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1
Ribbing, Jakob. "Covariate Model Building in Nonlinear Mixed Effects Models." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7923.
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Nagem, Mohamed O. "Diagnostics for Nonlinear Mixed-Effects Models." College Park, Md.: University of Maryland, 2009. http://hdl.handle.net/1903/9546.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2009.Thesis research directed by: Applied Mathematics & Statistics, and Scientific Computation Program. 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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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.
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Mahbouba, Raid. "Nonlinear mixed effects models for longitudinal DATA." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120579.
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The main objectives of this master thesis are to explore the effectiveness of nonlinear mixed effects model for longitudinal data. Mixed effect models allow to investigate the nature of relationship between the time-varying covariates and the response while also capturing the variations of subjects. I investigate the robustness of the longitudinal models by building up the complexity of the models starting from multiple linear models and ending up with additive nonlinear mixed models. I use a dataset where firms’ leverage are explained by four explanatory variables in addition to a grouping factor that is the firm factor. The models are compared using comparison statistics such as AIC, BIC and by a visual inspection of residuals. Likelihood ratio test has been used in some nested models only. The models are estimated by maximum likelihood and restricted maximum likelihood estimation. The most efficient model is the nonlinear mixed effects model which has lowest AIC and BIC. The multiple linear regression model failed to explain the relation and produced unrealistic statistics
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Barrowman, Nicholas J. "Nonlinear mixed effects models for meta-analysis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ57342.pdf.
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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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Baverel, Paul. "Development and Evaluation of Nonparametric Mixed Effects Models." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-144583.
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A nonparametric population approach is now accessible to a more comprehensive network of modelers given its recent implementation into the popular NONMEM application, previously limited in scope by standard parametric approaches for the analysis of pharmacokinetic and pharmacodynamic data. The aim of this thesis was to assess the relative merits and downsides of nonparametric models in a nonlinear mixed effects framework in comparison with a set of parametric models developed in NONMEM based on real datasets and when applied to simple experimental settings, and to develop new diagnostic tools adapted to nonparametric models. Nonparametric models as implemented in NONMEM VI showed better overall simulation properties and predictive performance than standard parametric models, with significantly less bias and imprecision in outcomes of numerical predictive check (NPC) from 25 real data designs. This evaluation was carried on by a simulation study comparing the relative predictive performance of nonparametric and parametric models across three different validation procedures assessed by NPC. The usefulness of a nonparametric estimation step in diagnosing distributional assumption of parameters was then demonstrated through the development and the application of two bootstrapping techniques aiming to estimate imprecision of nonparametric parameter distributions. Finally, a novel covariate modeling approach intended for nonparametric models was developed with good statistical properties for identification of predictive covariates. In conclusion, by relaxing the classical normality assumption in the distribution of model parameters and given the set of diagnostic tools developed, the nonparametric approach in NONMEM constitutes an attractive alternative to the routinely used parametric approach and an improvement for efficient data analysis.
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Janzén, David. "Structural identifiability and indistinguishability in mixed-effects models." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/93154/.
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The inverse problem, i.e., estimating parameters in an assumed model structure representing the system of interest, is central in mathematical modelling. Structural identifiability is a prerequisite to successful parameter estimation. If a model is structurally globally identifiable then there exists a unique solution to the inverse problem. Structural indistinguishability relates to the uniqueness of the structures in a set of candidate models. These two closely related concepts are of particular importance in the modelling of biological systems where conclusions are often drawn from the parameter estimates following parameter estimation and where candidate models are used to understand the underlying mechanisms of the biological system. In this thesis two new definitions of structural identifiability and indistinguishability are presented in which the two concepts have been generalised to now also include the mixed-effects modelling framework which is frequently used in pharmaceutical applications. Several analytical methods applicable to study these concepts in mixed-effects models are presented. These are applicable to any arbitrary mixed-effects models written in state-space form. The developed methods can be used to determine whether the distribution of the set of output functions uniquely, or otherwise, determine the parameter/model structure. Interesting results have followed from the application of these established techniques to mixed-effects models. It is shown using examples that result from either structural identifiability or indistinguishability analyses of non-mixed-effects models no longer necessarily hold for the corresponding mixed-effects model formulation. This is due to the random effects in the statistical sub-model in three different ways i) where the random effects enter into the structural model ii) the form of the random effects iii) the structure of the covariance matrix related to the random effects. These insights are collected in a set of conjectures. Several such examples are provided including the well-known unidentifiable one-compartment absorption model whose mixed-effects version is shown to be identifiable depending on the choice of the statistical sub-model. The contributions from this thesis are thus theoretical, but with direct practical use in a mixed-effects modelling context.
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Whitaker, Gavin Andrew. "Bayesian inference for stochastic differential mixed-effects models." Thesis, University of Newcastle upon Tyne, 2016. http://hdl.handle.net/10443/3398.
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Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units, SDE driven mixed- effects models allow the quantification of both between and within individual variation. Performing Bayesian inference for such models, using discrete-time data that may be incomplete and subject to measurement error, is a challenging problem and is the focus of this thesis. Since, in general, no closed form expression exists for the transition densities of the SDE of interest, a widely adopted solution works with the Euler-Maruyama approximation, by replacing the intractable transition densities with Gaussian approximations. These approximations can be made arbitrarily accurate by introducing intermediate time-points between observations. Integrating over the uncertainty associated with the process at these time-points necessitates the use of computationally intensive algorithms such as Markov chain Monte Carlo (MCMC). We extend a recently proposed MCMC scheme to include the SDE driven mixed-effects framework. Key to the development of an e fficient inference scheme is the ability to generate discrete-time realisations of the latent process between observation times. Such realisations are typically termed diffusion bridges. By partitioning the SDE into two parts, one that accounts for nonlinear dynamics in a deterministic way, and another as a residual stochastic process, we develop a class of novel constructs that bridge the residual process via a linear approximation. In addition, we adapt a recently proposed construct to a partial and noisy observation regime. We compare the performance of each new construct with a number of existing approaches, using three applications: a simple birth-death process, a Lotka-Volterra model and a model for aphid growth. We incorporate the best performing bridge construct within an MCMC scheme to determine the posterior distribution of the model parameters. This methodology is then applied to synthetic data generated from a simple SDE model of orange tree growth, and real data consisting of observations on aphid numbers recorded under a variety of different treatment regimes. Finally, we provide a systematic comparison of our approach with an inference scheme based on a tractable approximation of the SDE, that is, the linear noise approximation.
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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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Erkan, Ibrahim. "Mixed Effects Models For Time Series Gene Expression Data." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613913/index.pdf.
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The experimental factors such as the cell type and the treatment may have different impact on expression levels of individual genes which are quantitative measurements from microarrays. The measurements can be collected at a few unevenly spaced time points with replicates. The aim of this study is to consider cell type, treatment and short time series attributes and to infer about their effects on individual genes. A mixed effects model (LME) was proposed to model the gene expression data and the performance of the model was validated by a simulation study. Realistic data sets were generated preserving the structure of the sample real life data studied by Nymark et al. (2007). Predictive performance of the model was evaluated by performance measures, such as accuracy, sensitivity and specificity, as well as compared to the competing method by Smyth (2004), namely Limma. Both methods were also compared on real life data. Simulation results showed that the predictive performance of LME is as high as 99%, and it produces False Discovery Rate (FDR) as low as 0.4% whereas Limma has an FDR value of at least 32%. Moreover, LME has almost 99% predictive capability on the continuous time parameter where Limma has only about 67% and even it cannot handle continuous independent variables.
