A partial envelope approach for modelling multivariate spatial‐temporal data

Association testing has been widely used to study the relationship between genetic variants and phenotypes. Most association testing methods are genotype-based, i.e. first estimate genotype and then regress phenotype on estimated genotype and other variables. Directly testing methods based on next generation sequencing (NGS) data without genotype calling have been proposed and shown advantage over genotype-based methods in the scenarios when genotype calling is not accurate. NGS data-based single-variant testing have been proposed including our previously proposed single-variant testing method, i.e. UNC combo method [1]. NGS data-based group testing methods for continuous phenotype have also been proposed by us using a linear model framework which can handle continuous responses [2]. In this paper, we extend our linear model-based framework to a generalized linear model-based framework so that the methods can handle other types of responses especially binary responses which is commonly-faced in association studies. We have conducted extensive simulation studies to evaluate the performance of different estimators and compare our estimators with their corresponding genotype-based methods. We found that all methods have Type I errors controlled, and our NGS data-based testing methods have better performance than their corresponding genotype-based methods in the literature for other types of responses including binary responses (logistic regression) and count responses (Poisson regression especially when sequencing depth is low. In conclusion, we have extended our previous linear model (LM) framework to a generalized linear model (GLM) framework and derived NGS data-based testing methods for a group of genetic variants. Compared with our previously proposed LM-based methods [2], the new GLM-based methods can handle more complex responses (for example, binary responses and count responses) in addition to continuous responses. Our methods have filled the literature gap and shown advantage over their corresponding genotype-based methods in the literature.

The hybrid linear and nonlinear modeling framework has been widely used as a promising method for time series forecasting. However, there have been very few, if any, large scale comparative studies for the hybrid linear and nonlinear framework for air passenger traffic forecasting. So, we hope this study would fill this gap. The linear models selected are autoregressive integrated moving average model (ARIMA ) and seasonal autoregressive integrated moving average model (SARIMA). As for the nonlinear models, support vector machines (SVMs) and multi-layer feed-forward neural networks (FNN) are selected. Specifically, we employ these models on the four monthly air passenger traffic series of American airlines. The results demonstrate that significant improvement can be achieved with hybrid linear and nonlinear framework, particularly, hybrid framework combined by SARIMA and SVM models performed best in terms of symmetric mean absolute percentage error (SMAPE), multiple comparisons with the best (MCB), and fraction best (FRAC-BEST).

The large-scale circulation anomalies associated with the 1988 drought and the 1993 floods are investigated with the National Centers for Environmental Prediction Reanalysis data and a linear stationary wave model. The transient vorticity and thermal forcings are explicitly calculated and the diabatic heating is derived as a residual in the thermodynamic energy equation. Using the April‐June (AMJ) data for 1988, and June‐August (JJA) data for 1993, the linear stationary wave model is able to reproduce the main features of the geopotential height anomaly for the two seasons when all forcings are included. This provides a basis for further investigation of stationary wave response to different forcing mechanisms using the linear model. Within the linear model framework, the linear model responses to different forcings are examined separately. The results indicate that the 1988 anomaly over the United States is a result of both the diabatic heating and the transient vorticity and thermal forcings. The large anticyclonic anomalies over the North Pacific and Canada are forced mainly by the diabatic heating. The 1993 anomaly, however, is dominated by the response to transient vorticity forcing. By further separating the linear model responses to regional diabatic heating anomalies in 1988, the results indicate that the western North Pacific heating is entirely responsible for the anticyclonic center over the North Pacific, which causes the northward shift and intensification of the Pacific jet stream. The eastern North Pacific heating/cooling couplet is the most important for maintaining the North American circulation

First, we formulate some questions posed by the procedure recently proposed by Borcard et al. (1992) and Borcard and Legendre (1994) to partition the ecological variation of a community into different portions related to spatial and environmental descriptors. Working separately on the two steps of this procedure - linear modelling and ordinations on modelled tables - allows us to propose different solutions to these questions. These solutions, which use little-known proper- ties of a linear regression model with two additive factors and no interaction, are also adapted to the case of mixed factors (qualitative and quantitative). These properties are presented in the framework of canonical correlation analysis. In particular, they allow us to propose an alternative to partial regression, which avoids confounding. A detailed illustration is presented. © Rapid Science 1998

