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Dissertations / Theses on the topic 'Mixed linear models'
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1
Gory, Jeffrey J. "Marginally Interpretable Generalized Linear Mixed Models." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606.
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Möls, Märt. "Linear mixed models with equivalent predictors /." Online version, 2004. http://dspace.utlib.ee/dspace/bitstream/10062/1339/5/Mols.pdf.
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Randell, David. "Bayes linear variance learning for mixed linear temporal models." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/3646/.
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Modelling of complex corroding industrial systems is ritical to effective inspection and maintenance for ssurance of system integrity. Wall thickness and corrosion rate are modelled for multiple dependent corroding omponents, given observations of minimum wall thickness per component. At each inspection, partial observations of the system are considered. A Bayes Linear approach is adopted simplifying parameter estimation and avoiding often unrealistic distributional assumptions. Key system variances are modelled, making exchangeability assumptions to facilitate analysis for sparse inspection time-series. A utility based criterion is used to assess quality of inspection design and aid decision making. The model is applied to inspection data from pipework networks on a full-scale offshore platform.
4
Overstall, Antony Marshall. "Default Bayesian model determination for generalised linear mixed models." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/170229/.
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In this thesis, an automatic, default, fully Bayesian model determination strategy for GLMMs is considered. This strategy must address the two key issues of default prior specification and computation. Default prior distributions for the model parameters, that are based on a unit information concept, are proposed. A two-phase computational strategy, that uses a reversible jump algorithm and implementation of bridge sampling, is also proposed. This strategy is applied to four examples throughout this thesis.
5
Sima, Adam. "Accounting for Model Uncertainty in Linear Mixed-Effects Models." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/2950.
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Standard statistical decision-making tools, such as inference, confidence intervals and forecasting, are contingent on the assumption that the statistical model used in the analysis is the true model. In linear mixed-effect models, ignoring model uncertainty results in an underestimation of the residual variance, contributing to hypothesis tests that demonstrate larger than nominal Type-I errors and confidence intervals with smaller than nominal coverage probabilities. A novel utilization of the generalized degrees of freedom developed by Zhang et al. (2012) is used to adjust the estimate of the residual variance for model uncertainty. Additionally, the general global linear approximation is extended to linear mixed-effect models to adjust the standard errors of the parameter estimates for model uncertainty. Both of these methods use a perturbation method for estimation, where random noise is added to the response variable and, conditional on the observed responses, the corresponding estimate is calculated. A simulation study demonstrates that when the proposed methodologies are utilized, both the variance and standard errors are inflated for model uncertainty. However, when a data-driven strategy is employed, the proposed methodologies show limited usefulness. These methods are evaluated with a trial assessing the performance of cervical traction in the treatment of cervical radiculopathy.
6
Heinzl, Felix. "Clustering in linear and additive mixed models." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-157169.
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Casale, Francesco Paolo. "Multivariate linear mixed models for statistical genetics." Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/267465.
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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.
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Min, Min. "Asymptotic normality in generalized linear mixed models." College Park, Md.: University of Maryland, 2007. http://hdl.handle.net/1903/7758.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.<br>Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Lee, Yi-Ching. "An Approach to Estimation and Selection in Linear Mixed Models with Missing Data." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562754262770979.
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Greenaway, Mark Jonathan. "Numerically Stable Approximate Bayesian Methods for Generalized Linear Mixed Models and Linear Model Selection." Thesis, The University of Sydney, 2019. http://hdl.handle.net/2123/20233.
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Approximate Bayesian inference methods offer methodology for fitting Bayesian models as fast alternatives to Markov Chain Monte Carlo methods that sometimes have only a slight loss of accuracy. In this thesis, we consider variable selection for linear models, and zero inflated mixed models. Variable selection for linear regression models are ubiquitous in applied statistics. We use the popular g-prior (Zellner, 1986) for model selection of linear models with normal priors where g is a prior hyperparameter. We derive exact expressions for the model selection Bayes Factors in terms of special functions depending on the sample size, number of covariates and R-squared of the model. We show that these expressions are accurate, fast to evaluate, and numerically stable. An R package blma for doing Bayesian linear model averaging using these exact expressions has been released on GitHub. We extend the Particle EM method of (Rockova, 2017) using Particle Variational Approximation and the exact posterior marginal likelihood expressions to derive a computationally efficient algorithm for model selection on data sets with many covariates. Our algorithm performs well relative to existing algorithms, completing in 8 seconds on a model selection problem with a sample size of 600 and 7200 covariates. We consider zero-inflated models that have many applications in areas such as manufacturing and public health, but pose numerical issues when fitting them to data. We apply a variational approximation to zero-inflated Poisson mixed models with Gaussian distributed random effects using a combination of VB and the Gaussian Variational Approximation (GVA). We also incorporate a novel parameterisation of the covariance of the GVA using the Cholesky factor of the precision matrix, similar to Tan and Nott (2018) to resolve associated numerical difficulties.
