This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

Model-based estimation techniques have been widely used in small area estimation. This thesis focuses on the Hierarchical Bayes (HB) estimation techniques in application to small area estimation for survey data. We will study the impact of applying spatial structure to area-specific effects and utilizing a specific generalized linear mixed model in comparison with a traditional Fay-Herriot estimation model. We will also analyze different loss functions with applications to a small area estimation problem and compare estimates obtained under these loss functions. Overall, for the case study under consideration, area-specific geographical effects will be shown to have a significant effect on estimates. As well, using a generalized linear mixed model will prove to be more advantageous than the usual Fay-Herriot model. We will also demonstrate the benefits of using a weighted balanced-type loss function for the purpose of balancing the precision of estimates with their closeness to the direct estimates.

Model-based estimation techniques have been widely used in small area estimation. This thesis focuses on the Hierarchical Bayes (HB) estimation techniques in application to small area estimation for survey data. We will study the impact of applying spatial structure to area-specific effects and utilizing a specific generalized linear mixed model in comparison with a traditional Fay-Herriot estimation model. We will also analyze different loss functions with applications to a small area estimation problem and compare estimates obtained under these loss functions. Overall, for the case study under consideration, area-specific geographical effects will be shown to have a significant effect on estimates. As well, using a generalized linear mixed model will prove to be more advantageous than the usual Fay-Herriot model. We will also demonstrate the benefits of using a weighted balanced-type loss function for the purpose of balancing the precision of estimates with their closeness to the direct estimates.

Submitted by (ana.araujo@ufrpe.br) on 2016-08-16T14:52:45Z No. of bitstreams: 1 Tadeu Rodrigues da Costa.pdf: 720363 bytes, checksum: 0d88c29d42226d845c07376db4760d92 (MD5) / Made available in DSpace on 2016-08-16T14:52:45Z (GMT). No. of bitstreams: 1 Tadeu Rodrigues da Costa.pdf: 720363 bytes, checksum: 0d88c29d42226d845c07376db4760d92 (MD5) Previous issue date: 2010-06-04 / Lactation curves graphically represent individual milk or dairy herd production during their lactation period and they carry an unquestionable importance in terms of understanding the behavior of that particular herd production, which is fundamental to take decisions over conditions of the herd. Among many Brazilian dairy breeds that exist nowadays, the Sindhi breed has a special role in milk production because of its adaptation to the hard semiarid climate, turning it into a feasible alternative for milk production in Brazil´s Northeast. Therefore, the deal of this work was to use a linear mixed model in a database of a Sindhi breed herd, in order to verify milk production and animals individual forecast of this herd. Furthermore, the analysis of the waste and the sensitivity to verify model adaptability were done. The main result was that mixed linear model was suitable to study the behavior of each animal and the prediction of milk production. / Curvas de lactação representam, de forma gráfica, a produção de leite individual ou de um rebanho durante seu período de lactação e carregam uma importância indiscutível no que tange o entendimento do comportamento da produção daquele determinado rebanho, sendo fundamental na tomada de decisões acerca das condições do rebanho. Dentre as muitas raças leiteiras existentes hoje no Brasil, a raça Sindi tem um papel especial na produção de leite por se adaptar à rigorosidade do clima semi-árido, tornando-se uma alternativa viável para a produção de leite no Nordeste.Nesse sentido, o objetivo desse trabalho foi o de aplicar um modelo linear misto em um banco de dados de um rebanho da raça Sindi, com o intuito de verificar a produção de leite e a previsão individual dos animais desse rebanho. Além disso, foi feita a análise de resíduos e sensibilidade para verificação da adequacidade do modelo. Como resultado principal, o modelo linear misto foi considerado adequado para estudar o comportamento individual de cada animal e a previsão da produção de leite.

The diploma thesis deals with the issue of speech rate. The theoretical part briefly describes the investigation of speech tempo. It defines the types of tempo examined in this study (articulation rate and modified speaking rate) and factors that influence the tempo of speech. The practical part of the thesis aims to ascertain whether speech rate on the stage has increased and whether it is influenced by the type of text (monologue, dialogue, monological dialogue). The material consists of four theatre productions (Lakomec from 1972 and 2004 and Naši furianti from 1979 and 2006). Therefore we do not investigate gradual changes within the given periods, but instead compare two pairs of productions of the same dramatic text, realized with a time interval of approximately 30 years. A linear mixed-effects model was used as the main method for statistical evaluation of results gathered by measuring the speech rate. The results show that neither articulation rate nor modified speaking rate changed significantly in the observed productions. Differences with some statistical significance were obtained for comparison of tempo in texts of differing type, specifically in texts of different line lengths. The results relate especially to articulation rate, lesser to modified speaking rate.