Association testing has been widely used to study the relationship between phenotypes and genetic variants. Most testing methods are based on genotypes. To avoid genotype calling and directly test on next-generation sequencing (NGS) data, sequencing data-based methods have been proposed and shown advantages over genotype-based testing methods in scenarios where genotype calling is inaccurate. Most sequencing data-based testing methods are based on a single genetic marker. The objective of this paper is to extend the methods to allow testing for the association of a continuous response variable with a group of common variants or a group of rare variants without genotype calling. Our proposed methods are derived based on a standard linear model framework. We derive the joint significant test (JS) for a group of common genetic variables and the variable collapse test (VC) for a group of rare genetic variables. We have conducted extensive simulation studies to evaluate the performance of different estimators. According to our results, we found (1) all methods, including our proposed NGS data-based methods and genotype-based methods, can control the Type I error rate probability well; (2) our proposed NGS data-based methods can achieve better performance in terms of statistical power compared with their corresponding genotype-based methods in the literature; (3) when sequencing depth increases, the performance of all methods increases, and the difference between the performance of NGS data-based methods and corresponding genotype-based methods decreases. In conclusion, we have proposed NGS data-based methods that allow testing for the significance of a group of variants using a linear model framework and have shown the advantage of our NGS data-based methods over genotype-based methods in the literature.

교육평가는 집단 수준에서도 진단적 정보를 제공할 수 있다. 본 연구의 목적은 학교에서 사용할 수 있는 집단 수준 진단평가 모형을 일반화선형혼합모형의 틀에서 제시하고 그 모형을 이용한 진단 결과의 정확성을 확인하는 것이다. 그러한 목적을 달성하기 위해 먼저 연구 모형을 제시하고 분석 결과의 정확성을 확인하는 모의실험을 실시하였다. 모의실험의 조건은 문항 수, 인지요소의 수, 문항 당 인지요소의 비율 등이었다. 모의실험 분석 결과 인지요소의 효과 추정치에 대한 편파(bias)나 RMSE의 측면에서 볼 때, 어떤 조건에서도 편파는 발견되지 않았으며, RMSE는 문항 수가 증가할수록, 인지요소 수가 증가 할수록 낮아졌다. 다만 문항 당 인지요소의 비율은 중간 수준일 때 가장 낮은 RMSE를 보 였다. 이는 학교별 문항 난이도의 차이를 설명함에 있어 인지요소의 사용과 미사용이 균 형 잡힌 정보를 제공하기 때문인 것으로 추정된다. 학교에 대한 진단이 어떤 방식으로 이루어질 수 있는지가 예시와 함께 설명되었으며, 연구의 장단점과 후속 과제 또한 논의 되었다.Educational assessment can provide diagnostic information at group levels. The purpose of this study was to provide a group-level diagnostic assessment model for schools as a generalized linear mixed model and to examine the factors that influence the accuracy of the diagnosis. For that purpose, the research model was presented in a generalized linear mixed model framework, and simulation analyses were conducted. Simulation factors were the number of items, the number of attributes, and the proportion of attributes to item. As a result of the simulation analyses, no biases were observed under all conditions, and root mean squared errors (RMSEs) decreased as the number of items and attributes increased. For the proportion of attributes to item, the RMSEs were lowest when the proportion was moderate. The reason is estimated to be that the presence and absence of the attributes are balanced when explaining the differences of item difficulties by schools. It was also exemplified how the schools could be diagnosed using the model. The strengths and weaknesses of the model were discussed with directions for further studies.

The linear model often serves as a starting point for applying statistics in psychology. Often, formal training beyond the linear model is limited, creating a potential pedagogical gap because of the pervasiveness of data non-normality. We reviewed 61 recently published undergraduate and graduate textbooks on introductory statistics and the linear model, focusing on their treatment of non-normality. This review identified at least eight distinct methods suggested to address non-normality, which we organize into a new taxonomy according to whether the approach: (a) remains within the linear model, (b) changes the data, and (c) treats normality as informative or as a nuisance. Because textbook coverage of these methods was often cursory, and methodological papers introducing these approaches are usually inaccessible to non-statisticians, this review is designed to be the happy medium. We provide a relatively non-technical review of advanced methods which can address non-normality (and heteroscedasticity), thereby serving a starting point to promote best practice in the application of the linear model. We also present three empirical examples to highlight distinctions between these methods' motivations and results. The paper also reviews the current state of methodological research in addressing non-normality within the linear modeling framework. It is anticipated that our taxonomy will provide a useful overview and starting place for researchers interested in extending their knowledge in approaches developed to address non-normality from the perspective of the linear model.

