The multilevel model (MLM) is easily parameterized to handle partially clustered data (see, for example, Baldwin, Bauer, Stice, & Rohde, 2011). The current study evaluated the performance of this model under various departures from underlying assumptions, including assumptions of normally distributed and homoscedastic Level 1 residuals. Two estimating models – one assuming homoscedasticity, the other allowing for the estimation of unique Level 1 variance components – were compared. Results from a Monte Carlo simulation suggest that the MLM for partially clustered data yields consistently unbiased parameter estimates, except for an underestimation of the Level 2 variance component under heteroscedastic generating conditions. However, this negative parameter bias desisted when the MLM allowed for Level 1 heteroscedasticity. Standard errors for variance component estimates at both levels were underestimated in the presence of nonnormally distributed Level 1 residuals. A discussion of results, as well as suggestions for future research, is provided. / text

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One area of forest biometrics that continues to progress is the development of statistical models as tools to describe tree taper. Taper models allow for the prediction of multiple tree level attributes including: diameter at any height, total tree stem volume, merchantable volume and height to any upper stem diameter from any lower stem height, individual log volumes, and subsequently total tree value. In this work, we generalize segmented regression taper models to include multiple segments and compare it to the traditional 3-Segment (2-Knot) models commonly observed in the forestry literature. We then focus on predicting a future realization of diameter given previously observed data. This is accomplished by comparing a segmented taper model under both the Generalized Algebraic Difference Approach (GADA) and Nonlinear Mixed Effects Models (NLMM) methodologies. Both the GADA and NLMM allow for predictions at the individual tree level of a future realization diameter given a differing number of observed height-diameter pairs. Finally, we explore the prediction and cost/benefit of total tree volume obtained from an integrated taper equation with the incorporation of tree specific random effects given differing observed height-diameter pairs.

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La classe des M-estimateurs engendre des estimateurs classiques d’un paramètre de localisation multidimensionnel tels que l’estimateur du maximum de vraisemblance, la moyenne empirique et la médiane spatiale. Huber (1964) introduit les M-estimateurs dans le cadre de l’étude des estimateurs robustes. Parmi la littérature dédiée à ces estimateurs, on trouve en particulier les ouvrages de Huber (1981) et de Hampel et al. (1986) sur le comportement asymptotique et la robustesse via le point de rupture et la fonction d’influence (voir Ruiz-Gazen (2012) pour une synthèse sur ces notions). Plus récemment, des résultats sur la convergence et la normalité asymptotique sont établis par Van der Vaart (2000) dans le cadre multidimensionnel. Nevalainen et al. (2006, 2007) étudient le cas particulier de la médiane spatiale pondérée et non-pondérée dans le cas clusterisé. Nous généralisons ces résultats aux M-estimateurs pondérés. Nous étudions leur convergence presque sûre, leur normalité asymptotique ainsi que leur robustesse dans le cas de données clusterisées. / M-estimators were first introduced by Huber (1964) as robust estimators of location and gave rise to a substantial literature. For results on their asymptotic behavior and robustness (using the study of the influence func- tion and the breakdown point), we may refer in particular to the books of Huber (1981) and Hampel et al. (1986). For more recent references, we may cite the work of Ruiz-Gazen (2012) with a nice introductory presentation of robust statistics, and the book of Van der Vaart (2000) for results, in the independent and identically distributed setting, concerning convergence and asymptotic normality in the multivariate setting considered throughout this paper. Most of references address the case where the data are independent and identically distributed. However clustered, and hierarchical, data frequently arise in applications. Typically the facility location problem is an important research topic in spatial data analysis for the geographic location of some economic activity. In this field, recent studies perform spatial modelling with clustered data (see e.g. Liao and Guo, 2008; Javadi and Shahrabi, 2014, and references therein). Concerning robust estimation, Nevalainen et al. (2006) study the spatial median for the multivariate one-sample location problem with clustered data. They show that the intra-cluster correlation has an impact on the asymptotic covariance matrix. The weighted spatial median, introduced in their pioneer paper of 2007, has a superior efficiency with respect to its unweighted version, especially when clusters’ sizes are heterogenous or in the presence of strong intra-cluster correlation. The class of weighted M-estimators (introduced in El Asri, 2013) may be viewed as a generalization of this work to a broad class of estimators: weights are assigned to the objective function that defines M-estimators. The aim is, for example, to adapt M-estimators to the clustered structures, to the size of clusters, or to clusters including extremal values, in order to increase their efficiency or robustness. In this thesis, we study the almost sure convergence of unweighted and weighted M-estimators and establish their asymptotic normality. Then, we provide consistent estimators of the asymptotic variance and derived, numerically, optimal weights that improve the relative efficiency to their unweighted versions. Finally, from a weight-based formulation of the breakdown point, we illustrate how these optimal weights lead to an altered breakdown point.