Introduction and objectives In Vietnam, the forest resources have been declining and degrading severely in recent years. The degradation has decreased the natural forest area, changed the forest structure seriously and reduced timber volume and biodiversity. From 1999 to 2005, the rich forest area has decreased 10.2%, whereas the poor secondary forest has increased dramatically by 20.7%. Forest structure plays an important role in forestry research. Understanding forest structure will unlock an understanding of the history, function and future of a forest ecosystem (Spies, 1998). The forest structure is an excellent basis for restoration measures. Therefore, this research is necessary to contribute to improving forest area and quality, reducing difficulties in forest management. The study also enhances the grasp of forest structure, structure changes after harvesting and fills serious gaps in knowledge. In addition, the research results will contribute to improving and rescuing the poor secondary forest and restoring it, approaching the old-growth forest in Vietnam. Material and methods The study was conducted in Kon Ka Kinh national park. The park is located in the Northeastern region of Gia Lai province, 50 km from Pleiku city center to the Northeast. The park is distributed over seven different communes in three districts: K’Bang, Mang Yang and Đăk Đoa. Data were collected from 10 plots of secondary forests (Type IIb) and 10 plots of primeval forests (Type IV). Stratified random sampling was applied to select plot locations. 1 ha plots were used to investigate gaps. 2000 m2 plots were used to measure overstorey trees such as diameter at breast height, total height, crown width and species names. 500 m2 subplots were used to record tree positions. For regeneration, 25 systematic 4 m2 subplots were established inside 1 ha plots. After data were collected in the field, data analyses were conducted by using R and Excel. Firstly, some stand information, such as density, volume and so on, was calculated, and then descriptive statistics were computed for diameter and height variables. Linear mixed effect models were applied to analyze the difference of diameter and height and to check the effect of random factor between the two forest types. Diameter and height frequency distributions were also generated and compared by using permutational analysis of variance (PERMANOVA). Non-linear regression models were analyzed for diameter and height variables. Similar analyses were implemented for gaps. Regarding spatial point patterns of overstorey trees, replicated point pattern analysis techniques were applied in this research. For biodiversity, some calculations were run such as richness and biodiversity indices, comparison of biodiversity indices by using linear mixed models and biodiversity differences between two forest types tested again by permutational analysis of variance. In terms of regeneration, some analyses were implemented such as: height frequency distribution generation, frequency difference testing, biodiversity indices for the regeneration and spatial distribution checking by using a nonrandomness index. Results and discussion After analyzing the data, some essential findings were obtained as follows: Hypothesis H1 “The overstorey structure of secondary forests is more homogeneous and uniform than old-growth forests” is accepted. In other words, the secondary forest density is about 1.8 times higher than the jungle. However, the volume is only 0.56 times as large. The average diameter and height of the secondary forest is smaller by 5.71 cm and 3.73 m than the old-growth forest, respectively. Linear mixed effect model results indicate that this difference is statistically different and the effect of the random factor (Section) is not important. Type IIb has many small trees and the diameter frequency distribution is quite homogeneous. The old-growth forest has more big trees. For both forest stages, the height frequency distribution is positively skewed. PERMANOVA results illustrate that the frequency distribution is statistically different between the two forest types. Regression functions are also more variant and diverse in the old-growth forest, because all standard deviations of the parameters are greater there. Gap analysis results indicate that the number of gaps in the young forest is slightly higher, while the average gap size is much smaller. The gap frequency distribution is statistically different between the two types. In terms of the spatial point pattern of overlayer trees, the G-test and the pair correlation function results show that trees distribute randomly in the secondary forest. In contrast, the spatial point patterns of trees are more regular and diverse in the old-growth forest. The spatial point pattern difference is not significant, and this is proved by a permutational t-test for pair correlation function (pcf). Envelope function results indicate that the variation of pcf in young forests is much lower than in the primary forests. Hypothesis H2 “The overstorey species biodiversity of