Diabetes is one of the main public health chronic conditions that are potentially reaching epidemic proportions globally. Worldwide, the occurrence of these types of diseases are increasing sharply at a worrying degree, with death of around 18 million people every year from cardiovascular disease, for which diabetes and hypertension are major predisposing factors. Two major concerns are that much of this increase in Diabetes is predicated to be happened in developing countries, with a growing incidence of Type 2 Diabetes (T2D) at a younger age including some obese children even before puberty. However, in developed countries most people with diabetes are above the age of retirement. As such, understanding the aetiology of T2D is vital. It has been thought that T2D is resulting from the convergence of genetics, environment, diet and lifestyle risk factors; however, genetic susceptibility has been established as a key component of risk. Genome-wide association studies (GWAS) is a study design and analytic tool specifically developed for investigating the genetic architecture of human disease. The ultimate aim of GWAS is to identify the genetic risk factors for common complex diseases such as T2D. Traditional parametric statistical approaches such as linear modelling framework (e.g. logistic regression) have limited power for modelling the complexity of genotype-phenotype relationship that is characterized by non-linear interactions. These nonlinear interactions are necessary in discovering the aetiology of complex diseases. More specifically, the linear modelling model has some limitations such as examining each single nucleotide polymorphisms independently for the association to the phenotype ignoring the epistatic (gene-gene interactions) and non-genetics factors. This paper presents a novel approch based on the use of backpropogation technique inspired by image compression algorithm. The proposed classifier is fine-tuned for binary classification to predict those who could suffer from the disease among those who do not. Simulation results indicated that the proposed technique showed an area under the curve, true positive rate, true negative rate values of 0.92, 0.9 and 0.8 respectively when using 2500 hidden neurons.

General linear models have been the foundational statistical framework used to discover the ecological processes that explain the distribution and abundance of natural populations. Analyses of the rapidly expanding cache of environmental and ecological data, however, require advanced statistical methods to contend with complexities inherent to extremely large natural data sets. Modern machine learning frameworks such as gradient boosted trees efficiently identify complex ecological relationships in massive data sets, which are expected to result in accurate predictions of the distribution and abundance of organisms in nature. However, rigorous assessments of the theoretical advantages of these methodologies on natural data sets are rare. Here we compare the abilities of gradient boosted and linear models to identify environmental features that explain observed variations in the distribution and abundance of blacklegged tick (Ixodes scapularis) populations in a data set collected across New York State over a ten-year period. The gradient boosted and linear models use similar environmental features to explain tick demography, although the gradient boosted models found non-linear relationships and interactions that are difficult to anticipate and often impractical to identify with a linear modeling framework. Further, the gradient boosted models predicted the distribution and abundance of ticks in years and areas beyond the training data with much greater accuracy than their linear model counterparts. The flexible gradient boosting framework also permitted additional model types that provide practical advantages for tick surveillance and public health. The results highlight the potential of gradient boosted models to discover novel ecological phenomena affecting pathogen demography and as a powerful public health tool to mitigate disease risks.

General linear models have been the foundational statistical framework used to discover the ecological processes that explain the distribution and abundance of natural populations. Analyses of the rapidly expanding cache of environmental and ecological data, however, require advanced statistical methods to contend with complexities inherent to extremely large natural data sets. Modern machine learning frameworks such as gradient boosted trees efficiently identify complex ecological relationships in massive data sets, which are expected to result in accurate predictions of the distribution and abundance of organisms in nature. However, rigorous assessments of the theoretical advantages of these methodologies on natural data sets are rare. Here we compare the abilities of gradient boosted and linear models to identify environmental features that explain observed variations in the distribution and abundance of blacklegged tick (Ixodes scapularis) populations in a data set collected across New York State over a ten-year period. The gradient boosted and linear models use similar environmental features to explain tick demography, although the gradient boosted models found non-linear relationships and interactions that are difficult to anticipate and often impractical to identify with a linear modeling framework. Further, the gradient boosted models predicted the distribution and abundance of ticks in years and areas beyond the training data with much greater accuracy than their linear model counterparts. The flexible gradient boosting framework also permitted additional model types that provide practical advantages for tick surveillance and public health. The results highlight the potential of gradient boosted models to discover novel ecological phenomena affecting pathogen demography and as a powerful public health tool to mitigate disease risks.