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Kyriakou, S. "Reduced-bias estimation and inference for mixed-effects models." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10049958/.
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A popular method for reducing the mean and median bias of the maximum likelihood estimator in regular parametric models is through the additive adjustment of the score equation (Firth, 1993; Kenne Pagui et al., 2017). The current work focuses on mean and median bias-reducing adjusted score equations in models with latent variables. First, we give estimating equations based on a mean bias-reducing adjustment of the score function for mean bias reduction in linear mixed models. Second, we propose an extension of the adjusted score equation approach (Firth, 1993) to obtain bias-reduced estimates for models with either computationally infeasible adjusted score equations and/or intractable likelihood. The proposed bias-reduced estimator is obtained by solving an approximate adjusted score equation, which uses an approximation of the log-likelihood to obtain tractable derivatives, and Monte Carlo approximation of the bias function to get feasible expressions. Under certain general conditions, we prove that the feasible and tractable bias-reduced estimator is consistent and asymptotically normally distributed. The “iterated bootstrap with likelihood adjustment” algorithm is presented that can compute the solution of the new bias-reducing adjusted score equation. The effectiveness of the proposed method is demonstrated via simulation studies and real data examples in the case of generalised linear models and generalised linear mixed models. Finally, we derive the median bias-reducing adjusted scores for linear mixed models and random-effects meta-analysis and meta-regression models.
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Bakbergenuly, Ilyas. "Transformation bias in mixed effects models of meta-analysis." Thesis, University of East Anglia, 2017. https://ueaeprints.uea.ac.uk/65314/.
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When binary data exhibit the greater variation than expected, the statistical methods have to account for extra-binomial variation. Possible explanations for extra-binomial variation include intra-cluster dependence or the variability of binomial probabilities. Both of these reasons lead to overdispersion of binomial counts and the resulting heterogeneity in their meta-analysis. Variance stabilizing or normalizing transformations are often applied to binomial counts to enable the use of standard methods based on normality. In meta-analysis, this is routinely done for the inference on overall effect measure. However, these transformations might result in biases in the presence of overdispersion. We study biases arising in the result of transformations of binary variables in the random or mixed effects models. We demonstrate considerable biases arising from standard log-odds and arcsine transformations both for single studies and in meta-analysis. We also explore possibilities of bias correction. In meta-analysis, the heterogeneity of the log odds ratios across the studies is usually incorporated by standard (additive) random effects model (REM). An alternative, multiplicative random effects model is based on the concept of an overdispersion. The multiplicative factor in this overdispersed random effects model can be interpreted as an intra-class correlation parameter. This model arises when one or both binomial distributions in the 2 by 2 tables are changed to betabinomial distributions. The Mantel-Haenzsel and inverse-variance approaches are extended to this setting. The estimation of the random effect parameter is based on profiling the modified Breslow-Day test and improving the approximation for distribution of Q statistic in Mandel-Paule method. The biases and coverages from new methods are compared to standard methods through simulation studies. The misspecification of the REM in respect to the mechanism of its generation is an important issue which is also discussed in this thesis.
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Botha, Imke. "Bayesian inference for stochastic differential equation mixed effects models." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/198039/1/Imke_Botha_Thesis.pdf.
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Stochastic differential equation mixed effects models (SDEMEMs) are increasingly used in biomedical and pharmacokinetic/pharmacodynamic research. However, the complexity of these models means that previous research has focussed on approximate parameter estimation methods. This thesis develops three novel Bayesian parameter estimation methods for SDEMEMs. The new methods can produce parameter estimates that are more accurate and provide more reliable uncertainty quantification. The new methods are applied to both real and simulated data from a tumour xenography study on mice.
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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 DávilaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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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
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
Mestrado
Estatistica
Mestre em Estatística
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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 PhilosophyDepartment of Statistics
Gary L. Gadbury
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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Jia, Yanan Jia. "Generalized Bilinear Mixed-Effects Models for Multi-Indexed Multivariate Data." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1469180629.
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Kjellsson, Maria C. "Methodological Studies on Models and Methods for Mixed-Effects Categorical Data Analysis." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9333.
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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)Series: Research Report Series / Department of Statistics and Mathematics
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Du, Ye Ting. "Simultaneous fixed and random effects selection in finite mixtures of linear mixed-effects models." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110592.
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Linear mixed-effects (LME) models are frequently used for modeling longitudinal data. One complicating factor in the analysis of such data is that samples are sometimes obtained from a population with significant underlying heterogeneity, which would be hard to capture by a single LME model. Such problems may be addressed by a finite mixture of linear mixed-effects (FMLME) models, which segments the population into subpopulations and models each subpopulation by a distinct LME model. Often in the initial stage of a study, a large number of predictors are introduced. However, their associations to the response variable vary from one component to another of the FMLME model. To enhance predictability and to obtain a parsimonious model, it is of great practical interest to identify the important effects, both fixed and random, in the model. Traditional variable selection techniques such as stepwise deletion and subset selection are computationally expensive even with modest numbers of covariates and components in the mixture model. In this thesis, we introduce a penalized likelihood approach and propose a nested EM algorithm for efficient numerical computations. The estimators are shown to possess consistency and sparsity properties and asymptotic normality. We illustrate the performance of the proposed method through simulations and a real data example.Les modèles linéaires mixtes (LME) sont fréquemment employés pour la modélisation des données longitudinales. Un facteur qui complique l'analyse de ce genre de données est que les échantillons sont parfois obtenus à partir d'une population d'importante hétérogénéité sous-jacente, qui serait difficile à capter par un seul LME. De tels problèmes peuvent être surmontés par un mélange fini de modèles linéaires mixtes (FMLME), qui segmente la population en sous-populations et modélise chacune de ces dernières par un LME distinct. Souvent, un grand nombre de variables explicatives sont introduites dans la phase initiale d'une étude. Cependant, leurs associations à la variable réponse varient d'un composant à l'autre du modèle FMLME. Afin d'améliorer la prévisibilité et de recueillir un modèle parcimonieux, il est d'un grand intérêt pratique d'identifier les effets importants, tant fixes qu'aléatoires, dans le modèle. Les techniques conventionnelles de sélection de variables telles que la suppression progressive et la sélection de sous-ensembles sont informatiquement chères, même lorsque le nombre de composants et de covariables est relativement modeste. La présente thèse introduit une approche basée sur la vraisemblance pénalisée et propose un algorithme EM imbriqué qui est computationnellement efficace. On démontre aussi que les estimateurs possèdent des propriétés telles que la cohérence, la parcimonie et la normalité asymptotique. On illustre la performance de la méthode proposée au moyen de simulations et d'une application sur un vrai jeu de données.
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Xu, Xiaochen. "Estimation of structural parameters in credibility context using mixed effects models." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/b4020361x.
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Stirrup, O. T. "Extending mixed effects models for longitudinal data before and after treatment." Thesis, University College London (University of London), 2016. http://discovery.ucl.ac.uk/1530997/.
