No description available.

Linear mixed models are frequently used to analyze data with random effects and/or repeated measures. A common approach to such analyses requires choosing a covariance structure. Information criteria, such as AIC and BIC, are often used by statisticians to help with this task. However, these criteria do not always point to the true covariance structure and therefore the wrong covariance structure is sometimes chosen. Once this step is complete, Wald statistics are used to test fixed effects. Degrees of freedom for these statistics are not known. However, there are approximation methods, such as Kenward and Roger (KR) and Satterthwaite (SW) that have been shown to work well in some situations. Schaalje et al. (2002) concluded that the KR method would perform at least as well as or better than the SW method in many cases assuming that the covariance structure was known. On the other hand, Keselman et al. (1999) concluded that the performance of the SW method when the covariance structure was selected using AIC was poor for negative pairings of treatment sizes and covariance matrices and small sample sizes. Our study used simulations to investigate Type I error rates in test of fixed effects using Wald statistics with the KR adjustment method, incorporating the selection of the covariance structure using AIC and BIC. Performance of the AIC and BIC criteria in selecting the true covariance structure was also studied. The MIXED procedure (SAS v. 9) was used to analyze each simulated data set. Type I error rates from the best AIC and BIC models were always higher than target values. However, Type I error rates obtained by using the BIC criterion were better than those obtained by using the AIC criterion. Type I error rates for the correct models were often adequate depending on the sample size and complexity of covariance structure. Performance of AIC and BIC was poor. This could be a consequence of small sample sizes and the high number of covariance structures these criteria had to choose from.

The linear mixed model is widely implemented in the analysis of longitudinal data. Inference techniques and information criteria are available and well-studied for goodness-of-fit within the linear mixed model setting. Predictive approaches such as R-squared, PRESS, and CCC are available for the linear mixed model but require more research (Edward, 2005). This project used simulation to investigate the performance of R-squared, PRESS, CCC, Pseudo F-test and information criterion for goodness-of-fit within the linear mixed model framework. Marginal and conditional approaches for these predictive statistics were studied under different variance-covariance structures. For compound symmetry structure, the success rates for all 17 statistics (marginal and conditional R-squared, PRESS, CCC, F test, AIC and BIC) were high. The study suggested using marginal rather than conditional residuals for PRESS, CCC and R-squared. It suggested using REML likelihood function which has the determinant term for AIC and BIC. For CCC, R-squared, and the information criterion, there was no difference for the various parameter number adjustments. For autoregressive order 1 plus random effect, the study suggested using conditional residuals for PRESS, marginal residuals for CCC and R-squared, and using REML function with the determinant term for AIC and BIC. Also there was no difference for the different parameter number adjustments. The F-test performed well for all covariance structures. The study also indicated that characteristics of the data, such as the covariance structure, parameter values, and sample size, can greatly impact performance of various statistics. No one criterion is consistently better than the others in terms of selection performance in the simulation study.

No description available.

Most research on confirmatory factor analysis using global fit indices (AIC, BIC, AICc, and CAIC) has been in the structural equation modeling framework. Little research has been done concerning application of these indices to item response models, especially within the framework of multidimensional Rasch analysis. The results of two simulations studies that investigated how sample size, between-dimension correlation, and test length affect the accuracy of these indices in model recovery using a multidimensional Rasch analysis are described in this dissertation. The first study analyzed dichotomous data, with model-to-data misfit as an additional independent variable. The second study analyzed polytomous data, with rating scale structure as an additional independent variable. The interaction effect between global fit index and between-dimension correlation had very large effect sizes in both studies. At higher values of between-dimension correlation, AIC indicated the correct two-dimension generating structure slightly more often than does the BIC or CAIC. The correlation by test length interaction had an odds ratio indicating practical importance in the polytomous study but not the dichotomous study. The combination of shorter tests and higher correlations resulted in a difficult-to-detect distinction being modeled with less statistical information. The correlation by index interaction in the dichotomous study had an odds ratio indicating practical importance. As expected, the results demonstrated that violations of the Rasch model assumptions are magnified at higher between-dimension correlations. Recommendations for practitioners working with highly correlated multidimensional data include creating moderate length (roughly 40 items) instruments, minimizing data-to-model misfit in the choice of model used for confirmatory factor analysis (MRCMLM or other MIRT models), and making decisions based on multiple global indices instead of depending on one index in particular. / Ph. D.

The detection of multiple outliers can be interpreted as a model selection problem. Models that can be selected are the null model, which indicates an outlier free set of observations, or a class of alternative models, which contain a set of additional bias parameters. A common way to select the right model is by using a statistical hypothesis test. In geodesy data snooping is most popular. Another approach arises from information theory. Here, the Akaike information criterion (AIC) is used to select an appropriate model for a given set of observations. The AIC is based on the Kullback-Leibler divergence, which describes the discrepancy between the model candidates. Both approaches are discussed and applied to test problems: the fitting of a straight line and a geodetic network. Some relationships between data snooping and information criteria are discussed. When compared, it turns out that the information criteria approach is more simple and elegant. Along with AIC there are many alternative information criteria for selecting different outliers, and it is not clear which one is optimal.

