its reputation for fine performance in linear mixed models with normally distributed errors, the “DDFM = KENWARDROGER” option tended to perform poorly more often than the “DDFM = NONE” option in the logistic regression model with one random effect.

Background: By 2050, it is estimated that 14 million older Americans will live with Alzheimer’s disease (AD), a progressive form of dementia with unknown cause or cure. Persons with AD and related dementias (ADRD) become increasingly dependent on others as they experience cognitive decline, which concomitantly undermines individuals’ functional skills, social initiative, and quality of life. The Alzheimer’s Association advocates for interventions that address cognition, mood, behavior, social engagement, and by extension, quality of life – goals music therapists often address. Although a small but growing body of literature suggests that clinical music therapy may be effective, the evidentiary support for the use and appropriate application of music as a form of treatment with this population is currently limited. Objectives: This thesis consisted of the development of a Clinical Practice Model of music therapy for persons with ADRD. It also examined the effectiveness of a specific, protocol-based music therapy intervention, grounded in this model, relative to a verbal discussion activity. Methods: The Clinical Practice Model is theoretically grounded in the biopsychosocial model of healthcare (Engel, 1980) and Kitwood’s (1997) personhood framework, and I developed it through extensive literature review and expert input. It includes an organizational schema for applying intervention strategies, per six themes: cognition, attention, familiarity, audibility, structure, and autonomy. The initial model predicts that an intervention built upon this schema will influence social-affective responses, quality of life, and in turn, psychosocial symptoms of ADRD. I tested a singing-based music therapy intervention, grounded in this model, through a randomized clinical crossover trial. I compared participants’ responses to music therapy to a non-music verbal discussion activity, and both conditions followed a protocol. Dependent variables included: (1) affective responses (self-reported feelings, observed emotions, and observed mood), (2) social engagement, and (3) observed quality of life. Thirty-two individuals with ADRD (n = 6 men, n = 26 women) ages 65-97 years old (μ̂ = 84.13) participated in this study. I randomly assigned treatment order; each treatment occurred in small-group format, three times per week in the afternoon (25 minutes each session), for two consecutive weeks. A two-week “wash-out” period occurred between conditions. Credentialed music therapists led both study conditions. This study followed recommendations from the National Institutes of Health Behavior Change Consortium (Bellg et al., 2004) to enhance quality assurance in protocol administration and data collection. Results and Significance: I used a linear mixed model approach to analysis. Music therapy exacted a significant, positive effect on self-reported feelings, observed emotions, and constructive engagement, particularly for individuals with moderate dementia. Results also suggested that men’s feelings improved in response to music therapy only, whereas women responded positively to both conditions. Weekly observations failed to indicate a significant change in mood or quality of life across the eight-week study. Based on these findings, I revised the Clinical Practice Model to include wellbeing (an outcome more concordant with psychosocial change in response to music intervention) rather than global quality of life (affected by numerous aspects of the care milieu). In addition to the Clinical Practice Model to the music therapy profession, contributions of this thesis include a rigorous clinical study and practical implications for music therapy practice, including the importance of considering patient characteristics and careful selection and implementation of music in a music therapy intervention.

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Linear mixed models and generalized linear mixed models are random-effects models widely applied to analyze clustered or hierarchical data. Generally, random effects are often assumed to be normally distributed in the context of mixed models. However, in the mixed-effects logistic model, the violation of the assumption of normally distributed random effects may result in inconsistency for estimates of some fixed effects and the variance component of random effects when the variance of the random-effects distribution is large. On the other hand, summary statistics used for assessing goodness of fit in the ordinary logistic regression models may not be directly applicable to the mixed-effects logistic models. In this dissertation, we present our investigations of two independent studies related to goodness-of-fit tests in generalized linear mixed models. First, we consider a semi-nonparametric density representation for the random effects distribution and provide a formal statistical test for testing normality of the random-effects distribution in the mixed-effects logistic models. We obtain estimates of parameters by using a non-likelihood-based estimation procedure. Additionally, we not only evaluate the type I error rate of the proposed test statistic through asymptotic results, but also carry out a bootstrap hypothesis testing procedure to control the inflation of the type I error rate and to study the power performance of the proposed test statistic. Further, the methodology is illustrated by revisiting a case study in mental health. Second, to improve assessment of the model fit in the mixed-effects logistic models, we apply the nonparametric local polynomial smoothed residuals over within-cluster continuous covariates to the unweighted sum of squares statistic for assessing the goodness-of-fit of the logistic multilevel models. We perform a simulation study to evaluate the type I error rate and the power performance for detecting a missing quadratic or interaction term of fixed effects using the kernel smoothed unweighted sum of squares statistic based on the local polynomial smoothed residuals over x-space. We also use a real data set in clinical trials to illustrate this application.

