Master of Science / Department of Statistics / Gary L. Gadbury / This report presents an analysis of data resulting from a lipidomics experiment. The experiment sought to determine the changes in the lipidome of big bluestem prairie grass when exposed to stressors. The two stressors were drought (versus a watered condition) and a rust infection (versus no infection), and were whole plot treatments arranged in a 2 by 2 factorial. A split plot treatment factor was the position on a sampled leaf (top half versus bottom half). In addition, samples were analyzed at different times, representing a blocking factor. A total of 110 samples were used and, for each sample, concentrations of 137 lipids were obtained. Many lipids were not detected for certain samples and, in some cases, a lipid was not detected in most samples. Thus, each lipid was analyzed separately using a modeling strategy that involved a combination of mixed effects linear models and a categorical analysis technique, with the latter used for certain lipids to determine if a pattern of observed zeros was associated with the treatment condition(s). In addition, p-values from tests of fixed effects in a mixed effect model were computed three different ways and compared. Results in general show that the drought condition has the greatest effect on the concentrations of certain lipids, followed by the effect of position on the leaf. Of least effect on lipid concentrations was the rust condition.

Following the pioneering work of Allenby and Ginter (1995) and Lenk et al.(1994); we propose in Section 2 a mixed effect model allowing for fixed and random effects as possible statistical solution to the problems mentioned above. Parameter estimation using a new, efficient variant of a Markov Chain Monte Carlo method will be discussed in Section 3 together with problems of model comparison techniques in the context of random effect models. Section 4 presents an application of the former to a brand-price trade-off study from the Austrian mineral water market. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

A modelagem de predição de altura comumente exige um amplo conjunto de dados para a etapa de construção e ajuste. Ainda que este tipo de conjunto de dados tenha uma estrutura hierárquica natural, organizada pelas diferentes fazendas, talhões, parcelas, e etc., os modelos de regressão clássicos não consideram a possível variação dos parâmetros, entre os diversos grupos hierárquicos. Os modelos de efeitos mistos, em compensação, podem suportar essa variação, assumindo alguns dos parâmetros dos modelos como sendo estocásticos, além de mostrarem potencial com a possibilidade de diminuição de amostras. Esta técnica permite que a variação interindividual seja explicada considerando parâmetros de efeitos fixos (comuns à população) e parâmetros de efeitos aleatórios (específicos para cada indivíduo). Logo, é natural esperar que em povoamentos florestais com alta variação entre indivíduos, o modelo de efeito misto tenha desempenho superior ao modelo de efeito fixo. Por esta razão, os plantios de Tectona grandis L.f. podem ser considerados como uma população interessante para a modelagem de efeitos aleatórios, uma vez que tal espécie apresenta heterogeneidade de crescimento, sensibilidade à fertilidade e acidez do solo, e a maioria dos seus plantios estabelecidos no Brasil são seminais. Desta maneira este trabalho verifica o ajuste de modelos de efeitos mistos aplicados aos dados de altura total em plantios comerciais de Tectona grandis L.f, localizados no estado do Mato Grosso, com o objetivo na redução do número de amostras quando comparado ao modelo de efeitos fixos. Após a seleção do modelo linear de efeito fixo mais apropriado, testou-se quais dos coeficientes tem efeito aleatório nos diferentes agrupamentos dos dados. Em seguida, selecionou-se o grupo onde o desempenho do modelo de efeito misto em termos de ajuste e predição foi o melhor possível. Por fim, foi verificado a capacidade preditiva dos modelos ajustados por meio de processos de simulação e validação cruzada. Os resultados mostraram que o modelo misto calibrado fornece predições mais confiáveis do que a parte fixa. Este benefício ocorre mesmo ao longo das gradativas diminuições do número de árvores disponíveis para ajuste dentro conjunto de dados teste separados para a calibração do modelo misto. É possível concluir que o modelo calibrado ajustado por talhão, ao invés da parcela, propicia pouca perda de precisão. / Height prediction modeling commonly requires a broad set of data for the construction and adjustment step. Although this type of data set has a natural hierarchical structure, organized by the different farms, plots, plots, etc., the classical regression models do not consider the possible variation of the parameters among the hierarchical groups. The mixed effects models, in compensation, can support this variation, assuming some of the parameters of the models as being stochastic, besides showing potential with the possibility of sample reduction. This technique allows the interindividual variation to be explained considering parameters of fixed effects (common to the population) and parameters of random effects (specific for each individual). Therefore, it is natural to expect that in forest stands with high variation among individuals, the mixed effect model performs better than the fixed effect model. For this reason, the plantations of Tectona grandis L.f. can be considered as an interesting population for the modeling of random effects, since this species presents possible heterogeneity of growth since it is sensitive to the fertility and acidity of the soil, and most of its plantations established in Brazil are seminal. This work verifies the adjustment of mixed effects models applied to total height data in commercial plantations of Tectona grandis L.f, located in the state of Mato Grosso, with the objective of reducing the number of samples when compared to the fixed effects model. After selecting the most appropriate linear model of fixed effect, we tested which of the coefficients have random effect in the different groupings of the data. Then, we selected the group where the performance of the mixed effect model in terms of fit and prediction was the best possible. Finally, the predictive capacity of the adjusted models was verified through simulation and cross-validation processes. The results showed that the calibrated mixed model provides more reliable predictions than the fixed part. This benefit occurs even along the gradual decreases in the number of trees available to fit into separate set of test data for the calibration of the mixed model. It is possible to conclude that the calibrated model adjusted by stand, instead of the plot, provides little loss of precision.