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Wang, Wei. "Linear mixed effects models in functional data analysis." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/253.
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Regression models with a scalar response and
a functional predictor have been extensively
studied. One approach is to approximate the
functional predictor using basis function or
eigenfunction expansions. In the expansion,
the coefficient vector can either be fixed or
random. The random coefficient vector
is also known as random effects and thus the
regression models are in a mixed effects
framework.
The random effects provide a model for the
within individual covariance of the
observations. But it also introduces an
additional parameter into the model, the
covariance matrix of the random effects.
This additional parameter complicates the
covariance matrix of the observations.
Possibly, the covariance parameters of the
model are not identifiable.
We study identifiability in normal linear
mixed effects models. We derive necessary and
sufficient conditions of identifiability,
particularly, conditions of identifiability
for the regression models with a scalar
response and a functional predictor using
random effects.
We study the regression model using the
eigenfunction expansion approach with random
effects. We assume the random effects have a
general covariance matrix
and the observed values of the predictor are
contaminated with measurement error.
We propose methods of inference for the
regression model's functional coefficient.
As an application of the model, we analyze a
biological data set to investigate the
dependence of a mouse's wheel running
distance on its body mass trajectory.
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Fonseca, Miguel dos Santos. "Estimation and hypothesis testing in mixed linear models." Doctoral thesis, FCT - UNL, 2007. http://hdl.handle.net/10362/1989.
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Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia<br>This thesis focuses on inference and hypothesis testing for parameters in orthogonal
mixed linear models. A canonical form for such models is obtained using the matrices
in principal basis of the commutative Jordan algebra associated to the model.
UMVUE are derived and used for hypothesis tests. When usual F tests are not
possible to use, generalized F tests arise, and the distribution for the statistic of
such tests is obtained under some mild conditions. application of these results is
made to cross-nested models.
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Tran, Vuong. "Bayesian variable selection in linear mixed effects models." Thesis, Linköpings universitet, Statistik och maskininlärning, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-139069.
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Variable selection techniques have been well researched and used in many different fields. There is rich literature on Bayesian variable selection in linear regression models, but only few of them are about mixed effects. The topic of the thesis is Bayesian variable selection in linear mixed effect models. The choice of methods to achieve this goal is to induce different shrinkage priors. Both unimodal shrinkage priors and spike-and-slab priors are used and compared. The distributions that have been chosen, either as unimodal priors or parts of the spike-and-slab priors are the Normal distribution, the Student-t distribution and the Laplace distribution. Both the simulations and the real dataset studies have been carried out, with the intention of investigating and evaluating how good the chosen distributions are as shrinkage priors. Obtained results from the real dataset shows that spike-and-slab priors yield more shrinkage effect than what unimodal priors does. However, inducing spike-and-slab priors carelessly without any consideration if the size of the data is sufficiently large enough may lead to poor model parameter estimations. Results from the simulations studies indicates that a mixture of Laplace distribution for both the spike and slab components is the prior that yields the highest shrinkage effect among the investigated shrinkage priors.
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Gumedze, Freedom Nkhululeko. "A variance shilf model for outlier detection and estimation in linear and linear mixed models." Doctoral thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/4381.
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Includes abstract.<br>Includes bibliographical references.<br>Outliers are data observations that fall outside the usual conditional ranges of the response data.They are common in experimental research data, for example, due to transcription errors or faulty experimental equipment. Often outliers are quickly identified and addressed, that is, corrected, removed from the data, or retained for subsequent analysis. However, in many cases they are completely anomalous and it is unclear how to treat them. Case deletion techniques are established methods in detecting outliers in linear fixed effects analysis. The extension of these methods to detecting outliers in linear mixed models has not been entirely successful, in the literature. This thesis focuses on a variance shift outlier model as an approach to detecting and assessing outliers in both linear fixed effects and linear mixed effects analysis. A variance shift outlier model assumes a variance shift parameter, wi, for the ith observation, where wi is unknown and estimated from the data. Estimated values of wi indicate observations with possibly inflated variances relative to the remainder of the observations in the data set and hence outliers. When outliers lurk within anomalous elements in the data set, a variance shift outlier model offers an opportunity to include anomalies in the analysis, but down-weighted using the variance shift estimate wi. This down-weighting might be considered preferable to omitting data points (as in case-deletion methods). For very large values of wi a variance shift outlier model is approximately equivalent to the case deletion approach.