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For the analysis of longitudinal biomedical data in which the timing of observations in each patient is irregular and in which there is substantial loss to follow-up, it is important that statistical models adequately describe both the patterns of variation within the data and any relationships between the variable of interest and time, clinical characteristics and response to treatment. We develop novel statistical models motivated by the analysis of pre- and post-treatment CD4 cell counts from HIV-infected patients, using the UK Register of Seroconverters and CASCADE datasets. The addition of stochastic process components, specifically Brownian motion, to standard linear mixed effects models has previously been shown to improve model fit for pre-treatment CD4 cell counts. We review and further develop computational techniques for such models, and also propose the use of a more general ‘fractional Brownian motion’ process in this setting. Residual diagnostic plots for such models, based on a marginal multivariate normal distribution, show very heavy tails, and we address this issue by further extending the model to allow between-patient differences in variability over time. It is known from the literature that response to treatment in HIV-patients is dependent on their baseline CD4 level at initiation. In order to further investigate the factors that determine the characteristics of recovery in CD4 counts, we develop a framework for the combined modelling of pre- and post-treatment CD4 cell counts in which key features of the response to treatment for each patient are dependent on a latent variable representing the unobserved ‘true’ baseline value, conditioned on all pre-treatment data for each patient. We further develop the model structure to account for uncertainty in the exact time of seroconversion for each patient, by integration of the log-likelihood function over all possible dates.
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Alzubaidi, Samirah Hamid. "A case study on cumulative logit models with low frequency and mixed effects." Kansas State University, 2017. http://hdl.handle.net/2097/38252.
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Master of ScienceDepartment of Statistics
Perla E. Reyes Cuellar
Data with ordinal responses may be encountered in many research fields, such as social, medical, agriculture or financial sciences. In this paper, we present a case study on cumulative logit models with low frequency and mixed effects and discuss some strengths and limitations of the current methodology. Two plant pathologists requested our statistical advice to fit a cumulative logit mixed model seeking for the effect of six commercial products on the control of a seed and seedling disease in soybeans in vitro. In their attempt to estimate the model parameters using a generalized linear mixed model approach with PROC GLIMMIX, the model failed to converge. Three alternative approaches to solve the problem were examined: 1) stratifying the data searching for the random effect; 2) assuming the random effect would be small and reducing the model to a fixed model; and 3) combining the original categories of the response variable to a lower number of categories. In addition, we conducted a power analysis to evaluate the required sample size to detect treatment differences. The results of all the proposed solutions were similar. Collapsing categories for a cumulative/proportional odds model has little effect on estimation. The sample size used in the case study is enough to detect a large shift of frequencies between categories, but not for moderated changes. Moreover, we do not have enough information to estimate a random effect. Even when it is present, the results regarding the fixed factors: pathogen, evaluation day, and treatment effects are the same as the obtained by the fixed model alternatives. All six products had a significant effect in slowing the effect of the pathogen, but the effects vary between pathogen species and assessment timing or date.
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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.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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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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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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Mansour, Asmaâ. "Modeling outcome estimates in meta-analysis using fixed and mixed effects linear models." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=20585.
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The main objective of this thesis is to present a quantitative method for modeling data collected from different studies on a same research topic. This quantitative method is called meta-analysis.The first step of a meta-analysis is the literature search, conducted using computerized and manual search strategies to identify relevant studies. The second step is the data abstraction from different relevant papers. In general, at least two independent raters systematically abstract the information, and interrater reliability check is performed.
The next step is the quantitative analysis of the abstracted data. For this purpose, it is possible to use either fixed or mixed effects linear model. Under the fixed effects model, only the variability due to sampling error is considered. In contrast, under the mixed effects model, an additional random effects variance is being considered. Both, the method of moments and the method of maximum likelihood can be used to estimate the parameters of the model.
Finally, the use of the above mentioned models and methods of estimation is illustrated with a data set on the prognosis of depression in the elderly, made available by Dr. Martin Cole from the Department of Psychiatry at St. Mary's Hospital Center in Montreal.
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Maldonado, Lizmarie Gabriela. "Linear Mixed-Effects Models: Applications to the Behavioral Sciences and Adolescent Community Health." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4363.
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Linear mixed-effects (LME) modeling is a widely used statistical method for analyzing repeated measures or longitudinal data. Such longitudinal studies typically aim to investigate and describe the trajectory of a desired outcome. Longitudinal data have the advantage over cross-sectional data by providing more accuracy for the model. LME models allow researchers to account for random variation among individuals and between individuals.
In this project, adolescent health was chosen as a topic of research due to the many changes that occur during this crucial time period as a precursor to overall well-being in adult life. Understanding the factors that influence how adolescents' mental well-being is affected may aid in interventions to reduce the risk of a negative impact. Self-esteem, in particular, has been associated with many components of physical and mental health and is a crucial focus in adolescent health. Research in self-esteem is extensive yet, sometimes inconclusive or contradictory since past research has been cross-sectional in nature. Several factors associated with self-esteem development are considered. Participation in religious services has also been an interest in research for its impact on depression. Depression development and its predictors are evaluated using LME models. Along with this line, this project will address the research problems identified through the following specific topics (i) to investigate the impact of early adolescent anxiety disorders on self-esteem development from adolescence to young adulthood; (ii) to study the role of maternal self-esteem and family socioeconomic status on adolescent self-esteem development through young adulthood; and (iii) to explore the efficacy of religious service attendance in reducing depressive symptoms. These topics present a good introduction to the LME approach and are of significant public health importance.
The present study explores varying scenarios of the statistical methods and techniques employed in the analysis of longitudinal data. This thesis provides an overview of LME models and the model selection process with applications. Although this project is motivated by adolescent health study, the basic concepts of the methods introduced have generally broader applications in other fields provided that the relevant technical specifications are met.
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Chen, Ren. "Bayesian Inference on Mixed-effects Models with Skewed Distributions for HIV longitudinal Data." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4298.
Full textAbstract:
Statistical models have greatly improved our understanding of the pathogenesis of HIV-1 infection
and guided for the treatment of AIDS patients and evaluation of antiretroviral (ARV) therapies.
Although various statistical modeling and analysis methods have been applied for estimating the
parameters of HIV dynamics via mixed-effects models, a common assumption of distribution is
normal for random errors and random-effects. This assumption may lack the robustness against
departures from normality so may lead misleading or biased inference. Moreover, some covariates
such as CD4 cell count may be often measured with substantial errors. Bivariate clustered
(correlated) data are also commonly encountered in HIV dynamic studies, in which the data set particularly
exhibits skewness and heavy tails. In the literature, there has been considerable interest in,
via tangible computation methods, comparing different proposed models related to HIV dynamics,
accommodating skewness (in univariate) and covariate measurement errors, or considering skewness
in multivariate outcomes observed in longitudinal studies. However, there have been limited
studies that address these issues simultaneously.
One way to incorporate skewness is to use a more general distribution family that can provide
flexibility in distributional assumptions of random-effects and model random errors to produce robust
parameter estimates. In this research, we developed Bayesian hierarchical models in which the
skewness was incorporated by using skew-elliptical (SE) distribution and all of the inferences were
carried out through Bayesian approach via Markov chain Monte Carlo (MCMC). Two real data set
from HIV/AIDS clinical trial were used to illustrate the proposed models and methods.
This dissertation explored three topics. First, with an SE distribution assumption, we compared
models with different time-varying viral decay rate functions. The effect of skewness on the model
fitting was also evaluated. The associations between the estimated decay rates based on the best
fitted model and clinical related variables such as baseline HIV viral load, CD4 cell count and longterm
response status were also evaluated. Second, by jointly modeling via a Bayesian approach,
we simultaneously addressed the issues of outcome with skewness and a covariate process with measurement errors. We also investigated how estimated parameters were changed under linear,
nonlinear and semiparametric mixed-effects models. Third, in order to accommodate individual
clustering within subjects as well as the correlation between bivariate measurements such as CD4
and CD8 cell count measured during the ARV therapies, bivariate linear mixed-effects models with
skewed distributions were investigated. Extended underlying normality assumption with SE distribution
assumption was proposed. The impacts of different distributions in SE family on the model
fit were also evaluated and compared.