A modelagem de predição de altura comumente exige um amplo conjunto de dados para a etapa de construção e ajuste. Ainda que este tipo de conjunto de dados tenha uma estrutura hierárquica natural, organizada pelas diferentes fazendas, talhões, parcelas, e etc., os modelos de regressão clássicos não consideram a possível variação dos parâmetros, entre os diversos grupos hierárquicos. Os modelos de efeitos mistos, em compensação, podem suportar essa variação, assumindo alguns dos parâmetros dos modelos como sendo estocásticos, além de mostrarem potencial com a possibilidade de diminuição de amostras. Esta técnica permite que a variação interindividual seja explicada considerando parâmetros de efeitos fixos (comuns à população) e parâmetros de efeitos aleatórios (específicos para cada indivíduo). Logo, é natural esperar que em povoamentos florestais com alta variação entre indivíduos, o modelo de efeito misto tenha desempenho superior ao modelo de efeito fixo. Por esta razão, os plantios de Tectona grandis L.f. podem ser considerados como uma população interessante para a modelagem de efeitos aleatórios, uma vez que tal espécie apresenta heterogeneidade de crescimento, sensibilidade à fertilidade e acidez do solo, e a maioria dos seus plantios estabelecidos no Brasil são seminais. Desta maneira este trabalho verifica o ajuste de modelos de efeitos mistos aplicados aos dados de altura total em plantios comerciais de Tectona grandis L.f, localizados no estado do Mato Grosso, com o objetivo na redução do número de amostras quando comparado ao modelo de efeitos fixos. Após a seleção do modelo linear de efeito fixo mais apropriado, testou-se quais dos coeficientes tem efeito aleatório nos diferentes agrupamentos dos dados. Em seguida, selecionou-se o grupo onde o desempenho do modelo de efeito misto em termos de ajuste e predição foi o melhor possível. Por fim, foi verificado a capacidade preditiva dos modelos ajustados por meio de processos de simulação e validação cruzada. Os resultados mostraram que o modelo misto calibrado fornece predições mais confiáveis do que a parte fixa. Este benefício ocorre mesmo ao longo das gradativas diminuições do número de árvores disponíveis para ajuste dentro conjunto de dados teste separados para a calibração do modelo misto. É possível concluir que o modelo calibrado ajustado por talhão, ao invés da parcela, propicia pouca perda de precisão. / Height prediction modeling commonly requires a broad set of data for the construction and adjustment step. Although this type of data set has a natural hierarchical structure, organized by the different farms, plots, plots, etc., the classical regression models do not consider the possible variation of the parameters among the hierarchical groups. The mixed effects models, in compensation, can support this variation, assuming some of the parameters of the models as being stochastic, besides showing potential with the possibility of sample reduction. This technique allows the interindividual variation to be explained considering parameters of fixed effects (common to the population) and parameters of random effects (specific for each individual). Therefore, it is natural to expect that in forest stands with high variation among individuals, the mixed effect model performs better than the fixed effect model. For this reason, the plantations of Tectona grandis L.f. can be considered as an interesting population for the modeling of random effects, since this species presents possible heterogeneity of growth since it is sensitive to the fertility and acidity of the soil, and most of its plantations established in Brazil are seminal. This work verifies the adjustment of mixed effects models applied to total height data in commercial plantations of Tectona grandis L.f, located in the state of Mato Grosso, with the objective of reducing the number of samples when compared to the fixed effects model. After selecting the most appropriate linear model of fixed effect, we tested which of the coefficients have random effect in the different groupings of the data. Then, we selected the group where the performance of the mixed effect model in terms of fit and prediction was the best possible. Finally, the predictive capacity of the adjusted models was verified through simulation and cross-validation processes. The results showed that the calibrated mixed model provides more reliable predictions than the fixed part. This benefit occurs even along the gradual decreases in the number of trees available to fit into separate set of test data for the calibration of the mixed model. It is possible to conclude that the calibrated model adjusted by stand, instead of the plot, provides little loss of precision.