Event Abstract Back to Event Single-Trial Parameter Estimates in the Linear Ballistic Accumulator Model Leendert Van Maanen1*, Eric-Jan Wagenmakers2, Tom Eichele3, Scott W. Brown4 and Birte U. Forstmann1 1 University of Amsterdam, Department of Psychology, Netherlands 2 University of Amsterdam, Department of Psychology, Netherlands 3 University of Bergen, Department of Biological and Medical Psychology, Norway 4 University of Connecticut, Department of Educational Psychology, United States The Linear Ballistic Accumulator modeling framework (LBA) provides an elegant and simple way of summarizing behavioral decision-making data (Brown & Heathcote, 2008). In addition, the specific parametrization of the LBA model may be used to identify neural correlates of strategic decision making-processes (e.g., Forstmann et al, 2008; 2010). However, the LBA does not provide insights in the properties of single trials. In this work, we study how the parameters in default LBA emerge from parameters on a single trial level using Markov-Chain Monte Carlo simulations of the parameter distributions. This enables us to study individual trial fluctuations in neural activation and how these relate to decision making. Keywords: Decision Making, Linear Ballistic Accumulator modeling framework (LBA) Conference: Decision Neuroscience From Neurons to Societies, Berlin, Germany, 23 Sep - 25 Sep, 2010. Presentation Type: Poster Topic: Abstracts Citation: Van Maanen L, Wagenmakers E, Eichele T, Brown SW and Forstmann BU (2010). Single-Trial Parameter Estimates in the Linear Ballistic Accumulator Model. Front. Neurosci. Conference Abstract: Decision Neuroscience From Neurons to Societies. doi: 10.3389/conf.fnins.2010.82.00008 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 13 Aug 2010; Published Online: 07 Sep 2010. * Correspondence: Dr. Leendert Van Maanen, University of Amsterdam, Department of Psychology, Amsterdam, Netherlands, lvmaanen@gmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Leendert Van Maanen Eric-Jan Wagenmakers Tom Eichele Scott W Brown Birte U Forstmann Google Leendert Van Maanen Eric-Jan Wagenmakers Tom Eichele Scott W Brown Birte U Forstmann Google Scholar Leendert Van Maanen Eric-Jan Wagenmakers Tom Eichele Scott W Brown Birte U Forstmann PubMed Leendert Van Maanen Eric-Jan Wagenmakers Tom Eichele Scott W Brown Birte U Forstmann Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

In this paper, we propose and investigate an alternate approach to pseudo-likelihood model selection in the generalized linear mixed modeling framework. The problem with the natural approach to the computation of pseudo-likelihood model selection criteria is that the pseudo-data vary for each candidate model, leading to criteria based on fundamentally different goodness-of-fit statistics, rendering them incomparable. We propose a technique that circumvents this problem. This new approach can be implemented using a SAS macro that obtains and applies the pseudo-data from the full model to fitting candidate models based on all possible subsets of predictor variables. We justify the propriety of the resulting pseudo-likelihood selection criteria through an extensive study designed as a factorial experiment. We then illustrate this new method in a modeling application pertaining to bullying in public schools. The data set for the application is taken from three waves of the Iowa Youth Survey.

Interaction between genes and environments (G×E) can be well investigated in families due to the shared genes and environment among family members. However, the majority of the current tests of G×E interaction between a set of variants and an environment are only suitable for studies with unrelated subjects. In this paper, we extend several G×E interaction tests to a linear mixed model framework to study interaction between a set of correlated environments and a candidate gene in families. The correlated environments can either be modeled separately or jointly in one model. We demonstrate theoretically that the tests developed by modeling correlated environments separately are valid and present a computationally fast alternative to detect G×E interaction in families. For either strategy, we propose treating the genetic main effects as a random effect to reduce the number of main-effect parameters and thus improve the power to detect interactions. Additionally, we propose a generalization of a test of interaction that adaptively sums the interactions using a sequential algorithm. This generalized set of tests, referred to as the sequential algorithm for the sum of powered score (Seq-SPU) family of tests, can be expressed as a weighted version of the SPU. We find that the adaptive version of our test, Seq-aSPU, can outperform aSPU in cases where the interactions effects are in opposite directions. We applied these methods to the Minnesota Center for Twin and Family Research data set and found one significant gene in interaction with four psychosocial environmental factors affecting the alcohol consumption among the twins.

Genomic selection is revolutionizing both plant and animal breeding, with its practical application depending critically on high prediction accuracy. In this study, we aimed to enhance prediction accuracy by exploring the use of graph models within a linear mixed model framework. Our investigation revealed that incorporating the graph constructed with line connections alone resulted in decreased prediction accuracy compared to conventional methods that consider only genotype effects. However, integrating both genotype effects and the graph structure led to slightly improved results over considering genotype effects alone. These findings were validated across 14 datasets commonly used in plant breeding research.

We present a framework for meta-analysis of follow-up studies with constant or varying duration using the binary nature of the data directly. We use a generalized linear mixed model framework with the Poisson likelihood and the log link function. We fit models with fixed and random study effects using Stata for performing meta-analysis of follow-up studies with constant or varying duration. The methods that we present are capable of estimating all the effect measures that are widely used in such studies such as the Risk Ratio, the Risk Difference (in case of studies with constant duration), as well as the Incidence Rate Ratio and the Incidence Rate Difference (for studies of varying duration). The methodology presented here naturally extends previously published methods for meta-analysis of binary data in a generalized linear mixed model framework using the Poisson likelihood. Simulation results suggest that the method is uniformly more powerful compared to summary based methods, in particular when the event rate is low and the number of studies is small. The methods were applied in several already published meta-analyses with very encouraging results. The methods are also directly applicable to individual patients' data offering advanced options for modeling heterogeneity and confounders. Extensions of the models for more complex situations, such as competing risks models or recurrent events are also discussed. The methods can be implemented in standard statistical software and illustrative code in Stata is given in the appendix.