Real data sets from AIDS clinical trial studies were used to illustrate the proposed methodologies
based on the three topics and compare various potential models with different distribution
specifications. The results may be important for HIV/AIDS studies in providing guidance to better
understand the virologic responses to antiretroviral treatment. Although this research is motivated
by HIV/AIDS studies, the basic concepts of the methods developed here can have generally broader
applications in other fields as long as the relevant technical specifications are met. In addition, the
proposed methods can be easily implemented by using the publicly available WinBUGS package,
and this makes our approach quite accessible to practicing statisticians in the fields.
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Nyberg, Joakim. "Practical Optimal Experimental Design in Drug Development and Drug Treatment using Nonlinear Mixed Effects Models." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-160481.
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The cost of releasing a new drug on the market has increased rapidly in the last decade. The reasons for this increase vary with the drug, but the need to make correct decisions earlier in the drug development process and to maximize the information gained throughout the process is evident. Optimal experimental design (OD) describes the procedure of maximizing relevant information in drug development and drug treatment processes. While various optimization criteria can be considered in OD, the most common is to optimize the unknown model parameters for an upcoming study. To date, OD has mainly been used to optimize the independent variables, e.g. sample times, but it can be used for any design variable in a study. This thesis addresses the OD of multiple continuous or discrete design variables for nonlinear mixed effects models. The methodology for optimizing and the optimization of different types of models with either continuous or discrete data are presented and the benefits of OD for such models are shown. A software tool for optimizing these models in parallel is developed and three OD examples are demonstrated: 1) optimization of an intravenous glucose tolerance test resulting in a reduction in the number of samples by a third, 2) optimization of drug compound screening experiments resulting in the estimation of nonlinear kinetics and 3) an individual dose-finding study for the treatment of children with ciclosporin before kidney transplantation resulting in a reduction in the number of blood samples to ~27% of the original number and an 83% reduction in the study duration. This thesis uses examples and methodology to show that studies in drug development and drug treatment can be optimized using nonlinear mixed effects OD. This provides a tool than can lower the cost and increase the overall efficiency of drug development and drug treatment.
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Thorp, John III. "Joint Mixed-Effects Models for Longitudinal Data Analysis: An Application for the Metabolic Syndrome." VCU Scholars Compass, 2009. http://scholarscompass.vcu.edu/etd/1943.
Full textAbstract:
Mixed-effects models are commonly used to model longitudinal data as they can appropriately account for within and between subject sources of variability. Univariate mixed effect modeling strategies are well developed for a single outcome (response) variable that may be continuous (e.g. Gaussian) or categorical (e.g. binary, Poisson) in nature. Only recently have extensions been discussed for jointly modeling multiple outcome variables measures longitudinally. Many diseases processes are a function of several factors that are correlated. For example, the metabolic syndrome, a constellation of cardiovascular risk factors associated with an increased risk of cardiovascular disease and type 2 diabetes, is often defined as having three of the following: elevated blood pressure, high waist circumference, elevated glucose, elevated triglycerides, and decreased HDL. Clearly these multiple measures within a subject are not independent. A model that could jointly model two or more of these risk factors and appropriately account for between subjects sources of variability as well as within subject sources of variability due to the longitudinal and multivariate nature of the data would be more useful than several univariate models. In fact, the univariate mixed-effects model can be extended in a relatively straightforward fashion to define a multivariate mixed-effects model for longitudinal data by appropriately defining the variance-covariance structure for the random-effects. Existing software such as the PROC MIXED in SAS can be used to fit the multivariate mixed-effects model. The Fels Longitudinal Study data were used to illustrate both univariate and multivariate mixed-effects modeling strategies. Specifically, jointly modeled longitudinal measures of systolic (SBP) and diastolic (DBP) blood pressure during childhood (ages two to eighteen) were compared between participants who were diagnosed with at least three of the metabolic syndrome risk factors in adulthood (ages thirty to fifty-five) and those who were never diagnosed with any risk factors. By identifying differences in risk factors, such as blood pressure, early in childhood between those who go on to develop the metabolic syndrome in adulthood and those who do not, earlier interventions could be used to prevent the development cardiovascular disease and type 2 diabetes. As demonstrated by these analyses, the multivariate model is able to not only answer the same questions addressed as the univariate model, it is also able to answer additional important questions about the association in the evolutions of the responses as well as the evolution of the associations. Furthermore, the additional information gained by incorporating information about the correlations between the responses was able to reduce the variability (standard errors) in both the fixed-effects estimates (e.g. differences in groups, effects of covariates) as well as the random-effects estimates (e.g. variability).
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Tüchler, Regina. "Bayesian Variable Selection for Logistic Models Using Auxiliary Mixture Sampling." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2006. http://epub.wu.ac.at/984/1/document.pdf.
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The paper presents an Markov Chain Monte Carlo algorithm for both variable and covariance selection in the context of logistic mixed effects models. This algorithm allows us to sample solely from standard densities, with no additional tuning being needed. We apply a stochastic search variable approach to select explanatory variables as well as to determine the structure of the random effects covariance matrix. For logistic mixed effects models prior determination of explanatory variables and random effects is no longer prerequisite since the definite structure is chosen in a data-driven manner in the course of the modeling procedure. As an illustration two real-data examples from finance and tourism studies are given. (author's abstract)Series: Research Report Series / Department of Statistics and Mathematics
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Largajolli, Anna. "Nonlinear Mixed-Effects Intravenous and Oral Minimal Models to Assess Insulin Secretion and Action." Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3422635.
