Many advanced metabolomics experiments currently lead to data where a large number of response variables were measured while one or several factors were changed. Often the number of response ...variables vastly exceeds the sample size and well-established techniques such as multivariate analysis of variance (MANOVA) cannot be used to analyze the data.
ANOVA simultaneous component analysis (ASCA) is an alternative to MANOVA for analysis of metabolomics data from an experimental design. In this paper, we show that ASCA assumes that none of the metabolites are correlated and that they all have the same variance. Because of these assumptions, ASCA may relate the wrong variables to a factor. This reduces the power of the method and hampers interpretation.
We propose an improved model that is essentially a weighted average of the ASCA and MANOVA models. The optimal weight is determined in a data-driven fashion. Compared to ASCA, this method assumes that variables can correlate, leading to a more realistic view of the data. Compared to MANOVA, the model is also applicable when the number of samples is (much) smaller than the number of variables. These advantages are demonstrated by means of simulated and real data examples. The source code of the method is available from the first author upon request, and at the following github repository: https://github.com/JasperE/regularized-MANOVA.
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•MANOVA and ASCA have serious drawbacks for analysis of experimental designs.•We propose regularized MANOVA (rMANOVA) for analysis of such data.•rMANOVA is a weighted average of the ASCA and MANOVA models.•Thus the best properties of both models are combined and their pitfalls avoided.•rMANOVA is used to analyze data of a metabolomics nutritional intervention study.
This study presents new stable carbon and oxygen isotope data from Lower Cretaceous lacustrine carbonate rock samples recovered from a well drilled in the Santos Basin, offshore southeast Brazil. ...These samples represent a record of a continental environment just prior to the opening of the South Atlantic Ocean and the ultimate break-up of Gondwanaland. The geochemical data, along with carbonate mineralogy, indicate repeated cycles of lake level variation that could be attributed to climatic oscillations. Despite the absence of correlations between δ13C and δ18O values, facies analysis and the isotopic and mineralogical data suggest that lake hydrology was essentially closed for most of the depositional interval studied here. The existence of persisting trends of nearly constant δ13C values with a spread in δ18O values though, suggests long water residence times in the palaeolake, equilibrium between atmosphere and lake water CO2, as well as significant evaporation of water. The overall geological model that emerges unveils a more comprehensive picture of the depositional conditions that favoured the continuity of a significant carbonate factory in the middle of the Gondwanan continent, corroborating previous studies that suggested the lasting existence of a large and somewhat shallow endorheic lake in the area during the Early Cretaceous. As a result of this recorded trend strongly suggesting equilibrium between lake waters DIC (dissolved inorganic carbon) reservoir and atmospheric CO2, the data are most consistent with lacustrine deposition rather than precipitation of travertine, contrasting with some suggestions for the genesis of the carbonates of the Barra Velha Formation. Finally, this apparent equilibrium with the atmosphere likely left a preserved record in the continental carbonates of the final stages that preceded a major global environmental disturbance associated with an increase in atmospheric CO2, known for this time as the Oceanic Anoxic Event (OAE) 1a. If this is correct, it also helps to put further time constraints on this studied interval, which should not be younger than Barremian age, and to provide a regional continental perspective on a global event.
Principal component analysis (PCA) simplifies the complexity in high-dimensional data while retaining trends and patterns. It does this by transforming the data into fewer dimensions, which act as ...summaries of features.
Analyzing and presenting data from multiple groups are much more informative than that from two groups. However, common tools such as S plot and volcano plot are only available for identifying the ...significant features between two groups and are restricted to multiple-group comparisons. This study proposed novel visualization plots which not only overcame the restrictions of the above methods but also utilized the p values of multiple tests as the x-axis. The novel visualization plots included a parametric method and a nonparametric method. The parametric method was a combination of an analysis of variance and Welch’s analysis of variance; the nonparametric method used the Kruskal-Wallis test. During the selection of significant features, machine learning algorithms were used to determine the cutting points of the x-axis. As a proof of concept, the real data from the experiments of 4-MeO-α-PVP metabolites and fish spoilage metabolomics were illustrated via our visualization method. The results showed that the novel visualization plots were much efficiently presented to identify significant metabolites in multiple-group comparisons. Especially, the positive predicted values of the nonparametric method and the cutting points determined by logistic regression were higher than those of other machine learning algorithms in determining the cutting points for multiple groups.
•New visualization plots outweigh volcano plot and S plot for multiple-group study.•Parametric method requires normality of data and Bonferroni’s adjustment is suggested to utilize on cut point of x-axis.•Nonparametric method is flexible on data type and machine learning method is suggested to use on cut point of x-axis.•As proof-of-concept, two methods perform well for multiple-group comparisons.
