In this work, we study the so-called combined models, generalized linear mixed models with extension to allow for overdispersion, in the context of genetics and breeding. Such flexible models accommodates cluster-induced correlation and overdispersion through two separate sets of random effects and contain as special cases the generalized linear mixed models (GLMM) on the one hand, and commonly known overdispersion models on the other. We use such models while obtaining heritability coefficients for non-Gaussian characters. Heritability is one of the many important concepts that are often quantified upon fitting a model to hierarchical data. It is often of importance in plant and animal breeding. Knowledge of this attribute is useful to quantify the magnitude of improvement in the population. For data where linear models can be used, this attribute is conveniently defined as a ratio of variance components. Matters are less simple for non-Gaussian outcomes. The focus is on time-to-event and count traits, where the Weibull-Gamma-Normal and Poisson-Gamma-Normal models are used. The resulting expressions are sufficiently simple and appealing, in particular in special cases, to be of practical value. The proposed methodologies are illustrated using data from animal and plant breeding. Furthermore, attention is given to the occurrence of negative estimates of variance components in the Poisson-Gamma-Normal model. The occurrence of negative variance components in linear mixed models (LMM) has received a certain amount of attention in the literature whereas almost no work has been done for GLMM. This phenomenon can be confusing at first sight because, by definition, variances themselves are non-negative quantities. However, this is a well understood phenomenon in the context of linear mixed modeling, where one will have to make a choice between a hierarchical and a marginal view. The variance components of the combined model for count outcomes are studied theoretically and the plant breeding study used as illustration underscores that this phenomenon can be common in applied research. We also call attention to the performance of different estimation methods, because not all available methods are capable of extending the parameter space of the variance components. Then, when there is a need for inference on such components and they are expected to be negative, the accuracy of the method is not the only characteristic to be considered. / Neste trabalho foram estudados os chamados modelos combinados, modelos lineares generalizados mistos com extensão para acomodar superdispersão, no contexto de genética e melhoramento. Esses modelos flexíveis acomodam correlação induzida por agrupamento e superdispersão por meio de dois conjuntos separados de efeitos aleatórios e contem como casos especiais os modelos lineares generalizados mistos (MLGM) e os modelos de superdispersão comumente conhecidos. Tais modelos são usados na obtenção do coeficiente de herdabilidade para caracteres não Gaussianos. Herdabilidade é um dos vários importantes conceitos que são frequentemente quantificados com o ajuste de um modelo a dados hierárquicos. Ela é usualmente importante no melhoramento vegetal e animal. Conhecer esse atributo é útil para quantificar a magnitude do ganho na população. Para dados em que modelos lineares podem ser usados, esse atributo é convenientemente definido como uma razão de componentes de variância. Os problemas são menos simples para respostas não Gaussianas. O foco aqui é em características do tipo tempo-até-evento e contagem, em que os modelosWeibull-Gama-Normal e Poisson-Gama-Normal são usados. As expressões resultantes são suficientemente simples e atrativas, em particular nos casos especiais, pelo valor prático. As metodologias propostas são ilustradas usando dados de melhoramento animal e vegetal. Além disso, a atenção é voltada à ocorrência de estimativas negativas de componentes de variância no modelo Poisson-Gama- Normal. A ocorrência de componentes de variância negativos em modelos lineares mistos (MLM) tem recebido certa atenção na literatura enquanto quase nenhum trabalho tem sido feito para MLGM. Esse fenômeno pode ser confuso a princípio porque, por definição, variâncias são quantidades não-negativas. Entretanto, este é um fenômeno bem compreendido no contexto de modelagem linear mista, em que a escolha deverá ser feita entre uma interpretação hierárquica ou marginal. Os componentes de variância do modelo combinado para respostas de contagem são estudados teoricamente e o estudo de melhoramento vegetal usado como ilustração confirma que esse fenômeno pode ser comum em pesquisas aplicadas. A atenção também é voltada ao desempenho de diferentes métodos de estimação, porque nem todos aqueles disponíveis são capazes de estender o espaço paramétrico dos componentes de variância. Então, quando há a necessidade de inferência de tais componentes e é esperado que eles sejam negativos, a acurácia do método de estimação não é a única característica a ser considerada.

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The purpose of this dissertation was to examine patterns of antenatal stressful life events (SLEs) experienced by women in the United States (U.S.) and their association with postpartum depression (PPD). It further explored the role of women's state-level socio-economic status (SES) on PPD; the racial/ethnic dispartites in SLE-PPD relationship; and the role of provider communication on perinatal depression. Data from 2009–11 Pregnancy Risk Assessment Monitoring System (PRAMS) and SES indicators published by the Institute of Women’s Policy Research (IWPR) were used. Latent class analysis (LCA) was performed to identify unobserved class membership based on antenatal SLEs. Multilevel generalized linear mixed models examined whether state-level SES moderated the antenatal SLE-PPD relationship. Of 116,595 respondents to the PRAMS 2009-11, the sample size for our analyses ranged from 78% to 99%. The majority (64%) of participants were in low-stress class. The illness/death related-stress class (13%) had a high prevalence of severe illness (77%) and death (63%) of a family member or someone very close to them, while those in the multiple-stress (22%) class endorsed most other SLEs. Eleven percent had PPD; women who experienced all types of stressors, had the highest odds (adjusted odds ratio [aOR]: 5.43; 95% confidence interval [CI]: 5.36, 5.51) of PPD. The odds of PPD decreased with increasing state-level social/economic autonomy index (aOR: 0.75; 95% CI: 0.64, 0.88), with significant cross-level interaction between stressors and state-level SES. Among non-Hispanic blacks and non-Hispanic whites, husband/partner not wanting the pregnancy (aOR: 1.47; 95% CI: 1.14, 1.90) and drug/drinking problems of someone close (aOR: 1.37; 95% CI: 1.21, 1.55) were respectively associated with PPD. Provider communication was protective. That 1 out of every 5 and 1 out of every 8 women were in the high- and emotional-stress classes suggests that SLEs are common among pregnant women. Our results suggest that screening for antenatal SLEs might help identify women at risk for PPD. The finding that the odds of PPD decrease with increasing social/economic autonomy, could have policy implications and motivate efforts to improve these indices. This study also indicates the benefits of antenatal health care provider communication on perinatal depression.

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