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Diabetes is a serious metabolic disorder that according to the International Diabetes Federation (IDF) 2012 report affects about 371 million of people worldwide. This number is likely to increase in the next years especially due to the contribution of the emerging countries where health care is less effective. That is the reason why in these years scientific research has been carried out intensely facing diabetes with different field expertise from cellular biology to pharmacology to engineering and so on. Various scientific questions were answered but still many others are to come. For instance, different tests were developed to study the glucose-insulin system in vivo whose data were analyzed with model based approaches to extrapolate some knowledge of the underlying phenomena of the glycemic control. The research presented here aims to analyze data coming from different test by exploiting the nonlinear mixed-effects approach modeling population method (NLMEM) in order to study the glucose-insulin system. This statistical approach is largely employed in pharmacokinetics and pharmacodynamics (PKPD) studies during drug development but is not that much widespread in metabolic studies. This technique is really appealing because is able to quantify not only the individual and population parameters but also is able to identify the biological sources of inter-individual and intra-individual variability. Moreover the nonlinear mixed-effects approach is particularly recommended in "sparse dataset", the typical epidemiological study condition, where the standard individual techniques have difficulties in getting the physiological information from the data. In this case a complete statistical description is obtainable by borrowing the lack of information from the entire population thus potentially reducing the need for blood samples and invasive trials. Because of its potential, the nonlinear mixed-effects approach offers a valuable modeling tool to be investigated and validated on data coming from metabolic studies as those regarding the glucose-insulin systemIl diabete è una grave malattia metabolica che secondo l'International Diabetes Federation (IDF) colpisce circa 371 milioni di persone in tutto il mondo. Questo numero è destinato a crescere nei prossimi anni grazie al contributo dei paesi dove la sanità e la prevenzione sono meno efficaci. Questo è il motivo per cui in questi anni la ricerca scientifica è stata portata avanti intensamente studiando il diabete da diversi punti di vista: dalla biologia cellulare alla farmacologia alla ingegneria e via dicendo. Molti quesiti scientifici sono stati risolti ma molti altri sono ancora aperti. Recentemente sono stati sviluppati diversi test per studiare il sistema glucosio insulina in vivo i cui dati sono stati analizzati con approcci basati su modelli matematici che servono a estrapolare della conoscenza sui fenomeni sottostanti del controllo glicemico. La ricerca qui presentata si propone di analizzare i dati provenienti da test differenti sfruttando l' approccio di popolazione non lineare a effetti misti (NLMEM) per studiare il sistema glucosio-insulina. Questo approccio statistico è largamente impiegato in studi di farmacocinetica e farmacodinamica (PKPD) durante lo sviluppo di farmaci, ma non è molto diffuso negli studi metabolici. Questa tecnica è molto interessante perchè non solo è in grado di quantificare i parametri del l' individuo e della popolazione, ma è in grado di identificare le fonti biologiche della variabilità inter-individuale e intra-individuale. Inoltre l' approccio non lineare a effetti misti è particolarmente indicato in "dataset sparsi", la condizione tipica degli studi epidemiologici in cui le tecniche standard individuali hanno difficoltà ad ottenere le informazioni dai dati. In questo caso una descrizione completa statistica è ottenibile recuperando la mancanza di informazioni dalla popolazione riducendo così potenzialmente la necessità di campioni di sangue e di prove invasive. Grazie al suo potenziale, l' approccio non lineare a effetti misti offre un valido strumento di modellazione da utilizzare e convalidare su dati provenienti da studi metabolici, come quelli che riguardano il sistema glucosio-insulina
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Ernest, II Charles. "Benefits of Non-Linear Mixed Effect Modeling and Optimal Design : Pre-Clinical and Clinical Study Applications." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-209247.
Full textAbstract:
Despite the growing promise of pharmaceutical research, inferior experimentation or interpretation of data can inhibit breakthrough molecules from finding their way out of research institutions and reaching patients. This thesis provides evidence that better characterization of pre-clinical and clinical data can be accomplished using non-linear mixed effect modeling (NLMEM) and more effective experiments can be conducted using optimal design (OD). To demonstrate applicability of NLMEM and OD in pre-clinical applications, in vitro ligand binding studies were examined. NLMEMs were used to evaluate precision and accuracy of ligand binding parameter estimation from different ligand binding experiments using sequential (NLR) and simultaneous non-linear regression (SNLR). SNLR provided superior resolution of parameter estimation in both precision and accuracy compared to NLR. OD of these ligand binding experiments for one and two binding site systems including commonly encountered experimental errors was performed. OD was employed using D- and ED-optimality. OD demonstrated that reducing the number of samples, measurement times, and separate ligand concentrations provides robust parameter estimation and more efficient and cost effective experimentation. To demonstrate applicability of NLMEM and OD in clinical applications, a phase advanced sleep study formed the basis of this investigation. A mixed-effect Markov-chain model based on transition probabilities as multinomial logistic functions using polysomnography data in phase advanced subjects was developed and compared the sleep architecture between this population and insomniac patients. The NLMEM was sufficiently robust for describing the data characteristics in phase advanced subjects, and in contrast to aggregated clinical endpoints, which provide an overall assessment of sleep behavior over the night, described the dynamic behavior of the sleep process. OD of a dichotomous, non-homogeneous, Markov-chain phase advanced sleep NLMEM was performed using D-optimality by computing the Fisher Information Matrix for each Markov component. The D-optimal designs improved the precision of parameter estimates leading to more efficient designs by optimizing the doses and the number of subjects in each dose group. This thesis provides examples how studies in drug development can be optimized using NLMEM and OD. This provides a tool than can lower the cost and increase the overall efficiency of drug development.My name should be listed as "Charles Steven Ernest II" on cover.
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Wang, Liangliang. "Estimating nonlinear mixed-effects models by the generalized profiling method and its application to pharmacokinetics." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18424.
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Several methods with software tools have been developed to estimate nonlinear mixed-effects models. However, fewer have addressed the issue when nonlinear mixed-effects models are implicitly expressed as a set of ordinary differential equations (ODE's) while these ODE's have no closed-form solutions. The main objective of this thesis is to solve this problem based on the framework of the generalized profiling method proposed by Ramsay, Hooker, Campbell, and Cao (2007). Four types of parameters are identified and estimated in a cascaded way by a multiple-level nested optimization. In the outermost level, the smoothing parameter is selected by the criterion of generalized cross-validation (GCV). In the outer level, the structural parameters, including the fixed effects, the variance-covariance matrix for random effects, and the residual variance, are optimized by a criterion based on a first-order Taylor expansion of the nonlinear function. In the middle level, the random effects are optimized by the penalized nonlinear least squares. In the inner level, the coefficients of basis function expansions are optimized by penalized smoothing with the penalty defined by ODE's. Consequently, some types of parameters are expressed as explicit or implicit functions of other parameters. The dimensionality of the parameter space is reduced, and the optimization surface becomes smoother. The Newton-Raphson algorithm is applied to estimate parameters for each level of optimization with gradients and Hessian matrices worked out analytically with the Implicit Function Theorem. Our method, along with MATLAB codes, is tested by estimating several compartment models in pharmacokinetics from both simulated and real data sets. Results are compared with the true values or estimates obtained by the package nlme in R, and it turns out that the generalized profiling method can achieve reasonable estimates without solving ODE's directly.Il n'y a aucune solution de exacte pour beaucoup de modèles non-linéaires à effets mixtes (NLME) exprimés comme un ensemble d'équations ordinaires (ODE) en modèles de compartiment. Cette thèse passe en revue plusieurs méthodes et outils courants de logiciel pour NLME, et explore une nouvelle manière d'estimer des effets mixtes non-linéaires en modèles de compartiment basée sur le cadre de la méthode de profilage généralisée proposée par Ramsay, Hooker, Campbell, et Cao (2007). Quatre types de paramètres sont identifiés et estimés d'en cascade par une optimisation de multiple-niveau: le paramètre regularisateur est choisi par le critère de la contre-vérification généralisée (GCV); les paramètres structuraux, y compris les effets fixes, la matrice de variance-covariance pour les effets aléatoires, et la variance résiduelle sont optimisés par un critère basé sur une expansion de premier ordre de Taylor de fonction non-linéaire ; les effets aléatoires sont optimisés par une methode des moindres carrés non-linéaires pénalisés ; et les coefficients d'expansions de fonction de base sont optimisés par un lissage pénalisé avec la pénalité définie par l'equation differentielle. En conséquence, certains des paramètres sont exprimés en tant que fonctions explicites ou implicites d'autres paramètres. La dimensionnalité de l'espace des paramètres est réduite, et la surface d'optimisation devient plus lisse. L'algorithme de Newton-Raphson est appliqué aux paramètres d'évaluation pour chaque niveau d'optimisation, où le théorème des fonctions implicites est employé couramment pour établir les gradients et les matrices de Hessiennes de facon analytiques. La méthode proposée et des codes de MATLAB sont examinés par des applications à plusieurs modèles de compartiment en pharmacocinétique sur des donnees simulées et vraies. Des résultats sont comparés aux valeurs ou aux évaluations vraies obtenues pa
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Gentry, Amanda E. "Penalized mixed-effects ordinal response models for high-dimensional genomic data in twins and families." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5575.