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Gumedze, Freedom Nkhululeko. "A variance shift model for outlier detection and estimation in linear and linear mixed models." Doctoral thesis, University of Cape Town, 2009. http://hdl.handle.net/11427/4380.
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Outliers are data observations that fall outside the usual conditional ranges of the response data.They are common in experimental research data, for example, due to transcription errors or faulty experimental equipment. Often outliers are quickly identified and addressed, that is, corrected, removed from the data, or retained for subsequent analysis. However, in many cases they are completely anomalous and it is unclear how to treat them. Case deletion techniques are established methods in detecting outliers in linear fixed effects analysis. The extension of these methods to detecting outliers in linear mixed models has not been entirely successful, in the literature. This thesis focuses on a variance shift outlier model as an approach to detecting and assessing outliers in both linear fixed effects and linear mixed effects analysis. A variance shift outlier model assumes a variance shift parameter, !i, for the ith observation, where !i is unknown and estimated from the data. Estimated values of !i indicate observations with possibly inflated variances relative to the remainder of the observations in the data set and hence outliers. When outliers lurk within anomalous elements in the data set, a variance shift outlier model offers an opportunity to include anomalies in the analysis, but down-weighted using the variance shift estimate Ë!i. This down-weighting might be considered preferable to omitting data points (as in case-deletion methods). For very large values of !i a variance shift outlier model is approximately equivalent to the case deletion approach. We commence with a detailed review of parameter estimation and inferential procedures for the linear mixed model. The review is necessary for the development of the variance shift outlier model as a method for detecting outliers in linear fixed and linear mixed models. This review is followed by a discussion of the status of current research into linear mixed model diagnostics. Different types of residuals in the linear mixed model are defined. A decomposition of the leverage matrix for the linear mixed model leads to interpretable leverage measures. ii A detailed review of a variance shift outlier model in linear fixed effects analysis is given. The purpose of this review is firstly, to gain insight into the general case (the linear mixed model) and secondly, to develop the model further in linear fixed effects analysis. A variance shift outlier model can be formulated as a linear mixed model so that the calculations required to estimate the parameters of the model are those associated with fitting a linear mixed model, and hence the model can be fitted using standard software packages. Likelihood ratio and score test statistics are developed as objective measures for the variance shift estimates. The proposed test statistics initially assume balanced longitudinal data with a Gaussian distributed response variable. The dependence of the proposed test statistics on the second derivatives of the log-likelihood function is also examined. For the single-case outlier in linear fixed effects analysis, analytical expressions for the proposed test statistics are obtained. A resampling algorithm is proposed for assessing the significance of the proposed test statistics and for handling the problem of multiple testing. A variance shift outlier model is then adapted to detect a group of outliers in a fixed effects model. Properties and performance of the likelihood ratio and score test statistics are also investigated. A variance shift outlier model for detecting single-case outliers is also extended to linear mixed effects analysis under Gaussian assumptions for the random effects and the random errors. The variance parameters are estimated using the residual maximum likelihood method. Likelihood ratio and score tests are also constructed for this extended model. Two distinct computing algorithms which constrain the variance parameter estimates to be positive, are given. Properties of the resulting variance parameter estimates from each computing algorithm are also investigated. A variance shift outlier model for detecting single-case outliers in linear mixed effects analysis is extended to detect groups of outliers or subjects having outlying profiles with random intercepts and random slopes that are inconsistent with the corresponding model elements for the remaining subjects in the data set. The issue of influence on the fixed effects under a variance shift outlier model is also discussed.
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Kaart, Tanel. "The reliability of linear mixed models in genetic studies /." Online version, 2005. http://dspace.utlib.ee/dspace/bitstream/10062/1217/5/kaart.pdf.
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Ma, Renjun. "An orthodox BLUP approach to generalized linear mixed models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0024/NQ38934.pdf.
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Frühwirth-Schnatter, Sylvia, and Regina Tüchler. "Bayesian parsimonious covariance estimation for hierarchical linear mixed models." Institut für Statistik und Mathematik, WU Vienna University of Economics and Business, 2004. http://epub.wu.ac.at/774/1/document.pdf.