the secondary forest is less than in the old-growth forest” is rejected. Results show that the number of species of the secondary forest is much greater than in the old-growth forest, especially richness. The richness of the secondary forest is 1.16 times higher. The Simpson and Shannon indices are slightly smaller in the secondary forest. The average Simpson index for both forest stages is 0.898 and 0.920, respectively. However, the difference is not significant. Species accumulation curves become relatively flatter on the right, meaning a reasonable number of plots have been observed. Estimated number of species from accumulation curves in two forest types are 105 and 95/ha. PERMANOVA results show that number of species and proportion of individuals in each species are significantly different between forest types. Hypothesis H3 “The number regenerating species of the secondary forest is less and they distribute more regularly, compared to the old-growth forest” is rejected. There are both similarities and differences between the two types. The regeneration density of the stage IIb is 22,930 seedlings/ha, greater than the old forest by 9,030 seedlings. The height frequency distribution shows a decreasing trend. Similar to overstorey, the richness of the secondary forest is 141 species, higher than the old-growth forest by 9 species. Biodiversity indices are not statistically different between two types. PERMANOVA results indicate that the number of species and the proportion of individuals for each species are also not significantly different from observed forest types. Nonrandomness index results show that the regeneration distributes regularly. Up to 95% of the plots reflect this distribution trend. Hypothesis H4 “Restoration measures (with and without human intervention) could be implemented in the regenerating forest” is accepted. The investigated results show that the secondary forest still has mother trees, and it has enough seedlings to restore. Therefore, restoration solutions with and without human intervention can be implemented. Firstly, forest protection should be applied. This measure is relevant to national park regulations in Vietnam. Rangers and other related organizations will be responsible for carrying out protection activities. These activities will protect forest resources from illegal logging, grazing and tourist activities. Environmental education and awareness-raising activities for indigenous people is also important. Another measure is additional and enrichment planting. It should focus on exclusive species of the overstorey in Type IIb or exclusive species of the primary forest. Selection of these species will lead to species biodiversity increase in the future. This also meets the purpose of the maximum biodiversity solution. Conclusion Forest resources play a very important role in human life as well as maintaining the sustainability of ecosystems. However, at present, they are under serious threat, particularly in Vietnam. Central Highland, Vietnam, where forest resources are still relatively good, is also threatened by illegal logging, lack of knowledge of people and so on. Therefore, it needs the hands of the people, especially foresters and researchers. Through research, scientists can provide the knowledge and understanding of the forest, including the structure and forest restoration. This study has obtained important findings. The secondary forest is more homogeneous and uniform, while the old-growth forest is very diverse. Biodiversity of the overstorey in the secondary forest is more than the primary. The number of regenerating species in the secondary forest is higher, but other indices are not statistically different between two types. The regeneration distribute regularly on the ground. The secondary forest still has mother trees and sufficient regeneration, so some restoration measures can be applied here. Findings of the study contribute to improve people’s understanding of the structure and the structural changes after harvesting in Kon Ka Kinh national park, Gia Lai. That is a key to have better understandings of the history and values of the forests. These findings and the proposed restoration measures address rescuing degraded forests in Central Highland in particular and Vietnam in general. And further, this is a promising basis for the management and sustainable use of forest resources in the future.:TABLE OF CONTENTS ACKNOWLEDGEMENTS I TABLE OF CONTENTS III LIST OF FIGURES VIII LIST OF TABLES XI LIST OF ABBREVIATIONS XII SUMMARY XIII CHAPTER I: INTRODUCTION 1 1.1. The decline of natural forest resources, orientation of difficulty and development in Vietnam 1 1.1.1. Decline of forest resources 1 1.1.2. Difficulties in forestry management 1 1.1.3. Management strategies 2 1.2. Forest structure role 3 1.3. Forest restoration in Vietnam 4 1.4. Importance of old-growth and secondary forests 4 1.5. Aims, scope and hypotheses 6 1.5.1. Aims 6 1.5.1.1. General objective 6 1.5.1.2. Specific objective 6 1.5.2. Scope 6 1.5.3. Hypotheses 6 CHAPTER II: LITERATURE REVIEW 8 2.1. Tropical