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The Brisbane Longitudinal Twin Study (BLTS) was being conducted in Australia and was funded by the US National Institute on Drug Abuse (NIDA). Adolescent twins were sampled as a part of this study and surveyed about their substance use as part of the Pathways to Cannabis Use, Abuse and Dependence project. The methods developed in this dissertation were designed for the purpose of analyzing a subset of the Pathways data that includes demographics, cannabis use metrics, personality measures, and imputed genotypes (SNPs) for 493 complete twin pairs (986 subjects.) The primary goal was to determine what combination of SNPs and additional covariates may predict cannabis use, measured on an ordinal scale as: “never tried,” “used moderately,” or “used frequently”. To conduct this analysis, we extended the ordinal Generalized Monotone Incremental Forward Stagewise (GMIFS) method for mixed models. This extension includes allowance for a unpenalized set of covariates to be coerced into the model as well as flexibility for user-specified correlation patterns between twins in a family. The proposed methods are applicable to high-dimensional (genomic or otherwise) data with ordinal response and specific, known covariance structure within clusters.
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Kidney, Darren. "Random coeffcient models for complex longitudinal data." Thesis, University of St Andrews, 2014. http://hdl.handle.net/10023/6386.
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Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data. Biased inference can occur in linear mixed-effects modelling if subjects are drawn from a number of unknown sub-populations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a two-step approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially non-monotonic variance and correlation functions. Spatially explicit capture-recapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multi-occasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radio-tagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animal-level covariates.
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Forster, Jeri E. "Varying-coefficient models for longitudinal data : piecewise-continuous, flexible, mixed-effects models and methods for analyzing data with nonignorable dropout /." Connect to full text via ProQuest. Limited to UCD Anschutz Medical Campus, 2006.
Find full textAbstract:
Thesis (Ph.D. in Biostatistics) -- University of Colorado at Denver and Health Sciences Center, 2006.Typescript. Includes bibliographical references (leaves 72-75). Free to UCD Anschutz Medical Campus. Online version available via ProQuest Digital Dissertations;
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Zhang, Hanze. "Bayesian inference on quantile regression-based mixed-effects joint models for longitudinal-survival data from AIDS studies." Scholar Commons, 2017. https://scholarcommons.usf.edu/etd/7456.
Full textAbstract:
In HIV/AIDS studies, viral load (the number of copies of HIV-1 RNA) and CD4 cell counts are important biomarkers of the severity of viral infection, disease progression, and treatment evaluation. Recently, joint models, which have the capability on the bias reduction and estimates' efficiency improvement, have been developed to assess the longitudinal process, survival process, and the relationship between them simultaneously. However, the majority of the joint models are based on mean regression, which concentrates only on the mean effect of outcome variable conditional on certain covariates. In fact, in HIV/AIDS research, the mean effect may not always be of interest. Additionally, if obvious outliers or heavy tails exist, mean regression model may lead to non-robust results. Moreover, due to some data features, like left-censoring caused by the limit of detection (LOD), covariates with measurement errors and skewness, analysis of such complicated longitudinal and survival data still poses many challenges. Ignoring these data features may result in biased inference.
Compared to the mean regression model, quantile regression (QR) model belongs to a robust model family, which can give a full scan of covariate effect at different quantiles of the response, and may be more robust to extreme values. Also, QR is more flexible, since the distribution of the outcome does not need to be strictly specified as certain parametric assumptions. These advantages make QR be receiving increasing attention in diverse areas. To the best of our knowledge, few study focuses on the QR-based joint models and applies to longitudinal-survival data with multiple features.
Thus, in this dissertation research, we firstly developed three QR-based joint models via Bayesian inferential approach, including: (i) QR-based nonlinear mixed-effects joint models for longitudinal-survival data with multiple features; (ii) QR-based partially linear mixed-effects joint models for longitudinal data with multiple features; (iii) QR-based partially linear mixed-effects joint models for longitudinal-survival data with multiple features. The proposed joint models are applied to analyze the Multicenter AIDS Cohort Study (MACS) data. Simulation studies are also implemented to assess the performance of the proposed methods under different scenarios. Although this is a biostatistical methodology study, some interesting clinical findings are also discovered.
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Yan, Huan. "Statistical adjustment, calibration, and uncertainty quantification of complex computer models." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/52290.
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This thesis consists of three chapters on the statistical adjustment, calibration, and uncertainty quantification of complex computer models with applications in engineering. The first chapter systematically develops an engineering-driven statistical adjustment and calibration framework, the second chapter deals with the calibration of potassium current model in a cardiac cell, and the third chapter develops an emulator-based approach for propagating input parameter uncertainty in a solid end milling process.
Engineering model development involves several simplifying assumptions for the purpose of mathematical tractability which are often not realistic in practice. This leads to discrepancies in the model predictions. A commonly used statistical approach to overcome this problem is to build a statistical model for the discrepancies between the engineering model and observed data. In contrast, an engineering approach would be to find the causes of discrepancy and fix the engineering model using first principles. However, the engineering approach is time consuming, whereas the statistical approach is fast. The drawback of the statistical approach is that it treats the engineering model as a black box and therefore, the statistically adjusted models lack physical interpretability. In the first chapter, we propose a new framework for model calibration and statistical adjustment. It tries to open up the black box using simple main effects analysis and graphical plots and introduces statistical models inside the engineering model. This approach leads to simpler adjustment models that are physically more interpretable. The approach is illustrated using a model for predicting the cutting forces in a laser-assisted mechanical micromachining process and a model for predicting the temperature of outlet air in a fluidized-bed process.
The second chapter studies the calibration of a computer model of potassium currents in a cardiac cell. The computer model is expensive to evaluate and contains twenty-four unknown parameters, which makes the calibration challenging for the traditional methods using kriging. Another difficulty with this problem is the presence of large cell-to-cell variation, which is modeled through random effects. We propose physics-driven strategies for the approximation of the computer model and an efficient method for the identification and estimation of parameters in this high-dimensional nonlinear mixed-effects statistical model.
Traditional sampling-based approaches to uncertainty quantification can be slow if the computer model is computationally expensive. In such cases, an easy-to-evaluate emulator can be used to replace the computer model to improve the computational efficiency. However, the traditional technique using kriging is found to perform poorly for the solid end milling process. In chapter three, we develop a new emulator, in which a base function is used to capture the general trend of the output. We propose optimal experimental design strategies for fitting the emulator. We call our proposed emulator local base emulator. Using the solid end milling example, we show that the local base emulator is an efficient and accurate technique for uncertainty quantification and has advantages over the other traditional tools.
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Ospina, Arango Juan David. "Predictive models for side effects following radiotherapy for prostate cancer." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S046/document.