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We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian variable selection methods. With this method we are able to learn from the data for each effect, whether it is random or not, and whether covariances among random effects are zero or not. An application in marketing shows a substantial reduction of the number of free elements of the variance-covariance matrix. (author's abstract)<br>Series: Research Report Series / Department of Statistics and Mathematics
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Ogden, Helen E. "Inference for generalised linear mixed models with sparse structure." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/60467/.
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The likelihood for the parameters of a generalised linear mixed model involves an integral which may be of very high dimension. Because of this apparent intractability, many alternative methods have been proposed for inference in these models, but it is shown that all can fail when the model is sparse, in that there is only a small amount of information available on each random effect. The sequential reduction method developed in this thesis seeks to fill in this gap, by exploiting the dependence structure of the posterior distribution of the random effects to reduce dramatically the cost of approximating the likelihood in models with sparse structure. Examples are given to demonstrate the high quality of the new approximation relative to the available alternatives. Finally, robustness of various estimators to misspecification of the random effect distribution is considered. It is found that certain marginal composite likelihood estimators are not robust to such misspecification in situations in which the full maximum likelihood estimator is robust, providing a counterexample to the notion that composite likelihood estimators will always be at least as robust as the maximum likelihood estimator under model misspecification.
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Tang, On-yee, and 鄧安怡. "Estimation for generalized linear mixed model via multipleimputations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2005. http://hub.hku.hk/bib/B30687652.
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Yam, Ho-kwan, and 任浩君. "On a topic of generalized linear mixed models and stochastic volatility model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B29913342.
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Frühwirth-Schnatter, Sylvia, and Thomas Otter. "Conjoint Analysis Using Mixed Effect Models." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/806/1/document.pdf.
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Following the pioneering work of Allenby and Ginter (1995) and Lenk et al.(1994); we propose in Section 2 a mixed effect model allowing for fixed and random effects as possible statistical solution to the problems mentioned above. Parameter estimation using a new, efficient variant of a Markov Chain Monte Carlo method will be discussed in Section 3 together with problems of model comparison techniques in the context of random effect models. Section 4 presents an application of the former to a brand-price trade-off study from the Austrian mineral water market. (author's abstract)<br>Series: Forschungsberichte / Institut für Statistik
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Tang, On-yee. "Estimation for generalized linear mixed model via multiple imputations." Click to view the E-thesis via HKUTO, 2005. http://sunzi.lib.hku.hk/hkuto/record/B30687652.
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Tinti, Laura. "Mixed Integer Linear Programming Models for a Stowage Planning Problem." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018.
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The aim of this thesis is to deepen the Containership Stowage Planning Problem (CSPP). In general terms, this problem consists of finding optimal plans for stowing containers into a containership, satisfying several restrictions. This topic has a lot of variations regarding the objective functions and the constraints required, depending on the situation taken into account. This dissertation is developed by referring to a real case, with its specific objective function and restrictions. In the first part of this thesis, an overview on the different approaches given by the literature is provided. After this outline, a Mixed Integer Linear Programming Model is proposed with the goal of finding feasible solutions for the CSPP. A consistent number of instances is generated to analyze how the model performs depending on the input parameters. The model is then tested by using CPLEX Solver in the mathematical programming and optimization modelling language AMPL. Finally, the importance of the stability of the vessel is underlined. Constraints concerning the ship stability are added to the model and, throughout other tests in AMPL, the computational results and the comparison to the results previously obtained are evaluated.
25
Richardson, Troy E. "Treatment heterogeneity and potential outcomes in linear mixed effects models." Diss., Kansas State University, 2013. http://hdl.handle.net/2097/15950.
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Doctor of Philosophy<br>Department of Statistics<br>Gary L. Gadbury<br>Studies commonly focus on estimating a mean treatment effect in a population. However, in some applications the variability of treatment effects across individual units may help to characterize the overall effect of a treatment across the population. Consider a set of treatments, {T,C}, where T denotes some treatment that might be applied to an experimental unit and C denotes a control. For each of N experimental units, the duplet {r[subscript]i, r[subscript]Ci}, i=1,2,…,N, represents the potential response of the i[superscript]th experimental unit if treatment were applied and the response of the experimental unit if control were applied, respectively. The causal effect of T compared to C is the difference between the two potential responses, r[subscript]Ti- r[subscript]Ci. Much work has been done to elucidate the statistical properties of a causal effect, given a set of particular assumptions. Gadbury and others have reported on this for some simple designs and primarily focused on finite population randomization based inference. When designs become more complicated, the randomization based approach becomes increasingly difficult.