abstract: Researchers are often interested in estimating interactions in multilevel models, but many researchers assume that the same procedures and interpretations for interactions in single-level models apply to multilevel models. However, estimating interactions in multilevel models is much more complex than in single-level models. Because uncentered (RAS) or grand mean centered (CGM) level-1 predictors in two-level models contain two sources of variability (i.e., within-cluster variability and between-cluster variability), interactions involving RAS or CGM level-1 predictors also contain more than one source of variability. In this Master’s thesis, I use simulations to demonstrate that ignoring the four sources of variability in a total level-1 interaction effect can lead to erroneous conclusions. I explain how to parse a total level-1 interaction effect into four specific interaction effects, derive equivalencies between CGM and centering within context (CWC) for this model, and describe how the interpretations of the fixed effects change under CGM and CWC. Finally, I provide an empirical example using diary data collected from working adults with chronic pain. / Dissertation/Thesis / Masters Thesis Psychology 2015

Orientador: Víctor Hugo Lachos Dávila / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T02:34:17Z (GMT). No. of bitstreams: 1 GalvisSoto_DianaMilena_D.pdf: 1208980 bytes, checksum: edbc193912a2a800da4936526ed79fa3 (MD5) Previous issue date: 2014 / Resumo: Dados no intervalo (0,1) geralmente representam proporções, taxas ou índices. Porém, é possível observar situações práticas onde as proporções sejam zero e/ou um, representando ausência ou presença total da característica de interesse. Nesses casos, os modelos que analisam o efeito de covariáveis, tais como a regressão beta, beta retangular e simplex não são convenientes. Com o intuito de abordar este tipo de situações, considera-se como alternativa aumentar os valores zero e/ou um ao suporte das distribuições previamente mencionadas. Nesta tese, são propostos modelos de regressão de efeitos mistos para dados de proporções aumentados de zeros e uns, os quais permitem analisar o efeito de covariáveis sobre a probabilidade de observar ausência ou presença total da característica de interesse, assim como avaliar modelos com respostas correlacionadas. A estimação dos parâmetros de interesse pode ser via máxima verossimilhança ou métodos Monte Carlo via Cadeias de Markov (MCMC). Nesta tese, será adotado o enfoque Bayesiano, o qual apresenta algumas vantagens em relação à inferência clássica, pois não depende da teoria assintótica e os códigos são de fácil implementação, através de softwares como openBUGS e winBUGS. Baseados na distribuição marginal, é possível calcular critérios de seleção de modelos e medidas Bayesianas de divergência q, utilizadas para detectar observações discrepantes / Abstract: Continuous data in the unit interval (0,1) represent, generally, proportions, rates or indices. However, zeros and/or ones values can be observed, representing absence or total presence of a carachteristic of interest. In that case, regression models that analyze the effect of covariates such as beta, beta rectangular or simplex are not appropiate. In order to deal with this type of situations, an alternative is to add the zero and/or one values to the support of these models. In this thesis and based on these models, we propose the mixed regression models for proportional data augmented by zero and one, which allow analyze the effect of covariates into the probabilities of observing absence or total presence of the interest characteristic, besides of being possivel to deal with correlated responses. Estimation of parameters can follow via maximum likelihood or through MCMC algorithms. We follow the Bayesian approach, which presents some advantages when it is compared with classical inference because it allows to estimate the parameters even in small size sample. In addition, in this approach, the implementation is straightforward and can be done using software as openBUGS or winBUGS. Based on the marginal likelihood it is possible to calculate selection model criteria as well as q-divergence measures used to detect outlier observations / Doutorado / Estatistica / Doutora em Estatística

Family-centered care (FCC) focuses on considering the family in planning/implementing care and is associated with increased patient satisfaction. Little is known about factors that influence FCC. Using linear mixed modeling and Generalized Estimating Equations to analyze data from a cross-sectional survey of primary care practices in Ontario, this study sought to determine whether models of primary care service delivery differ in their provision of FCC and to identify characteristics of primary care practices associated with FCC. Patient-reported scores of FCC were high, but did not differ significantly among primary care models. After accounting for patient characteristics, practice characteristics were not significantly associated with patient-reported FCC. Provider-reported scores of FCC were significantly higher in Community Health Centres than in Family Health Networks. Higher numbers of nurse practitioners and clinical services on site were associated with higher FCC scores but scores decreased as the number of family physicians at a site increased.

Family-centered care (FCC) focuses on considering the family in planning/implementing care and is associated with increased patient satisfaction. Little is known about factors that influence FCC. Using linear mixed modeling and Generalized Estimating Equations to analyze data from a cross-sectional survey of primary care practices in Ontario, this study sought to determine whether models of primary care service delivery differ in their provision of FCC and to identify characteristics of primary care practices associated with FCC. Patient-reported scores of FCC were high, but did not differ significantly among primary care models. After accounting for patient characteristics, practice characteristics were not significantly associated with patient-reported FCC. Provider-reported scores of FCC were significantly higher in Community Health Centres than in Family Health Networks. Higher numbers of nurse practitioners and clinical services on site were associated with higher FCC scores but scores decreased as the number of family physicians at a site increased.

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