Repeatability (more precisely the common measure of repeatability, the intra‐class correlation coefficient, ICC) is an important index for quantifying the accuracy of measurements and the constancy ...of phenotypes. It is the proportion of phenotypic variation that can be attributed to between‐subject (or between‐group) variation. As a consequence, the non‐repeatable fraction of phenotypic variation is the sum of measurement error and phenotypic flexibility. There are several ways to estimate repeatability for Gaussian data, but there are no formal agreements on how repeatability should be calculated for non‐Gaussian data (e.g. binary, proportion and count data). In addition to point estimates, appropriate uncertainty estimates (standard errors and confidence intervals) and statistical significance for repeatability estimates are required regardless of the types of data. We review the methods for calculating repeatability and the associated statistics for Gaussian and non‐Gaussian data. For Gaussian data, we present three common approaches for estimating repeatability: correlation‐based, analysis of variance (ANOVA)‐based and linear mixed‐effects model (LMM)‐based methods, while for non‐Gaussian data, we focus on generalised linear mixed‐effects models (GLMM) that allow the estimation of repeatability on the original and on the underlying latent scale. We also address a number of methods for calculating standard errors, confidence intervals and statistical significance; the most accurate and recommended methods are parametric bootstrapping, randomisation tests and Bayesian approaches. We advocate the use of LMM‐ and GLMM‐based approaches mainly because of the ease with which confounding variables can be controlled for. Furthermore, we compare two types of repeatability (ordinary repeatability and extrapolated repeatability) in relation to narrow‐sense heritability. This review serves as a collection of guidelines and recommendations for biologists to calculate repeatability and heritability from both Gaussian and non‐Gaussian data.
The robustness of F-test to non-normality has been studied from the 1930s through to the present day. However, this extensive body of research has yielded contradictory results, there being evidence ...both for and against its robustness. This study provides a systematic examination of F-test robustness to violations of normality in terms of Type I error, considering a wide variety of distributions commonly found in the health and social sciences.
We conducted a Monte Carlo simulation study involving a design with three groups and several known and unknown distributions. The manipulated variables were: Equal and unequal group sample sizes; group sample size and total sample size; coefficient of sample size variation; shape of the distribution and equal or unequal shapes of the group distributions; and pairing of group size with the degree of contamination in the distribution.
The results showed that in terms of Type I error the F-test was robust in 100% of the cases studied, independently of the manipulated conditions.
The generalized polynomial chaos (gPC) method recently advocated in the literature, exhibits impressive efficiency and accuracy in probabilistic power flow (PPF) calculations of small-scale power ...systems. However, it suffers from the "curse of dimensionality" and can only be applied to systems with input random variables that follow a set of standard probability distributions. This paper overcome these weaknesses by developing a hierarchical polynomial chaos analysis of variance (ANOVA) method that shows excellent performances in terms of accuracy, efficiency, rationality, and adaptability, for small- to large-scale power systems. By proving the equivalence between the polynomial chaos expansion and the ANOVA decomposition, which is executed at no extra computational cost, the dimensionality of the polynomial chaos expansion can be adaptively reduced to improve the computational efficiency of the generalized polynomial chaos method in high-dimensional problems. Furthermore, by resorting to the Stieltjes procedure, it is extended to any assumed probability distributions of the input random variables. Simulation results carried out on the IEEE 118-bus system and the 1354-bus European high voltage system with correlated renewable energy generations reveal that the developed method outperforms the generalized polynomial chaos method and the Monte Carlo (MC) method while being compatible with real-time applications in power systems.
The anova to mixed model transition Boisgontier, Matthieu P.; Cheval, Boris
Neuroscience and biobehavioral reviews,
September 2016, 2016-Sep, 2016-09-00, 20160901, Volume:
68
Journal Article
Peer reviewed
A transition towards mixed models is underway in science. This transition started up because the requirements for using analyses of variances are often not met and mixed models clearly provide a ...better framework. Neuroscientists have been slower than others in changing their statistical habits and are now urged to act.
This article provides a Bayes factor approach to multiway analysis of variance (ANOVA) that allows researchers to state graded evidence for effects or invariances as determined by the data. ANOVA is ...conceptualized as a hierarchical model where levels are clustered within factors. The development is comprehensive in that it includes Bayes factors for fixed and random effects and for within-subjects, between-subjects, and mixed designs. Different model construction and comparison strategies are discussed, and an example is provided. We show how Bayes factors may be computed with BayesFactor package in R and with the JASP statistical package.
Translational Abstract
This article provides a Bayes factor approach to multiway analysis of variance (ANOVA) that allows researchers to state graded evidence for effects or invariances as determined by the data. ANOVA is conceptualized as a hierarchical model where levels are clustered within factors. The development is comprehensive in that it includes Bayes factors for fixed and random effects and for within-subjects, between-subjects, and mixed designs. Different model construction and comparison strategies are discussed, and an example is provided. We show how Bayes factors may be computed with BayesFactor package in R and with the JASP statistical package.
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