Since linear mixed effects models are particularly useful for modeling data from complex designs, their role in modeling treatment heterogeneity is investigated. It is shown that an individual treatment effect can be conceptualized as a linear combination of fixed treatment effects and random effects. The random effects are assumed to have variance components specified in a mixed effects “potential outcomes” model when both potential outcomes, r[subscript]T,r[subscript]C, are variables in the model. The variance of the individual causal effect is used to quantify treatment heterogeneity. Post treatment assignment, however, only one of the two potential outcomes is observable for a unit. It is then shown that the variance component for treatment heterogeneity becomes non-estimable in an analysis of observed data. Furthermore, estimable variance components in the observed data model are demonstrated to arise from linear combinations of the non-estimable variance components in the potential outcomes model. Mixed effects models are considered in context of a particular design in an effort to illuminate the loss of information incurred when moving from a potential outcomes framework to an observed data analysis.
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Hapuhinna, Nelum Shyamali Sri Manik. "Bootstrap Methods for Estimation in Linear Mixed Models with Heteroscedasticity." Bowling Green State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1626097766716384.
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Atutey, Olivia Abena. "Linear Mixed Model Selection via Minimum Approximated Information Criterion." Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1594910831256966.
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Pan, Juming. "Adaptive LASSO For Mixed Model Selection via Profile Log-Likelihood." Bowling Green State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1466633921.
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Greven, Sonja. "Non-standard problems in inference for additive and linear mixed models." Göttingen Cuvillier, 2007.
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Lindsten, Fredrik, Pete Bunch, Simon J. Godsill, and Thomas B. Schön. "Rao-Blackwellized particle smoothers for mixed linear/nonlinear state-space models." Linköpings universitet, Reglerteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-93460.
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We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction.<br>CNDM<br>CADICS
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Atamtürk, Alper. "Conflict graphs and flow models for mixed-integer linear optimization problems." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/26002.
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Weidenhammer, Beate [Verfasser]. "The Consistency of Quantile Regression in Linear Mixed Models / Beate Weidenhammer." Berlin : Freie Universität Berlin, 2019. http://d-nb.info/1182314503/34.
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Mostafa, S. M. "Estimation of variance components in balanced random and mixed linear models." Thesis, University of Strathclyde, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382394.
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Zhai, Jing. "Efficient Exact Tests in Linear Mixed Models for Longitudinal Microbiome Studies." Thesis, The University of Arizona, 2016. http://hdl.handle.net/10150/612412.
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Microbiome plays an important role in human health. The analysis of association between microbiome and clinical outcome has become an active direction in biostatistics research. Testing the microbiome effect on clinical phenotypes directly using operational taxonomic unit abundance data is a challenging problem due to the high dimensionality, non-normality and phylogenetic structure of the data. Most of the studies only focus on describing the change of microbe population that occur in patients who have the specific clinical condition. Instead, a statistical strategy utilizing distance-based or similarity-based non-parametric testing, in which a distance or similarity measure is defined between any two microbiome samples, is developed to assess association between microbiome composition and outcomes of interest. Despite the improvements, this test is still not easily interpretable and not able to adjust for potential covariates. A novel approach, kernel-based semi-parametric regression framework, is applied in evaluating the association while controlling the covariates. The framework utilizes a kernel function which is a measure of similarity between samples' microbiome compositions and characterizes the relationship between the microbiome and the outcome of interest. This kernel-based regression model, however, cannot be applied in longitudinal studies since it could not model the correlation between the repeated measurements. We proposed microbiome association exact tests (MAETs) in linear mixed model can deal with longitudinal microbiome data. MAETs can test not only the effect of overall microbiome but also the effect from specific cluster of the OTUs while controlling for others by introducing more random effects in the model. The current methods for multiple variance component testing are based on either asymptotic distribution or parametric bootstrap which require large sample size or high computational cost. The exact (R)LRT tests, an computational efficient and powerful testing methodology, was derived by Crainiceanu. Since the exact (R)LRT can only be used in testing one variance component, we proposed an approach that combines the recent development of exact (R)LRT and a strategy for simplifying linear mixed model with multiple variance components to a single case. The Monte Carlo simulation studies present correctly controlled type I error and provided superior power in testing association between microbiome and outcomes in longitudinal studies. Finally, the MAETs were applied to longitudinal pulmonary microbiome datasets to demonstrate that microbiome composition is associated with lung function and immunological outcomes. We also successfully found two interesting genera Prevotella and Veillonella which are associated with forced vital capacity.