Made available in DSpace on 2014-06-11T19:31:37Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-11-16Bitstream added on 2014-06-13T21:02:57Z : No. of bitstreams: 1 barbosa_l_dr_botfca.pdf: 2587351 bytes, checksum: 76e343f1e0edbbbee5cb996188d8efd2 (MD5) / É bastante comum na área agrícola, experimentos cujas variáveis respostas são contagens ou proporções. Para esse tipo de dados, utiliza-se a metodologia de modelos lineares generalizados quando as respostas são independentes. Por outro lado, quando as respostas são dependentes, há uma correlação entre as observações e isso tem que ser levado em consideração na análise, para evitar inferências incorretas sobre os coeficientes de regressão. Na literatura há técnicas disponíveis para a modelagem e análise desses dados, sendo os modelos disponíveis extensões dos modelos lineares generalizados. No presente trabalho, utiliza-se a metodologia de equação de estimação generalizada, que inclui no modelo uma matriz de correlação para a obtenção de um melhor ajuste. Outra alternativa, também abordada neste trabalho, é a utilização de um modelo linear generalizado misto, no qual o uso de efeitos aleatórios também introduz uma correlação entre observações que tenham algum efeito em comum. Essas duas metodologias são aplicadas a um conjunto de dados obtidos de um experimento para avaliar certas condições na germinação de sementes de mamona da cultivar AL Guarany 2002, com o objetivo de se verificar qual o melhor modelo de estimação para esses dados / Experiments whose response variables are counts or proportions are very common in agriculture. For this type of data, if the observational units are independent, the methodology of generalized linear models can be appropriate. On the other hand, when responses are dependent or clustered, there is a correlation between the observations and that has to be taken into consideration in the analysis to avoid incorrect inferences about the regression coefficients. In the literature there are techniques available for modeling and analyzing such type data, the models being extensions of generalized linear models. The present study explores the use of: 1) generalized estimation equations, that includes a correlation matrix to obtain a better fit; 2) generalized linear mixed models, that introduce a correlation between clustered observations though the addition of random effects in the model. These two methodologies are applied to a data set obtained from an experiment to evaluate certain conditions on the germination of seeds of castor bean cultivar AL Guarany 2002 with the objective of determining the best estimation model for such data

abstract: Though the likelihood is a useful tool for obtaining estimates of regression parameters, it is not readily available in the fit of hierarchical binary data models. The correlated observations negate the opportunity to have a joint likelihood when fitting hierarchical logistic regression models. Through conditional likelihood, inferences for the regression and covariance parameters as well as the intraclass correlation coefficients are usually obtained. In those cases, I have resorted to use of Laplace approximation and large sample theory approach for point and interval estimates such as Wald-type confidence intervals and profile likelihood confidence intervals. These methods rely on distributional assumptions and large sample theory. However, when dealing with small hierarchical datasets they often result in severe bias or non-convergence. I present a generalized quasi-likelihood approach and a generalized method of moments approach; both do not rely on any distributional assumptions but only moments of response. As an alternative to the typical large sample theory approach, I present bootstrapping hierarchical logistic regression models which provides more accurate interval estimates for small binary hierarchical data. These models substitute computations as an alternative to the traditional Wald-type and profile likelihood confidence intervals. I use a latent variable approach with a new split bootstrap method for estimating intraclass correlation coefficients when analyzing binary data obtained from a three-level hierarchical structure. It is especially useful with small sample size and easily expanded to multilevel. Comparisons are made to existing approaches through both theoretical justification and simulation studies. Further, I demonstrate my findings through an analysis of three numerical examples, one based on cancer in remission data, one related to the China’s antibiotic abuse study, and a third related to teacher effectiveness in schools from a state of southwest US. / Dissertation/Thesis / Doctoral Dissertation Statistics 2017