This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, with the intention of offering an up-to-date account of theory and methods in ...analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed model diagnostics, mixed model selection and jackknife method in the context of mixed models.The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis. The book is suitable for a course in a M.S. program in statistics, provided that the section of further results and technical notes in each of the first four chapters is skipped. If these four sections are included, the book may be used for a course in a Ph. D. program in statistics. A first course in mathematical statistics, the ability to use computer for data analysis and familiarity with calculus and linear algebra are prerequisites. Additional statistical courses such as regression analysis and a good knowledge about matrices would be helpful.
Background: We report an update on a web-based tool for analysis of experiments using indirect calorimetry to assess physiological energy balance. CaIR simplifies the process to import raw data ...files, generate plots, and determine the most appropriate statistical tests for interpretation. Methods: Analysis using the generalized linear model (which includes ANOVA and ANCOVA) allows for flexibility in interpreting diverse experimental designs including those of obesity and thermogenesis. CaIR has been used to analyze more than 45,000 experiments. Results: Several features are incorporated in to this new version. Users can now calculate energy balance: the difference between energy consumed and energy expended. Additional features include a conservation-of-mass plot to quantify whether the calculated energy balance results are consistent with changes in body mass. This feature adds a layer of quality control to experimental analysis. Lastly, CaIR 2.0 will enable users to calculate the statistical power of their experiment based on the observed effect size and variation. Conclusions: The provided tools will enable the transparency necessary to enhance consistency, rigor, and reproducibility for obesity research. CaIR is accessible at https://www.CalRapp.org/.
Panning for gold Candès, Emmanuel; Fan, Yingying; Janson, Lucas ...
Journal of the Royal Statistical Society. Series B, Statistical methodology,
June 2018, Letnik:
80, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Many contemporary large-scale applications involve building interpretable models linking a large set of potential covariates to a response in a non-linear fashion, such as when the response is ...binary. Although this modelling problem has been extensively studied, it remains unclear how to control the fraction of false discoveries effectively even in high dimensional logistic regression, not to mention general high dimensional non-linear models. To address such a practical problem, we propose a new framework of ‘model-X’ knockoffs, which reads from a different perspective the knockoff procedure that was originally designed for controlling the false discovery rate in linear models. Whereas the knockoffs procedure is constrained to homoscedastic linear models with n ⩾ p, the key innovation here is that model-X knockoffs provide valid inference from finite samples in settings in which the conditional distribution of the response is arbitrary and completely unknown. Furthermore, this holds no matter the number of covariates. Correct inference in such a broad setting is achieved by constructing knockoff variables probabilistically instead of geometrically. To do this, our approach requires that the covariates are random (independent and identically distributed rows) with a distribution that is known, although we provide preliminary experimental evidence that our procedure is robust to unknown or estimated distributions. To our knowledge, no other procedure solves the controlled variable selection problem in such generality but, in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case–control study of Crohn’s disease in the UK, making twice as many discoveries as the original analysis of the same data.
The purpose of the current study is to produce landslide susceptibility maps using different data mining models. Four modeling techniques, namely random forest (RF), boosted regression tree (BRT), ...classification and regression tree (CART), and general linear (GLM) are used, and their results are compared for landslides susceptibility mapping at the Wadi Tayyah Basin, Asir Region, Saudi Arabia. Landslide locations were identified and mapped from the interpretation of different data types, including high-resolution satellite images, topographic maps, historical records, and extensive field surveys. In total, 125 landslide locations were mapped using ArcGIS 10.2, and the locations were divided into two groups; training (70 %) and validating (25 %), respectively. Eleven layers of landslide-conditioning factors were prepared, including slope aspect, altitude, distance from faults, lithology, plan curvature, profile curvature, rainfall, distance from streams, distance from roads, slope angle, and land use. The relationships between the landslide-conditioning factors and the landslide inventory map were calculated using the mentioned 32 models (RF, BRT, CART, and generalized additive (GAM)). The models’ results were compared with landslide locations, which were not used during the models’ training. The receiver operating characteristics (ROC), including the area under the curve (AUC), was used to assess the accuracy of the models. The success (training data) and prediction (validation data) rate curves were calculated. The results showed that the AUC for success rates are 0.783 (78.3 %), 0.958 (95.8 %), 0.816 (81.6 %), and 0.821 (82.1 %) for RF, BRT, CART, and GLM models, respectively. The prediction rates are 0.812 (81.2 %), 0.856 (85.6 %), 0.862 (86.2 %), and 0.769 (76.9 %) for RF, BRT, CART, and GLM models, respectively. Subsequently, landslide susceptibility maps were divided into four classes, including low, moderate, high, and very high susceptibility. The results revealed that the RF, BRT, CART, and GLM models produced reasonable accuracy in landslide susceptibility mapping. The outcome maps would be useful for general planned development activities in the future, such as choosing new urban areas and infrastructural activities, as well as for environmental protection.
Exposure mixtures frequently occur in data across many domains, particularly in the fields of environmental and nutritional epidemiology. Various strategies have arisen to answer questions about ...exposure mixtures, including methods such as weighted quantile sum (WQS) regression that estimate a joint effect of the mixture components.
We demonstrate a new approach to estimating the joint effects of a mixture: quantile g-computation. This approach combines the inferential simplicity of WQS regression with the flexibility of g-computation, a method of causal effect estimation. We use simulations to examine whether quantile g-computation and WQS regression can accurately and precisely estimate the effects of mixtures in a variety of common scenarios.