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Nelson, Kerrie P. "Generalized linear mixed models : development and comparison of different estimation methods /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/8960.
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Wenren, Cheng. "Mixed Model Selection Based on the Conceptual Predictive Statistic." Bowling Green State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1403735738.
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Hossain, Mohammad Zakir. "A small-sample randomization-based approach to semi-parametric estimation and misspecification in generalized linear mixed models." Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/24641.
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In a generalized linear mixed model (GLMM), the random effects are typically uncorrelated and assumed to follow a normal distribution. However, findings from recent studies on how the misspecification of the random effects distribution affects the estimated model parameters are inconclusive. In the thesis, we extend the randomization approach for deriving linear models to the GLMM framework. Based on this approach, we develop an algorithm for estimating the model parameters of the randomization-based GLMM (RBGLMM) for the completely randomized design (CRD) which does not require normally distributed random effects. Instead, the discrete uniform distribution on the symmetric group of permutations is used for the random effects. Our simulation results suggest that the randomization-based algorithm may be an alternative when the assumption of normality is violated. In the second part of the thesis, we consider an RB-GLMM for the randomized complete block design (RCBD) with random block effects. We investigate the effect of misspecification of the correlation structure and of the random effects distribution via simulation studies. In the simulation, we use the variance covariance matrices derived from the randomization approach. The misspecified model with uncorrelated random effects is fitted to data generated from the model with correlated random effects. We also fit the model with normally distributed random effects to data simulated from models with different random effects distributions. The simulation results show that misspecification of both the correlation structure and of the random effects distribution has hardly any effect on the estimates of the fixed effects parameters. However, the estimated variance components are frequently severely biased and standard errors of these estimates are substantially higher.
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Heinzl, Felix Verfasser], and Gerhard [Akademischer Betreuer] [Tutz. "Clustering in linear and additive mixed models / Felix Heinzl. Betreuer: Gerhard Tutz." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2013. http://d-nb.info/1035066823/34.
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MARTELOTTE, MARCELA COHEN. "USING LINEAR MIXED MODELS ON DATA FROM EXPERIMENTS WITH RESTRICTION IN RANDOMIZATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=16422@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>Esta dissertação trata da aplicação de modelos lineares mistos em dados provenientes de experimentos com restrição na aleatorização. O experimento utilizado neste trabalho teve como finalidade verificar quais eram os fatores de controle do processo de laminação a frio que mais afetavam a espessura do material utilizado na fabricação das latas para bebidas carbonatadas. A partir do experimento, foram obtidos dados para modelar a média e a variância da espessura do material. O objetivo da modelagem era identificar quais fatores faziam com que a espessura média atingisse o valor desejado (0,248 mm). Além disso, era necessário identificar qual a combinação dos níveis desses fatores que produzia a variância mínima na espessura do material. Houve replicações neste experimento, mas estas não foram executadas de forma aleatória, e, além disso, os níveis dos fatores utilizados não foram reinicializados, nas rodadas do experimento. Devido a estas restrições, foram utilizados modelos mistos para o ajuste da média, e da variância, da espessura, uma vez que com tais modelos é possível trabalhar na presença de dados auto-correlacionados e heterocedásticos. Os modelos mostraram uma boa adequação aos dados, indicando que para situações onde existe restrição na aleatorização, a utilização de modelos mistos se mostra apropriada.<br>This dissertation presents an application of linear mixed models on data from an experiment with restriction in randomization. The experiment used in this study was aimed to verify which were the controlling factors, in the cold-rolling process, that most affected the thickness of the material used in the carbonated beverages market segment. From the experiment, data were obtained to model the mean and variance of the thickness of the material. The goal of modeling was to identify which factors were significant for the thickness reaches the desired value (0.248 mm). Furthermore, it was necessary to identify which combination of levels, of these factors, produced the minimum variance in the thickness of the material. There were replications of this experiment, but these were not performed randomly. In addition, the levels of factors used were not restarted during the trials. Due to these limitations, mixed models were used to adjust the mean and the variance of the thickness. The models showed a good fit to the data, indicating that for situations where there is restriction on randomization, the use of mixed models is suitable.
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Ntirampeba, D. "Modelling growth patterns of bird species using non-linear mixed effects models." Master's thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/19032.