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La radiothérapie externe (EBRT en anglais pour External Beam Radiotherapy) est l'un des traitements référence du cancer de prostate. Les objectifs de la radiothérapie sont, premièrement, de délivrer une haute dose de radiations dans la cible tumorale (prostate et vésicules séminales) afin d'assurer un contrôle local de la maladie et, deuxièmement, d'épargner les organes à risque voisins (principalement le rectum et la vessie) afin de limiter les effets secondaires. Des modèles de probabilité de complication des tissus sains (NTCP en anglais pour Normal Tissue Complication Probability) sont nécessaires pour estimer sur les risques de présenter des effets secondaires au traitement. Dans le contexte de la radiothérapie externe, les objectifs de cette thèse étaient d'identifier des paramètres prédictifs de complications rectales et vésicales secondaires au traitement; de développer de nouveaux modèles NTCP permettant l'intégration de paramètres dosimétriques et de paramètres propres aux patients; de comparer les capacités prédictives de ces nouveaux modèles à celles des modèles classiques et de développer de nouvelles méthodologies d'identification de motifs de dose corrélés à l'apparition de complications. Une importante base de données de patients traités par radiothérapie conformationnelle, construite à partir de plusieurs études cliniques prospectives françaises, a été utilisée pour ces travaux. Dans un premier temps, la fréquence des symptômes gastro-Intestinaux et génito-Urinaires a été décrite par une estimation non paramétrique de Kaplan-Meier. Des prédicteurs de complications gastro-Intestinales et génito-Urinaires ont été identifiés via une autre approche classique : la régression logistique. Les modèles de régression logistique ont ensuite été utilisés dans la construction de nomogrammes, outils graphiques permettant aux cliniciens d'évaluer rapidement le risque de complication associé à un traitement et d'informer les patients. Nous avons proposé l'utilisation de la méthode d'apprentissage de machine des forêts aléatoires (RF en anglais pour Random Forests) pour estimer le risque de complications. Les performances de ce modèle incluant des paramètres cliniques et patients, surpassent celles des modèle NTCP de Lyman-Kutcher-Burman (LKB) et de la régression logistique. Enfin, la dose 3D a été étudiée. Une méthode de décomposition en valeurs populationnelles (PVD en anglais pour Population Value Decomposition) en 2D a été généralisée au cas tensoriel et appliquée à l'analyse d'image 3D. L'application de cette méthode à une analyse de population a été menée afin d'extraire un motif de dose corrélée à l'apparition de complication après EBRT. Nous avons également développé un modèle non paramétrique d'effets mixtes spatio-Temporels pour l'analyse de population d'images tridimensionnelles afin d'identifier une région anatomique dans laquelle la dose pourrait être corrélée à l'apparition d'effets secondairesExternal beam radiotherapy (EBRT) is one of the cornerstones of prostate cancer treatment. The objectives of radiotherapy are, firstly, to deliver a high dose of radiation to the tumor (prostate and seminal vesicles) in order to achieve a maximal local control and, secondly, to spare the neighboring organs (mainly the rectum and the bladder) to avoid normal tissue complications. Normal tissue complication probability (NTCP) models are then needed to assess the feasibility of the treatment and inform the patient about the risk of side effects, to derive dose-Volume constraints and to compare different treatments. In the context of EBRT, the objectives of this thesis were to find predictors of bladder and rectal complications following treatment; to develop new NTCP models that allow for the integration of both dosimetric and patient parameters; to compare the predictive capabilities of these new models to the classic NTCP models and to develop new methodologies to identify dose patterns correlated to normal complications following EBRT for prostate cancer treatment. A large cohort of patient treated by conformal EBRT for prostate caner under several prospective French clinical trials was used for the study. In a first step, the incidence of the main genitourinary and gastrointestinal symptoms have been described. With another classical approach, namely logistic regression, some predictors of genitourinary and gastrointestinal complications were identified. The logistic regression models were then graphically represented to obtain nomograms, a graphical tool that enables clinicians to rapidly assess the complication risks associated with a treatment and to inform patients. This information can be used by patients and clinicians to select a treatment among several options (e.g. EBRT or radical prostatectomy). In a second step, we proposed the use of random forest, a machine-Learning technique, to predict the risk of complications following EBRT for prostate cancer. The superiority of the random forest NTCP, assessed by the area under the curve (AUC) of the receiving operative characteristic (ROC) curve, was established. In a third step, the 3D dose distribution was studied. A 2D population value decomposition (PVD) technique was extended to a tensorial framework to be applied on 3D volume image analysis. Using this tensorial PVD, a population analysis was carried out to find a pattern of dose possibly correlated to a normal tissue complication following EBRT. Also in the context of 3D image population analysis, a spatio-Temporal nonparametric mixed-Effects model was developed. This model was applied to find an anatomical region where the dose could be correlated to a normal tissue complication following EBRT
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Flask, Thomas V. "An Application of Multi-Level Bayesian Negative Binomial Models with Mixed Effects on Motorcycle Crashes in Ohio." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1333046055.
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Johansson, Åsa M. "Methodology for Handling Missing Data in Nonlinear Mixed Effects Modelling." Doctoral thesis, Uppsala universitet, Institutionen för farmaceutisk biovetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-224098.
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To obtain a better understanding of the pharmacokinetic and/or pharmacodynamic characteristics of an investigated treatment, clinical data is often analysed with nonlinear mixed effects modelling. The developed models can be used to design future clinical trials or to guide individualised drug treatment. Missing data is a frequently encountered problem in analyses of clinical data, and to not venture the predictability of the developed model, it is of great importance that the method chosen to handle the missing data is adequate for its purpose. The overall aim of this thesis was to develop methods for handling missing data in the context of nonlinear mixed effects models and to compare strategies for handling missing data in order to provide guidance for efficient handling and consequences of inappropriate handling of missing data. In accordance with missing data theory, all missing data can be divided into three categories; missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). When data are MCAR, the underlying missing data mechanism does not depend on any observed or unobserved data; when data are MAR, the underlying missing data mechanism depends on observed data but not on unobserved data; when data are MNAR, the underlying missing data mechanism depends on the unobserved data itself. Strategies and methods for handling missing observation data and missing covariate data were evaluated. These evaluations showed that the most frequently used estimation algorithm in nonlinear mixed effects modelling (first-order conditional estimation), resulted in biased parameter estimates independent on missing data mechanism. However, expectation maximization (EM) algorithms (e.g. importance sampling) resulted in unbiased and precise parameter estimates as long as data were MCAR or MAR. When the observation data are MNAR, a proper method for handling the missing data has to be applied to obtain unbiased and precise parameter estimates, independent on estimation algorithm. The evaluation of different methods for handling missing covariate data showed that a correctly implemented multiple imputations method and full maximum likelihood modelling methods resulted in unbiased and precise parameter estimates when covariate data were MCAR or MAR. When the covariate data were MNAR, the only method resulting in unbiased and precise parameter estimates was a full maximum likelihood modelling method where an extra parameter was estimated, correcting for the unknown missing data mechanism's dependence on the missing data. This thesis presents new insight to the dynamics of missing data in nonlinear mixed effects modelling. Strategies for handling different types of missing data have been developed and compared in order to provide guidance for efficient handling and consequences of inappropriate handling of missing data.
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Kliegl, Reinhold, Ping Wei, Michael Dambacher, Ming Yan, and Xiaolin Zhou. "Experimental effects and individual differences in linear mixed models: Estimating the relationship between spatial, object, and attraction effects in visual attention." Universität Potsdam, 2011. http://opus.kobv.de/ubp/volltexte/2011/5685/.