Il a été démontré que l’hétérotachie, variation du taux de substitutions au cours du temps et entre les sites, est un phénomène fréquent au sein de données réelles. Échouer à modéliser l’hétérotachie peut potentiellement causer des artéfacts phylogénétiques. Actuellement, plusieurs modèles traitent l’hétérotachie : le modèle à mélange des longueurs de branche (MLB) ainsi que diverses formes du modèle covarion. Dans ce projet, notre but est de trouver un modèle qui prenne efficacement en compte les signaux hétérotaches présents dans les données, et ainsi améliorer l’inférence phylogénétique. Pour parvenir à nos fins, deux études ont été réalisées. Dans la première, nous comparons le modèle MLB avec le modèle covarion et le modèle homogène grâce aux test AIC et BIC, ainsi que par validation croisée. A partir de nos résultats, nous pouvons conclure que le modèle MLB n’est pas nécessaire pour les sites dont les longueurs de branche diffèrent sur l’ensemble de l’arbre, car, dans les données réelles, le signaux hétérotaches qui interfèrent avec l’inférence phylogénétique sont généralement concentrés dans une zone limitée de l’arbre. Dans la seconde étude, nous relaxons l’hypothèse que le modèle covarion est homogène entre les sites, et développons un modèle à mélanges basé sur un processus de Dirichlet. Afin d’évaluer différents modèles hétérogènes, nous définissons plusieurs tests de non-conformité par échantillonnage postérieur prédictif pour étudier divers aspects de l’évolution moléculaire à partir de cartographies stochastiques. Ces tests montrent que le modèle à mélanges covarion utilisé avec une loi gamma est capable de refléter adéquatement les variations de substitutions tant à l’intérieur d’un site qu’entre les sites. Notre recherche permet de décrire de façon détaillée l’hétérotachie dans des données réelles et donne des pistes à suivre pour de futurs modèles hétérotaches. Les tests de non conformité par échantillonnage postérieur prédictif fournissent des outils de diagnostic pour évaluer les modèles en détails. De plus, nos deux études révèlent la non spécificité des modèles hétérogènes et, en conséquence, la présence d’interactions entre différents modèles hétérogènes. Nos études suggèrent fortement que les données contiennent différents caractères hétérogènes qui devraient être pris en compte simultanément dans les analyses phylogénétiques. / Heterotachy, substitution rate variation across sites and time, has shown to be a frequent phenomenon in the real data. Failure to model heterotachy could potentially cause phylogenetic artefacts. Currently, there are several models to handle heterotachy, the mixture branch length model (MBL) and several variant forms of the covarion model. In this project, our objective is to find a model that efficiently handles heterotachous signals in the data, and thereby improves phylogenetic inference. In order to achieve our goal, two individual studies were conducted. In the first study, we make comparisons among the MBL, covarion and homotachous models using AIC, BIC and cross validation. Based on our results, we conclude that the MBL model, in which sites have different branch lengths along the entire tree, is an over-parameterized model. Real data indicate that the heterotachous signals which interfere with phylogenetic inference are generally limited to a small area of the tree. In the second study, we relax the assumption of the homogeneity of the covarion parameters over sites, and develop a mixture covarion model using a Dirichlet process. In order to evaluate different heterogeneous models, we design several posterior predictive discrepancy tests to study different aspects of molecular evolution using stochastic mappings. The posterior predictive discrepancy tests demonstrate that the covarion mixture +Γ model is able to adequately model the substitution variation within and among sites. Our research permits a detailed view of heterotachy in real datasets and gives directions for future heterotachous models. The posterior predictive discrepancy tests provide diagnostic tools to assess models in detail. Furthermore, both of our studies reveal the non-specificity of heterogeneous models. Our studies strongly suggest that different heterogeneous features in the data should be handled simultaneously.