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Includes bibliographical references.<br>The analysis of growth data is important as it allows us to assess how fast things grow and determine various factors that have impact on their growth. In the current study, growth measurements on body features (body mass, wing length, head length, bill (culmen) length, foot length, and tarsus length) for Grey-headed Gulls populating Bonaero Park and Modderfontein Pan in Gauteng province, South Africa, and for Swift Terns on Robben Island were taken. Different methods such as polynomial regressions, non-parametric models and non-linear mixed effects models have been used to fit models to growth data. In recent years, non-linear mixed effects models have become an important tool for growth models. We have fitted univariate inverse exponential, Gompertz, logistic, and Richards non-linear mixed effects models to each of the six body features. We have modeled these six features simultaneously by adding a categorical covariate, which distinguishes between different features, to the model. This approach allows for straightforward comparison of growth between the different body features. In growth studies, the knowledge of the age of each individual is an essential information for growth analysis. For Swift Terns, the exact age of most chicks was unknown, but a small portion of the sample was followed from nestling up to the end of the study period. For chicks with unknown age, we estimated age by fitting the growth curve, obtained from birds with known age, to the mass measurements of the chick with unknown age. It was found that the logistic models were most appropriate to describe the growth of body mass and wing length while the Gompertz models provided best fits for bill, tarsus, head and foot for Grey-headed Gulls. For Swift Terns, the inverse exponential model provided the best univariate fit for four of six features. The logistic model, with a variance function increasing as a power of fitted values, with a different power for each feature and autoregressive correlation structure for within bird errors with errors from different features within the same subject assumed to be independent, gave the best model to describe the growth of all body features taken simultaneously for both Grey-headed Gull and Swift Tern data. It was shown that growth of Grey-headed Gull and Swift Tern chicks occurs in the following order (foot, body mass, tarsus)-(bill, head)-( wing) and (tarsus, foot)-(body mass, bill, head)-(wing) , respectively.
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Heinzl, Felix [Verfasser], and Gerhard [Akademischer Betreuer] Tutz. "Clustering in linear and additive mixed models / Felix Heinzl. Betreuer: Gerhard Tutz." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2013. http://d-nb.info/1035066823/34.
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Evangelou, Evangelos A. Smith Richard L. "Bayesian and frequentist methods for approximate inference in generalized linear mixed models." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2009. http://dc.lib.unc.edu/u?/etd,2607.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2009.<br>Title from electronic title page (viewed Oct. 5, 2009). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Statistics and Operations Research Statistics." Discipline: Statistics and Operations Research; Department/School: Statistics and Operations Research.
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Galarza, Morales Christian Eduardo 1988. "Quantile regression for mixed-effects models = Regressão quantílica para modelos de efeitos mistos." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306681.
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Orientador: Víctor Hugo Lachos Dávila<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-27T06:40:31Z (GMT). No. of bitstreams: 1
GalarzaMorales_ChristianEduardo_M.pdf: 5076076 bytes, checksum: 0967f08c9ad75f9e7f5df339563ef75a (MD5)
Previous issue date: 2015<br>Resumo: Os dados longitudinais são frequentemente analisados usando modelos de efeitos mistos normais. Além disso, os métodos de estimação tradicionais baseiam-se em regressão na média da distribuição considerada, o que leva a estimação de parâmetros não robusta quando a distribuição do erro não é normal. Em comparação com a abordagem de regressão na média convencional, a regressão quantílica (RQ) pode caracterizar toda a distribuição condicional da variável de resposta e é mais robusta na presença de outliers e especificações erradas da distribuição do erro. Esta tese desenvolve uma abordagem baseada em verossimilhança para analisar modelos de RQ para dados longitudinais contínuos correlacionados através da distribuição Laplace assimétrica (DLA). Explorando a conveniente representação hierárquica da DLA, a nossa abordagem clássica segue a aproximação estocástica do algoritmo EM (SAEM) para derivar estimativas de máxima verossimilhança (MV) exatas dos efeitos fixos e componentes de variância em modelos lineares e não lineares de efeitos mistos. Nós avaliamos o desempenho do algoritmo em amostras finitas e as propriedades assintóticas das estimativas de MV através de experimentos empíricos e aplicações para quatro conjuntos de dados reais. Os algoritmos SAEMs propostos são implementados nos pacotes do R qrLMM() e qrNLMM() respectivamente<br>Abstract: Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation for non-normal error distributions. Compared to the conventional mean regression approach, quantile regression (QR) can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. This thesis develops a likelihood-based approach to analyzing QR models for correlated continuous longitudinal data via the asymmetric Laplace distribution (ALD). Exploiting the nice hierarchical representation of the ALD, our classical approach follows the stochastic Approximation of the EM (SAEM) algorithm for deriving exact maximum likelihood (ML) estimates of the fixed-effects and variance components in linear and nonlinear mixed effects models. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to four real life datasets. The proposed SAEMs algorithms are implemented in the R packages qrLMM() and qrNLMM() respectively<br>Mestrado<br>Estatistica<br>Mestre em Estatística
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Croxton, Keely L., Bernard Gendon, and Thomas L. Magnanti. "A Comparison of Mixed-Integer Programming Models for Non-Convex Piecewise Linear Cost Minimization Problems." Massachusetts Institute of Technology, Operations Research Center, 2002. http://hdl.handle.net/1721.1/5233.