forest structure analysis 8 2.1.1. History 8 2.1.1.1. Overstorey 8 2.1.1.2. Regeneration 12 2.1.2. Structural attributes of tropical forests 13 2.1.2.1. Overstorey 14 a. Analyzed attributes 14 b. Relevant attributes to this study 15 2.1.2.2. Regeneration 21 2.2. Secondary tropical forest restoration 22 2.2.1. Strategies for secondary forest restoration 23 2.2.1.1. Protection and natural recovery 24 2.2.1.2. Natural regeneration management 24 a. Growing conditions and yield of desirable regeneration improvement 24 b. Desirable regeneration assistance 25 2.2.1.3. Accelerated Natural Regeneration (ANR) 25 2.2.1.4. Enrichment planting 25 2.2.1.5. The framework species method 26 2.2.1.6. Maximum diversity planting method 26 CHAPTER III: MATERIAL 27 3.1. Natural conditions of the study area 27 3.1.1 Geographic location, boundaries and area of Kon Ka Kinh national park 27 3.1.2. Topography, geology and soil 28 3.1.2.1. Topography 28 3.1.2.2. Geology and soil 29 3.1.3. Climate and hydrology 30 3.1.3.1. Climate 30 3.1.3.2. Hydrology 31 3.2. Vegetation in Kon Ka Kinh national park 31 3.2.1. The area of land use types 31 3.2.2. Plant biodiversity 33 3.2.3. The flora and forest vegetation 33 3.2.3.1. Flora 33 3.2.3.2. Forest vegetation 34 3.2.3.3. History of forest exploitation in the park 35 3.3. Assessing the natural conditions and vegetation of the park 37 3.4. Population, ethnicity and labor 38 3.4.1. Population 38 3.4.2. Labor and ethnicity 39 3.4.3. Poverty status 40 3.5. Forest resources classification 40 3.5.1. The Loeschau’s classification system 40 3.5.2. The relationship between forest types with development phases 42 CHAPTER IV: METHODOLOGY 45 4.1. Plot establishment method 45 4.2. Data collection method 47 4.2.1. Data collection for overstorey stem maps 47 4.2.1.1. Tree data collection 47 4.2.1.2. Tree positions 50 4.2.1.3. Gap inventory 51 4.2.2. Data collection for regeneration 52 4.3. Data analysis method 55 4.3.1. Applied methods for the upper layer 55 4.3.1.1. Stand information 55 a. Calculation for each tree 55 b. Calculation for a stand 55 4.3.1.2. Descriptive statistics for height and diameter variables 56 a. Central tendency 56 b. Dispersion and variability 56 c. Measures of distribution shape 57 4.3.1.3. Linear mixed-effects analysis 59 a. Applications with this study and data arrangement 60 b. Homoscedasticity checking 61 c. Checking autocorrelation 63 d. Checking normal distribution of the residuals 66 e. Model selection and information summary 67 4.3.1.4. Frequency distribution 68 a. Generating frequency distributions 68 b. Frequency distribution difference testing 69 4.3.1.5. Diameter-height regression analysis 70 a. Used function forms 70 b. Theoretical calculations 71 c. Model selection 73 4.3.1.6. Gap analysis 74 a. Descriptive statistics for gaps 74 b. Calculating the gap area proportion for each forest type 74 c. Gap size frequency distribution 74 d. Gap size frequency distribution difference testing 75 4.3.1.7. Spatial point patterns of tree species 75 a. Applications 76 b. Tree density analysis 77 c. Testing for randomness 78 d. Comparing point pattern variation 83 e. Testing the difference between forest types 84 4.3.1.8. Overstorey tree species diversity analysis 85 a. Richness and species importance value index (SIVI) 85 b. Species diversity index 86 c. Species accumulation curve 88 d. Biodiversity index comparison 88 e. Tree species diversity comparison 89 4.3.2. Regenerating tree storey structure analysis 90 4.3.2.1. Frequency distribution of regeneration 90 4.3.2.2. Height frequency distribution difference testing 91 4.3.2.3. Biodiversity indices for regeneration 91 4.3.2.4. Biodiversity index comparison by using LMM 91 4.3.2.5. Regeneration species diversity comparison 91 4.3.2.6. Regeneration spatial distribution checking 91 a. Nonrandomness index 91 b. Nonrandomness index value comparison 92 CHAPTER V: RESULTS 93 5.1. Overstorey structure analysis results 93 5.1.1. Stand information 93 5.1.2. Descriptive statistics results 95 5.1.3. Linear mixed effect model results 97 5.1.3.1. Box plots for the diameter and height variables 97 5.1.3.2. Model analysis and adaptation 97 5.1.3.3. Model parameter estimation 100 5.1.4. Frequency distributions 101 5.1.4.1. Frequency distribution results for both types 101 5.1.4.2. Frequency distribution difference 107 5.1.5. Diameter-height regression results 107 5.1.5.1. Estimated parameters 107 5.1.5.2. Model selection 110 5.1.5.3. Regression charts 110 5.1.6. Gap analysis 116 5.1.6.1. Gap descriptive information 116 5.1.6.2. Gap area ratio 117 5.1.6.3. Gap size frequency distribution 117 5.1.6.4. Gap size frequency distribution difference testing results 120 5.1.7. Spatial distribution analysis 120 5.1.7.1. Density testing results 120 5.1.7.2. Randomness checking results 122 5.1.7.3. Variation difference between two types 123 5.1.7.4. Point pattern difference testing between two types 124 5.1.8. Overstorey species diversity analysis results 125 5.1.8.1. Richness, SIVI and biodiversity indices 125 5.1.8.2. Biodiversity index comparison by using LMM 