Il a été démontré que l’hétérotachie, variation du taux de substitutions au cours du temps et entre les sites, est un phénomène fréquent au sein de données réelles. Échouer à modéliser l’hétérotachie peut potentiellement causer des artéfacts phylogénétiques. Actuellement, plusieurs modèles traitent l’hétérotachie : le modèle à mélange des longueurs de branche (MLB) ainsi que diverses formes du modèle covarion. Dans ce projet, notre but est de trouver un modèle qui prenne efficacement en compte les signaux hétérotaches présents dans les données, et ainsi améliorer l’inférence phylogénétique. Pour parvenir à nos fins, deux études ont été réalisées. Dans la première, nous comparons le modèle MLB avec le modèle covarion et le modèle homogène grâce aux test AIC et BIC, ainsi que par validation croisée. A partir de nos résultats, nous pouvons conclure que le modèle MLB n’est pas nécessaire pour les sites dont les longueurs de branche diffèrent sur l’ensemble de l’arbre, car, dans les données réelles, le signaux hétérotaches qui interfèrent avec l’inférence phylogénétique sont généralement concentrés dans une zone limitée de l’arbre. Dans la seconde étude, nous relaxons l’hypothèse que le modèle covarion est homogène entre les sites, et développons un modèle à mélanges basé sur un processus de Dirichlet. Afin d’évaluer différents modèles hétérogènes, nous définissons plusieurs tests de non-conformité par échantillonnage postérieur prédictif pour étudier divers aspects de l’évolution moléculaire à partir de cartographies stochastiques. Ces tests montrent que le modèle à mélanges covarion utilisé avec une loi gamma est capable de refléter adéquatement les variations de substitutions tant à l’intérieur d’un site qu’entre les sites. Notre recherche permet de décrire de façon détaillée l’hétérotachie dans des données réelles et donne des pistes à suivre pour de futurs modèles hétérotaches. Les tests de non conformité par échantillonnage postérieur prédictif fournissent des outils de diagnostic pour évaluer les modèles en détails. De plus, nos deux études révèlent la non spécificité des modèles hétérogènes et, en conséquence, la présence d’interactions entre différents modèles hétérogènes. Nos études suggèrent fortement que les données contiennent différents caractères hétérogènes qui devraient être pris en compte simultanément dans les analyses phylogénétiques. / Heterotachy, substitution rate variation across sites and time, has shown to be a frequent phenomenon in the real data. Failure to model heterotachy could potentially cause phylogenetic artefacts. Currently, there are several models to handle heterotachy, the mixture branch length model (MBL) and several variant forms of the covarion model. In this project, our objective is to find a model that efficiently handles heterotachous signals in the data, and thereby improves phylogenetic inference. In order to achieve our goal, two individual studies were conducted. In the first study, we make comparisons among the MBL, covarion and homotachous models using AIC, BIC and cross validation. Based on our results, we conclude that the MBL model, in which sites have different branch lengths along the entire tree, is an over-parameterized model. Real data indicate that the heterotachous signals which interfere with phylogenetic inference are generally limited to a small area of the tree. In the second study, we relax the assumption of the homogeneity of the covarion parameters over sites, and develop a mixture covarion model using a Dirichlet process. In order to evaluate different heterogeneous models, we design several posterior predictive discrepancy tests to study different aspects of molecular evolution using stochastic mappings. The posterior predictive discrepancy tests demonstrate that the covarion mixture +Γ model is able to adequately model the substitution variation within and among sites. Our research permits a detailed view of heterotachy in real datasets and gives directions for future heterotachous models. The posterior predictive discrepancy tests provide diagnostic tools to assess models in detail. Furthermore, both of our studies reveal the non-specificity of heterogeneous models. Our studies strongly suggest that different heterogeneous features in the data should be handled simultaneously.

The detection of multiple outliers can be interpreted as a model selection problem. Models that can be selected are the null model, which indicates an outlier free set of observations, or a class of alternative models, which contain a set of additional bias parameters. A common way to select the right model is by using a statistical hypothesis test. In geodesy data snooping is most popular. Another approach arises from information theory. Here, the Akaike information criterion (AIC) is used to select an appropriate model for a given set of observations. The AIC is based on the Kullback-Leibler divergence, which describes the discrepancy between the model candidates. Both approaches are discussed and applied to test problems: the fitting of a straight line and a geodetic network. Some relationships between data snooping and information criteria are discussed. When compared, it turns out that the information criteria approach is more simple and elegant. Along with AIC there are many alternative information criteria for selecting different outliers, and it is not clear which one is optimal.

Doctor of Philosophy / Department of Entomology / James F. Campbell / Thomas W. Phillips / Movement is a fundamental feature of animals that impacts processes across multiple scales in space and time. Due to the heterogeneous and fragmented nature of habitats that make up landscapes, movement is not expected to be random in all instances, and an increase in fitness is an expected consequence for those that can optimize movement to find valuable and scarce recourses. I studied the movement of Rhyzopertha dominica (Coleoptera: Bostrichidae), one of the most important pests of stored grain worldwide, within and between resource patches. At a fine spatial scale, I identified factors that contribute to overall and upward movement in the grain mass. Three-week-old insects tented to stay closer to the surface than one or two-week-old insects. Females tended to be more active and to explore more than males. I also found that males tended to stay closer to the surface than females and that might be related to the ability to attract females from outside the patch since there was no significant difference regarding female’s attraction within the grain patch. Interaction with feeding sites or other individuals of the same sex creates positive feedback and a more clumped spatial pattern of feeding and foraging behavior. On the other hand, interaction with individuals of different sex creates negative feedback and a more random or overdispersed pattern. At a broad spatial scale, I studied the long-term consequence of R. dominica movement on the development of population structure within the U.S. To evaluate population structure, I used reduced representation of the genome followed by direct sequencing of beetles collected from different locations across the U.S where wheat or rice is produced and stored. Ecoregions were more important in explaining structure of R. dominica populations than crop type. I also found significant isolation by distance; however, model selection primarily elected grain production and movement variables to explain population differentiation and diversity. Understanding animal movement is essential to establishing relationships between distribution and surrounding landscape, and this knowledge can improve conservation and management strategies.