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We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.
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Shieh, Yann-yann. "An evaluation of mixed effects multilevel modeling under conditions of error term nonnormality /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
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Hercz, Daniel. "Flexible modeling with generalized additive models and generalized linear mixed models: comprehensive simulation and case studies." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=114300.
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This thesis compares GAMs and GLMMs in the context of modeling nonlinear curves. The study contains a comprehensive simulation and a few real life data analyses. The simulation uses thousands of generated datasets to compare and contrast the two models' (and linear models as a benchmark) fit, extent of nonlinearity, and shape of the resulting curve. The data analyses extend the results of the simulation to GLMM/GAM curves of lung function with measures of smoking as the independent variable. An additional and larger real life data analysis with dichotomous outcomes rounds out the study and allow for more representative results.<br>Cette these compare des GAM et GLMM dans le cadre de la modélisation des courbes non-linéaires. L'étude comprend une simulation complète et quelques analyses réelles. La simulation utilise des milliers de 'datasets' générés pour comparer forme entres les deux modèles (et les modèles linéaires comme point de repère), l'étendue de la non-linéarité, et la forme de la courbe obtenue. Les analyses d'étendre les résultats de la simulation à courbes de la fonction pulmonaire avec de GLMM / GAM avec mesures du tabagisme (la variable indépendante). Un autre analyse réelle avec les résultats dichotomiques complète l'étude et que les résultats soient plus représentatifs.
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Jensen, Willis Aaron. "Profile Monitoring for Mixed Model Data." Diss., Virginia Tech, 2006. http://hdl.handle.net/10919/27054.
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The initial portion of this research focuses on appropriate parameter estimators within a general context of multivariate quality control. The goal of Phase I analysis of multivariate quality control data is to identify multivariate outliers and step changes so that the estimated control limits are sufficiently accurate for Phase II monitoring. High breakdown estimation methods based on the minimum volume ellipsoid (MVE) or the minimum covariance determinant (MCD) are well suited to detecting multivariate outliers in data. Because of the inherent difficulties in computation many algorithms have been proposed to
obtain them. We consider the subsampling algorithm to obtain the MVE estimators and the FAST-MCD algorithm to obtain the MCD estimators. Previous studies have not clearly determined which of these two estimation methods is best for control chart applications. The comprehensive simulation study here gives guidance for when to use which estimator. Control limits are provided. High breakdown estimation methods such as MCD and MVE can be applied to a wide variety of multivariate quality control data.
The final, lengthier portion of this research considers profile monitoring. Profile monitoring is a relatively new technique in quality control used when the product or process quality is best
represented by a profile (or a curve) at each time period. The essential idea is often to model the profile via some parametric method and then monitor the estimated parameters over time to
determine if there have been changes in the profiles. Because the estimated parameters may be correlated, it is convenient to monitor them using a multivariate control method such as the T-squared statistic. Previous modeling methods have not incorporated the correlation structure within the profiles. We propose the use of mixed models (both linear and nonlinear) to monitor linear and
nonlinear profiles in order to account for the correlation structure within a profile. We consider various data scenarios and show using simulation when the mixed model approach is preferable to an approach that ignores the correlation structure. Our focus is on Phase I control chart applications.<br>Ph. D.
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Ho, Kwok Wah. "RJMCMC algorithm for multivariate Gaussian mixtures with applications in linear mixed-effects models /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?ISMT%202005%20HO.
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Mansour, Asmaa. "Modeling outcome estimates in meta-analysis using fixed and mixed effects linear models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0001/MQ44216.pdf.
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Jung, Jungah. "Using generalized linear models with a mixed random component to analyze count data." Fogler Library, University of Maine, 2001. http://www.library.umaine.edu/theses/pdf/JungJX2001.pdf.
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