Master of Science / Department of Statistics / Shie-Shien Yang / In fitting linear models, R[superscript]2 statistic has been wildly used as one of the measures to assess the goodness-of-fit and prediction power of the model. Unlike fixed linear models, at this time there is no single universally accepted measure for assessing goodness-of-fit and prediction power of a linear mixed model. In this report, we reviewed seven different approaches proposed to define a measure analogous to the usual R[superscript]2 statistic for assessing mixed models. One of seven statistics,Rc, has both conditional and marginal versions. Association mapping is an efficient way to link the genotype data with the phenotype diversity. When applying the R[superscript]2 statistic to the association mapping application, it can determine how well genetic polymorphisms, which are the explanatory variables in the mixed models, explain the phenotypic variation, which is the dependent variation. A linear mixed model method recently has been developed to control the spurious associations due to population structure and relative kinship among individuals of an association mapping. We assess seven definitions of R[superscript]2 statistic for the linear mixed model using data from two empirical association mapping samples: a sample with 277 diverse maize inbred lines and a global sample of 95 Arabidopsis thaliana accessions using the new method. R[superscript]2[subscript]LR statistic derived from the log-likelihood principle follows all the criterions of R[superscript]2 statistic and can be used to understand the overlap between population structure and relative kinship in controlling for sample relatedness. From our results,R[superscript]2[subscript]LR statistic is an appropriate R[superscript]2 statistic for comparing models with different fixed and random variables. Therefore, we recommend using RLR statistic for linear mixed models in association mapping.

This thesis was aimed to evaluate if sentiment related to stocks expressed on the subforum “Wallstreetbets” also reflects the traded volume in the stock market. For this purpose, a collection of comment data from posts filtered under the “Hot” section was issued between the 6th of April 2021 and the 20th of April 2021 on daily basis at 22.00 (GMT+2). The comments were preprocessed to filter out noise, and thereafter comments that contained mentions of stocks were analyzed using VADER, an algorithm for grading sentiment. In total sentiment regarding 13 different stocks were fitted into a mixed effect model with random slopes and intercepts. The results showed a positive correlation between sentiment expressed and the traded volume. This indicates that by studying the forum we can better understand how people invested in stocks make investment decisions, which potentially could lead to a competitive advantage over time.

The current study aims at investigating the mixed effect of family and neighborhood contexts on juveniles’ violence in South Korea. By addressing four different theoretical frames, the current study assumes that family and neighborhood are directly or indirectly influencing juveniles’ delinquency. The target of analysis is respondents of Korean Youth Panel Survey (KYPS)(N=2,248). By using Stata 14, the current study conducted multi-level regression. The current study suggests several meaningful findings as follow: 1) positive family (i.e. parental attachment and parental supervision) and neighborhood (i.e. collective efficacy) contexts directly reduce juvenile’s violence, 2) negative family aspects (i.e. family conflict and emotional strain by family) directly increase juvenile’s violence, 3) negative neighborhood contexts do not necessarily lead to juveniles’ violence, and 4) family contexts mediate the relationship between neighborhood environments and juveniles’ violence. Based on the finding, the current study explains South Korean cultural background, which contributed to the unique findings. In addition, policy implication is also addressed.

Spatiotemporal dynamics of resource availability can produce markedly different patterns of landscape utilization which necessitates studying habitat selection across biologically relevant extents. Feral pigs (Sus scrofa) are a prolifically expanding, generalist species and researchers have yet to understand fundamental drivers of space use in agricultural landscapes within the United States. To study multi-scale habitat selection patterns, I deployed 13 GPS collars on feral pigs within the Mississippi Alluvial Valley. I estimated resource selection using mixed-effects models to determine how feral pigs responded to changes in forage availability and incorporated those results with autocorrelated kernel density home range estimates. My results indicated season-specific habitat functional responses to changes in agricultural phenology and illustrated the interdependencies of landscape composition, hierarchical habitat selection, and habitat functional responses. These results indicate fundamental drivers of feral pig spatial distributions in an agricultural landscape which I used to predict habitat use to direct feral pig management.

No description available.

Aggregate models incorporate the variation between individual parameters of individualbased models to construct a population-based model. This thesis focuses on the comparison of two different methods for creating these population-based models. The first method, the individual parameter distribution technique (IPD) focuses on the similarities and variation of parameters in an individual-based model as calculated using individual data sets [4]. The second method we consider is the nonlinear mixed effect method (NLME), which is primarily used in modeling repeated measurement data. In the NLME approach, both the fixed effects and random effects of the parameter values are estimated in the model by assuming a normal distribution for the parameter values across individuals[2]. Both methods were implemented on a one-compartment pharmacokinetic concentration model. Using the variation in parameters estimated using the two different approaches, a population model was generated and then compared to the dynamics seen in the individual data sets. We compare three features of the concentration data to the simulated population models. The values for all three features were captured by both methods; however, the biggest difference observed is 2 that there is a longer tail in the distribution for the population model developed using NLME than observed in the dynamics in the original data.