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Linear mixed models (LMMs) provide a still underused methodological perspective on combining experimental and individual-differences research. Here we illustrate this approach with two-rectangle cueing in visual attention (Egly et al., 1994). We replicated previous experimental cue-validity effects relating to a spatial shift of attention within an object (spatial effect), to attention switch between objects (object effect), and to the attraction of attention toward the display centroid (attraction effect), also taking into account the design-inherent imbalance of valid and other trials. We simultaneously estimated variance/covariance components of subject-related random effects for these spatial, object, and attraction effects in addition to their mean reaction times (RTs). The spatial effect showed a strong positive correlation with mean RT and a strong negative correlation with the attraction effect. The analysis of individual differences suggests that slow subjects engage attention more strongly at the cued location than fast subjects. We compare this joint LMM analysis of experimental effects and associated subject-related variances and correlations with two frequently used alternative statistical procedures
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Charpentier, Bernadette. "The Role of Colony Size in the Resistance and Tolerance of Scleractinian Corals to Bleaching Caused by Thermal Stress." Thèse, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/30662.
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In 2005 and 2010, high sea surface temperatures caused widespread coral bleaching on Jamaica’s north coast reefs. Three shallow (9m) reef sites were surveyed during each event to quantify the prevalence and intensity of coral bleaching. In October 2005, 29-57% of the colonies surveyed were bleached. By April 2006, 10% of the corals remained pale/partially bleached. Similarly, in October 2010, 23-51% of corals surveyed at the same sites were bleached. By April 2011, 12% of the colonies remained pale/partially bleached. Follow-up surveys revealed low coral mortality following both events, with an overall mean of 4% partial colony mortality across all species and sites observed in April 2006, and 2% in April 2011. Mixed effects models were used to quantify the relationship between colony size and (a) bleaching intensity, and (b) bleaching related mortality among coral species. The bleaching intensity model explained 51% of the variance in the bleaching response observed during the two events. Of this 51%, fixed effects accounted for ~26% of the variance, 17% of which was attributed to species-specific susceptibility to bleaching , 5% to colony size, <1% colony morphology and 4% to the difference in bleaching intensity between the two events. The random factor (site) accounted for the remaining ~25% of the variance. The mortality model explained 16% of the variance in post bleaching mortality with fixed effects, including colony size, morphology and species explaining ~11% of the variance, and the random effect (site) explaining 5%. On average, there was a twofold difference in bleaching intensity between the smallest and the largest size classes. Modelling the relationship between colony level characteristics and site-specific environmental factors on coral species’ susceptibility to thermal stress can shed light on community level responses to future disturbances.
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Cohen, Rachel. "Estimating the above-ground biomass of mangrove forests in Kenya." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/9956.
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Robust estimates of forest above-ground biomass (AGB) are needed in order to constrain the uncertainty in regional and global carbon budgets, predictions of global climate change and remote sensing efforts to monitor large scale changes in forest cover and biomass. Estimates of AGB and their associated uncertainty are also essential for international forest-based climate change mitigation strategies such as REDD+. Mangrove forests are widely recognised as globally important carbon stores. Continuing high rates of global mangrove deforestation represent a loss of future carbon sequestration potential and could result in significant release into the atmosphere of the carbon currently being stored within mangroves. The main aims of this thesis are 1) to provide information on the current AGB stocks of mangrove forests in Kenya at spatial scales relevant for climate change research, forest management and REDD+ and 2) to evaluate and constrain the uncertainty associated with these AGB estimates. This thesis adopted both a ground-based statistical approach and a remote sensing based approach to estimating mangrove AGB in Kenya. Allometric equations were developed for Kenyan mangroves using mixed-effects regression analysis and uncertainties were fully propagated (using a Monte Carlo based approach) to estimates of AGB at all spatial scales (tree, plot, region and landscape). In this study, species and site effects accounted for a large proportion (41%) of the total variability in mangrove AGB. The generic biomass equation produced for Kenyan mangroves has the potential for broad application as it can be used to estimate the AGB of new trees where there is no pre-existing knowledge of the specific species-site allometric relationship. The 95% prediction intervals for landscape scale estimates of total AGB suggest that between 5.4 and 7.2 megatonnes (Mt) of AGB is currently held in Kenyan mangrove forests. An in-depth evaluation of the relative contribution of various components of uncertainty (measurement, parameter and residual uncertainty) to the magnitude of the total uncertainty of AGB estimates was carried out. This evaluation was undertaken using both the mixed-effects regression model and a standard ordinary least squares (OLS) regression model. The exclusion of measurement uncertainty during the biomass estimation process had negligible impact on the magnitude of the uncertainty regardless of spatial scale or tree size. Excluding the uncertainty due to species and site effects (from the mixed-effects model) consistently resulted in a large reduction (~ 70%) in the overall uncertainty. Estimates of the uncertainty produced by the OLS model were unrealistically low which is illustrative of the general need to account for group effects in biomass regression models. L-band Synthetic Aperture Radar (SAR) was used to estimate the AGB of Kenyan mangroves. There was an observable relationship (R2 = 0.45) between L-band HH and AGB with HH backscatter found to decrease as a function of increasing AGB. There was no significant relationship found between L-band HV and AGB. The negative relationship between HH and AGB in this study can possibly be attributed to enhanced backscatter at lower AGB due to strong double-bounce and direct surface scattering from short stature/open forests and attenuation of the SAR signal at higher AGB. The SAR-derived estimate of total AGB for Kenyan mangroves was 5.32 Mt ± 18.6%. However, due to the unexpected nature of the HH-AGB relationship found in this study the SAR-derived estimates of mangrove AGB in this study should be considered with caution.
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Policastro, Catherine. "The Effects of Ecological Context and Individual Characteristics on Stereotyped Displays in Male Anolis carolinensis." ScholarWorks@UNO, 2013. http://scholarworks.uno.edu/td/1757.
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Displays are ubiquitous throughout the animal kingdom. While many have been thoroughly documented, the factors affecting the expression of such displays are still not fully understood. We tested the hypotheses that display production would be affected by ecological context (i.e. the identity of the receiver) and intrinsic qualities of the signaler (i.e. heavyweight and lightweight size class) in the green anole lizard, Anolis carolinensis. Our results supported these predictions and show that a) ecological context, specifically displaying to conspecifics, has the greatest impact on display production; b) size class influenced display rate with heavyweight males displaying more to green females and lightweight males displaying more to green males in similar frequency between the two size classes to their respective target stimuli. Furthermore, our results provide empirical support for differential use of the three major display types (A, B and C displays), and uncover unexpected complexity in green anole display production.
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Robertson, Rebecca. "Examining the Effects of Mixed-Models and Self-Observation on Motor Skill Acquisition Within a Gymnastics Environment." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34241.
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Watching oneself on video (self-observation) compared to self-observation coupled with a skilled model video (mixed-models) was examined in a gymnastics environment to determine whether combining two model types would be better than just one. Twenty-one gymnasts learned one gymnastics skill with mixed-models and a second skill with self-observation across pre-test, three learning sessions, and post-test. Physical performance, scored by two evaluators, revealed a significant condition by session interaction (F(3,51) = 3.329, p = .027). At session 3 and post-test, scores obtained with mixed-models were significantly higher than those with self-observation. Cognitive representation of the skills was measured at pre-test and post-test via error detection and recognition tests, analyzed using signal detection. Participants had significantly higher response sensitivity scores with mixed-models (F(1,14) = 10.810, p = .005) compared to self-observation. The conclusion drawn is that it is better to incorporate self and skilled models in a gymnastics setting than self-observation alone.
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Savaþcý, Duygu. "Three studies on semi-mixed effects models." Doctoral thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-000D-F1E3-3.
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