We examine the bias, confidence interval (CI) coverage, and bias-variance tradeoff of quantile g-computation and WQS regression and how these quantities are impacted by the presence of noncausal exposures, exposure correlation, unmeasured confounding, and nonlinearity of exposure effects.
Quantile g-computation, unlike WQS regression, allows inference on mixture effects that is unbiased with appropriate CI coverage at sample sizes typically encountered in epidemiologic studies and when the assumptions of WQS regression are not met. Further, WQS regression can magnify bias from unmeasured confounding that might occur if important components of the mixture are omitted from the analysis.
Unlike inferential approaches that examine the effects of individual exposures while holding other exposures constant, methods like quantile g-computation that can estimate the effect of a mixture are essential for understanding the effects of potential public health actions that act on exposure sources. Our approach may serve to help bridge gaps between epidemiologic analysis and interventions such as regulations on industrial emissions or mining processes, dietary changes, or consumer behavioral changes that act on multiple exposures simultaneously. https://doi.org/10.1289/EHP5838.
We investigated the effects of violations of the sphericity assumption on Type I error rates for different methodical approaches of repeated measures analysis using a simulation approach. In contrast ...to previous simulation studies on this topic, up to nine measurement occasions were considered. Effects of the level of inter-correlations between measurement occasions on Type I error rates were considered for the first time. Two populations with non-violation of the sphericity assumption, one with uncorrelated measurement occasions and one with moderately correlated measurement occasions, were generated. One population with violation of the sphericity assumption combines uncorrelated with highly correlated measurement occasions. A second population with violation of the sphericity assumption combines moderately correlated and highly correlated measurement occasions. From these four populations without any between-group effect or within-subject effect 5,000 random samples were drawn. Finally, the mean Type I error rates for Multilevel linear models (MLM) with an unstructured covariance matrix (MLM-UN), MLM with compound-symmetry (MLM-CS) and for repeated measures analysis of variance (rANOVA) models (without correction, with Greenhouse-Geisser-correction, and Huynh-Feldt-correction) were computed. To examine the effect of both the sample size and the number of measurement occasions, sample sizes of
= 20, 40, 60, 80, and 100 were considered as well as measurement occasions of
= 3, 6, and 9. With respect to rANOVA, the results plead for a use of rANOVA with Huynh-Feldt-correction, especially when the sphericity assumption is violated, the sample size is rather small and the number of measurement occasions is large. For MLM-UN, the results illustrate a massive progressive bias for small sample sizes (
= 20) and
= 6 or more measurement occasions. This effect could not be found in previous simulation studies with a smaller number of measurement occasions. The proportionality of bias and number of measurement occasions should be considered when MLM-UN is used. The good news is that this proportionality can be compensated by means of large sample sizes. Accordingly, MLM-UN can be recommended even for small sample sizes for about three measurement occasions and for large sample sizes for about nine measurement occasions.
•Tutorial on contrast coding in R.•Discussion of treatment, sum, repeated, polynomial, and custom contrasts.•Interactions between contrasts and ANOVA.•Explains how to generate contrast matrices from ...hypotheses.•Introduces the hypothesis matrix and the generalized inverse.
Factorial experiments in research on memory, language, and in other areas are often analyzed using analysis of variance (ANOVA). However, for effects with more than one numerator degrees of freedom, e.g., for experimental factors with more than two levels, the ANOVA omnibus F-test is not informative about the source of a main effect or interaction. Because researchers typically have specific hypotheses about which condition means differ from each other, a priori contrasts (i.e., comparisons planned before the sample means are known) between specific conditions or combinations of conditions are the appropriate way to represent such hypotheses in the statistical model. Many researchers have pointed out that contrasts should be “tested instead of, rather than as a supplement to, the ordinary ‘omnibus’ F test” (Hays, 1973, p. 601). In this tutorial, we explain the mathematics underlying different kinds of contrasts (i.e., treatment, sum, repeated, polynomial, custom, nested, interaction contrasts), discuss their properties, and demonstrate how they are applied in the R System for Statistical Computing (R Core Team, 2018). In this context, we explain the generalized inverse which is needed to compute the coefficients for contrasts that test hypotheses that are not covered by the default set of contrasts. A detailed understanding of contrast coding is crucial for successful and correct specification in linear models (including linear mixed models). Contrasts defined a priori yield far more useful confirmatory tests of experimental hypotheses than standard omnibus F-tests. Reproducible code is available from https://osf.io/7ukf6/.
Linear mixed models are a powerful statistical tool for identifying genetic associations and avoiding confounding. However, existing methods are computationally intractable in large cohorts and may ...not optimize power. All existing methods require time cost O(MN(2)) (where N is the number of samples and M is the number of SNPs) and implicitly assume an infinitesimal genetic architecture in which effect sizes are normally distributed, which can limit power. Here we present a far more efficient mixed-model association method, BOLT-LMM, which requires only a small number of O(MN) time iterations and increases power by modeling more realistic, non-infinitesimal genetic architectures via a Bayesian mixture prior on marker effect sizes. We applied BOLT-LMM to 9 quantitative traits in 23,294 samples from the Women's Genome Health Study (WGHS) and observed significant increases in power, consistent with simulations. Theory and simulations show that the boost in power increases with cohort size, making BOLT-LMM appealing for genome-wide association studies in large cohorts.
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