127 5.1.8.3. Tree species diversity comparison 127 5.2. Regeneration storey structure analysis results 128 5.2.1. Height frequency distribution 128 5.2.2. Height frequency distribution difference testing 130 5.2.3. Biodiversity index for regeneration 131 5.2.4. Biodiversity index difference comparison 133 5.2.5. Regeneration species diversity comparison 133 5.2.6. Regeneration spatial distribution 134 5.2.6.1. Nonrandomness index results 134 5.2.6.2. Nonrandomness index value testing results 134 CHAPTER VI: DISCUSSION 135 6.1. Overstorey structure differentiation 135 6.1.1. Structure and spatial distribution difference 135 6.1.1.1. Stand information 135 6.1.1.2. Statistical descriptions for diameter and height 136 6.1.1.3. Diameter and height growth difference testing by linear mixed effect models 137 6.1.1.4. Frequency distribution dissimilarity 138 6.1.1.5. Diameter-height regression 139 6.1.1.6. Canopy gaps 140 6.1.1.7. Spatial distribution patterns 141 6.1.2. Biodiversity distinction of overstorey trees 143 6.2. Regeneration dissimilarity 145 6.2.1. Density and frequency distribution 145 6.2.2. Biodiversity indices 146 6.2.3. Spatial distribution of regeneration 147 6.3. Proposing restoration measures 147 6.4. Improved points in this research 150 CHAPTER VII: CONCLUSION AND RECOMMENDATION 152 7.1. Conclusion 152 7.2. Suggestions for further research 154 REFERENCES 156 APPENDIX 180

In this thesis, we set out to model the market risk exposure for 251 stocks in the S&P 500 index, during a ten-year period between 2011-04-30 and 2021-03-31. The study brings to light a model not often mentioned in the scientific literature focused on market risk estimation, the linear mixed model. The linear mixed model makes it possible to model a time-varying market risk, as well as adding structure to the idiosyncratic risk, which is often assumed to be a stationary process. The results show that the mixed model is able to produce more accurate estimates for the market risk, compared to the baseline, which is here defined as a CAPM model. The success of the mixed model, which we in the study will refer to as the ADAPT model (adaptive APT), most certainly lies in its ability to create a hierarchical regression model. This makes it possible to not just view the set of observations as a single population, but let us group the observations into different clusters and in such a way makes it possible to construct a time-varying exposure. In the last part of the thesis, we highlight possible improvements for future works, which could make the estimation even more accurate and also more efficient.

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This dissertation aims to develop statistical methodologies for estimating the effects of time-fixed and time-varying factors in recurrent events modeling context. The research is motivated by the traffic safety research question of evaluating the influence of crash on driving risk and driver behavior. The methodologies developed, however, are general and can be applied to other fields. Four alternative approaches based on various data settings are elaborated and applied to 100-Car Naturalistic Driving Study in the following Chapters. Chapter 1 provides a general introduction and background of each method, with a sketch of 100-Car Naturalistic Driving Study. In Chapter 2, I assessed the impact of crash on driving behavior by comparing the frequency of distraction events in per-defined windows. A count-based approach based on mixed-effect binomial regression models was used. In Chapter 3, I introduced intensity-based recurrent event models by treating number of Safety Critical Incidents and Near Crash over time as a counting process. Recurrent event models fit the natural generation scheme of the data in this study. Four semi-parametric models are explored: Andersen-Gill model, Andersen-Gill model with stratified baseline functions, frailty model, and frailty model with stratified baseline functions. I derived model estimation procedure and and conducted model comparison via simulation and application. The recurrent event models in Chapter 3 are all based on proportional assumption, where effects are constant. However, the change of effects over time is often of primary interest. In Chapter 4, I developed time-varying coefficient model using penalized B-spline function to approximate varying coefficients. Shared frailty terms was used to incorporate correlation within subjects. Inference and statistical test are also provided. Frailty representation was proposed to link time-varying coefficient model with regular frailty model. In Chapter 5, I further extended framework to accommodate multi-type recurrent events with time-varying coefficient. Two types of recurrent-event models were developed. These models incorporate correlation among intensity functions from different type of events by correlated frailty terms. Chapter 6 gives a general review on the contributions of this dissertation and discussion of future research directions. / Ph. D.

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.